FM
(FOR ACCOUNTING AND FINANCE EXECUTIVES AND PROFESSIONAL COURSE STUDENTS)
 ALOK RANJAN : CA FINAL 

 MOBILE NO: 9516266979
 WHAT’S NO : 9155420612

Currently associated with: JK LAKSHMI CEMENT LTD DURG

MY FIRST COMICS ON CAPITAL BUGDETING.

MY SECOND COMICS ON PORTFOLIO MANAGEMENT LAUNCHED WITHIN ONE MONTH. YOU CAN BUY MY E-COMMERCE BOOK BY EMAILD ID ranjanalokraj@gmail.com. 

AUTHORS,

I read many books but all books same. If , we talk about capex book then many Books are available in the market but none of book read by me who clear the vision. I want to say that when we read my comics related with CAPEX then please think pictorial. 

Dedicated to my

Mother, Father &           my guru

Coverage:
In this Book, ALOK and BIKRANT, fictional characters, will be discussing about

a)	Fundamentals of Investment Decisions; 
b)	How to evaluate Investment Decisions? 

c)	Tools and Techniques available for evaluating Investment Decisions like 

i.	Payback Period; 
ii.	Net Present Value Technique; 
iii.	Internal Rate of Return; 

iv.	Profitability Index Method; 

v.	Discounted Pay Back Period; 
vi.	Modified Internal Rate of Return; 
vii.	Accounting Rate of Return. 

d)	How to overcome conflicts among tools. 

e)	Importance of Capital Budgeting Process. 
Structure of the Book:

a)	Two fictional characters – ALOK and BIKRANT – will be discussing / talking about each and every topic in an informal style / dialogue. 

b)	Each and every topic will be discussed with practical examples. 

c)	Each and every topic will be covered through separate sections. 
	Section 1	BIKRANT requesting ALOK’s help for teaching	Pg.5		
		basics of Capital Budgeting Process.			
	Section 2	ALOK explains why anyone would make	Pg.6		
		Investment?			
	Section 3	BIKRANT understands Return on Investment and	Pg.7-10		
		 Cost of Capital?			
	Section 4	ALOK goes deep to explain Cash inflows	Pg.11-16		
		from operations.			
	Section 5	ALOK explains how to build projections and	Pg.17-22		
		derive cash flows for the project life cycle			
	Section 6	ALOK explains Pay Back Period concept and	Pg.23-27		
		also clears why mere cash flows are not			
		sufficient for Investment Decision Making			
	Section 7	ALOK takes BIKRANT through Future Value,	Pg.28-34		
		Present Value and Net Present Value (NPV)			
		2			

		Concepts and teaches him how to take			
		Investment Decision using NPV Technique.			
	Section 8	ALOK explains Internal Rate of Return (IRR)	Pg.35-42		
		Concept  and  how  to  take  Investment			
		Decisions using IRR Technique.			
	Section 9	ALOK and BIKRANT works out IRR for their	Pg.43-48		
		Project Investment for Rs.100 Crs.			
	Section 10	ALOK explains other tools available for	Pg.49-51		
		evaluating Investment Decisions and starts			
		with Discounted Pay Back Period.			
	Section 11	ALOK explains Profitability Index Tool for	Pg.52-57		
		evaluating Investment Decisions.			
	Section 12	ALOK explains short comings of IRR and	Pg.58-60		
		introduces Modified Internal Rate of Return.			
	Section 13	ALOK explains Accounting (Average) Rate of	Pg.61-62		
		Return Method (ARR) in Capital Budgeting.			
	Section 14	BIKRANT raises his concern about too many	Pg.63-65		
		techniques  and  which  one  to  use  for			
		decision making! ALOK cools BIKRANT through			
		his explanation and chapter comes to an			
		end.			

Section 1:

BIKRANT requesting ALOK’s help for teaching basics of Capital Budgeting

Process.

ALOK	Hi BIKRANT! How are you?		
			
BIKRANT	I am fine ALOK! I need your Guidance.		
			
ALOK	With pleasure! But, for what?		
			
BIKRANT	Our company has plans to take up an investment project. I have to advice		
	my management, whether they should take up a new project now? For that		
	I have to brush up my basics in Evaluating Investment Proposals. Can you		
	help me out?		
ALOK	Fine! It’s not an issue. So, you want to revise your knowledge in Capital		
	Budgeting Process. I’ll explain you.		
BIKRANT	Thanks ALOK! Assume, I know nothing about Financial Management and		
	guide me.		
ALOK	That’s the fact right?		
			
BIKRANT	L		

ALOK	Ok! Ok! Jokes apart!		
	Before going technical, let us make ourselves comfortable in Fundamentals.		
BIKRANT	Ok!		

Section 2:

ALOK explains why anyone would make Investment?

ALOK	Why would you invest huge money in a Project?	
		
BIKRANT	Obviously for getting returns! For making money out of it!	
		
ALOK	Fine! How much returns?	
		
BIKRANT	Returns generally available for any business!	
		
ALOK	Please modify that Statement. Returns which you should get from	
	Investment should not only be equal to returns available for any business,	
	but it should also be greater than or equal to the cost of capital of business.	
BIKRANT	Correct! When we invest in a project, it may be funded with debt & equity.	
	Both the Funds have cost and returns should cover at least the cost!	
ALOK	Well said!	
	Returns > cost of capital.	
	That should be the objective of any investment.	

Section 3:

BIKRANT understands Return on Investment and Cost of Capital?

ALOK		Now tell me, how do you measure returns?	
						
BIKRANT		I am sorry ALOK, I didn’t get you!	
						
ALOK		I asked ‘What is return for investing in project or what is the return for	
		making any investment’?			
BIKRANT		Profits!				
						
ALOK		Which profit? There are so many profits in Business. You have	
		a)	Gross profit.			
		b)	Operating Profit			
		c)	Profit before Tax			
		d)	Profit after Tax			
		e)	Retained profit			
		Which profit is return for investment?	
BIKRANT		Now, this buzzes me! Please help me out!	
						
ALOK		Ok! Let us assume you are taking up a project at a cost of Rs.100 Crs and it	
		will be funded by debt and equity.	
BIKRANT		Ok.					
						
ALOK		Let’s assume, Debt Equity combination as 50:50	
			
BIKRANT		So funding composition should be like this?	
		Source of Fund	Proportion	Value		
		Equity	50%	50 Crs		
		Debt		50%	50 Crs		
		Is it right?				
ALOK		Yes! Now tell me, what is the profits / return available for owners	
		(shareholders)?				
BIKRANT		It is Dividend.				
			
ALOK		No! It is not mere dividend. It is entire Profit after Tax.	
			
BIKRANT		But only Dividend is paid to shareholders. Not the entire profits.	
			
ALOK		Yes! Only Dividend are paid or say distributed to the owners and balance is	
		just unpaid. But still, it is payable to them. So it is also part of returns earned	
		by the shareholders right?			
BIKRANT		Yes! Yes!				
		I got it!				
				6			

	So Profit after Tax matters!	
		
ALOK	Yes! But that is only for the shareholders. What is the returns for Bankers	
	(Lenders)? They have also invested equally in your project (50%).	
BIKRANT	It is Interest!	
		
ALOK	That’s good. So return for Bankers are Interest and Return for Shareholders	
	are Profit after Tax. So, if you sum up both the numbers, you would get the	
	return expected out of the project. Is that right?	
BIKRANT	Yes! It makes sense. Can we understand this with some numbers?	
		
ALOK	Ok! Take it now!	
	Your 100 Crs project is funded with Debt  – 50 Cr and Equity – 50 Cr.	
BIKRANT	That’s already available. What is the cost of these funds?	
		
ALOK	Say, Debt would cost 15% and Equity????	
	Can you assume a rate for Cost of Equity?	
BIKRANT	Equity, Shall we assume it as 10%?	
		
ALOK	Then in that case, you should have invested your money in simple deposit	
	with Banks / FIs which has less risk. Why anyone will invest huge money in	
	business just to get 10% Return?	
	Cost of equity would always be higher than cost of risk free investment and	
	debt.	
BIKRANT	But why’s that?	
		
ALOK	Equity investors assume bigger risk!	
	They are responsible for running the business.	
	They take the risk of	
	-facing losses,	
	-fluctuating returns,	
	-business failure,	
	-insolvency	
	and so many.	
	So obviously they would expect high returns.	
	Whereas lenders (Bankers) will get back their return whether the business	
	makers profit or suffers loss. Since they takes less risk, their return would	
	also be less.	
BIKRANT	Ok! Got that! Then shall we assume cost of Equity as 25%	
		
ALOK	Fine! That’s reasonable for the effect and risk to be taken! Can you calculate	
	and tabulate the cost of funds.	
BIKRANT	Yes!	
		
	7	

					(Rs. In Cr.)	
		Nature of Fund	Amt	Cost (%)	Cost		
					(Value)		
		Equity	50	25%	12.50		
		Debt	50	15%	7.50		
		Total	100		20.00		
ALOK	Good!					
	The table says, You are raising Rs.100 Crs and cost of the funds is Rs.20 Crs.	
BIKRANT	Yes!					
	Rs.20 Crs is the cost for raising Rs.100 Crs.				
	So, the cost of capital is 20%					
							
		Total Cost (a)	20.00				
		Total Funds (b)	100.00				
		Cost of Funds (a)/(b) x 100	20%				
ALOK	That’s right!					
	Your cost of capital is 20%. It is also called as Weighted Average Cost of	
	Capital (WACC). It means, if you earn 20% from this project, you will meet	
	the expectation of Banker and Shareholders.			
	Both the group will be happy. What will happen if you earn 30%?	
BIKRANT	Cost of capital is only 20%. So if I earn 30%, I will have additional earnings	
	of 10%. It’s a bonus for me!					
ALOK	Yes! It’s for you! Meaning, it’s for shareholders.			
	This additional Earnings is reward for the additional risk taken.	
	What will happen if you earn only 13%				
BIKRANT	In that case, earnings from the project will be 100 x 13% = 13 Crs.	
	I should pay to two groups now.					
	One to lenders: They will rank first In view of agreement.	
	As per agreement, I have to pay Rs.7.50 Cr [50 x 15%] to them.	
ALOK	So after paying 7.50 Cr to the Bankers you will be left with only 6.50 Cr	
						
BIKRANT	Yes!					
				
ALOK	What was the expected return of Shareholders?			
						
BIKRANT	It is 25% in 50 Crs. , 12.50 Cr					
		
ALOK	So expected return was 12.50 Cr whereas actual is going to be only 6.50 Cr.	
		
BIKRANT	Ya! 6.50 Cr on 50 Cr works out to 13% return against expected 25% return	
	8					

ALOK	So, this is the risk which shareholders are exposed to whereas lenders	
	would pocket their return whether your business makes profit or suffers	
	loss!	
	If your business doesn’t have cash generation to pay return to the lenders,	
	they will not mind in forcing you to close the business, sell the assets and	
	take back their money invested along with returns.	
BIKRANT	Very True!	
		
ALOK	So the message is, before investing in any project, you have to work out the	
	returns that can be generated which will match the expectations of both	
	the investor groups. i.e. Both the lenders and shareholders.	
BIKRANT	Correct! The profit that will be generated should be sufficient enough to	
	meet the expectation of both the groups. So if we take up any Project with	
	returns lower than Cost of capital then in those projects the losers will be	
	shareholders.	
ALOK	Absolutely in those cases it would be ideal to abandon those Projects which	
	will help to avoid opportunity losses.	
BIKRANT	That’s clear now! So we should look for appropriate profit for evaluating	
	the investment proposals. Is that right?	
ALOK	A slight modification. Have your focus on cash flows than the profits.	
BIKRANT	What that mean?	

Section 4:

ALOK goes deep to explain Cash inflows from operations:

ALOK		Always remember profit can be influenced by accounting policies. What is	
		real is cash flow.			
		So you should evaluate investment proposals by analysing cash flows.	
BIKRANT		Ya! I could recollect Profit is different from Cash. So please tell me how to	
		find out Cash generated from Operations?	
ALOK		It is very simple. You have to make some minor adjustments to the Profits.	
BIKRANT		Like?			
ALOK		The Profit you derive would be after providing for expenses like Interest,	
		Depreciation, Taxes and some non-cash items, right?	
BIKRANT		Correct!			
ALOK		What you should do is, remove non-cash items from Profit to find out the	
		cash profit.			
BIKRANT		How would I do that?			
ALOK		Let’s take extension of our example.			
BIKRANT		Ok!			
ALOK		Let’s say, if you take up this Rs.100 Cr Project, you will have Annual sales of	
		around Rs.150 Crs.			
BIKRANT		Ok!			
ALOK		You will also have expenses for Production and other operations to the tune	
		of Rs.100 Crs.			
BIKRANT		Fine!			
ALOK		You should also be paying interest on your Bank loan of Rs.50 Cr	
		@ 15% right?			
BIKRANT		Yes! It would work out to Rs.7.50 Cr.			
ALOK		You will also depreciate your asset right?	
BIKRANT		Yes!			
ALOK		Assume 8 years life for the asset and depreciate it equally using Straight	
		Line Method.			
BIKRANT		So my depreciation should be			
		Cost of Asset	Rs.100 Crs		
		Life	8 Years		
		Depreciation	100/8 Years = Rs.12.50 Cr		
ALOK		Correct!			
		Can you tabulate all these and derive your profit?	

10

BIKRANT		Yes!					
		Sales			150.00		
		Less: Production & operating Expenses		(100.00)		
		Earnings before Depreciation, Interest and Tax		50.00		
		Less:	Depreciation		(12.50)		
		Earnings before Interest and Tax		37.50		
		Less: Interest		(7.50)		
		Earnings before Tax		30.00		
ALOK		Good!					
		You have sales of Rs.150 Crs; Expenses of Rs.120 Crs and Profit of Rs.30 Crs	
BIKRANT		Oh! No!					
		I have not considered the effect of Tax pay-out. Should I?	
ALOK		Yes! You should!			
		Assume you have to pay Tax @ 30% on your profit and work out your profit	
		after Tax.			
BIKRANT		Ok!					
			Rs. In Crs			
		Sales			150.00		
		Less: Production & operating Expenses		(100.00)		
		Earnings before Depreciation, Interest and Tax		50.00		
		Less:	Depreciation		(12.50)		
		Earnings before Interest and Tax		37.50		
		Less: Interest		(7.50)		
		Earnings before Tax		30.00		
		Less: Tax @ 30%		(9.00)		
		Earnings after Tax		21.00		
ALOK		Now your Income Statement is complete. Let us try to understand the	
		return earned for the project.			
BIKRANT		Ok!					
ALOK		Which profit reflect returns now?			
		Is it PAT/PBT/EBIT/EBDIT?			
BIKRANT		PAT?					
					
ALOK		Ok! Let’s analyse that!			
		Returns for this Project means, the profit that is available to meet the cost	
		of both the investors (Lender & Equity) group, right?			
BIKRANT		Yes!					
			
ALOK		From your Profit after Tax you will be able to able to pay shareholders right?	
BIKRANT		Yes! Very much! It is from PAT, we pay dividend to the shareholders!	
					
ALOK		Ok! But, will you be able to pay your lender???			
			11				

BIKRANT		Lender??? Oops! This Profit after Tax is after paying interest!	
							
ALOK		Yes! So understand Profit after Tax would reflect return for shareholders	
		only but not for lenders.	
		Since you are interested in finding return for both the group, what you	
		should do is???					
BIKRANT		Add back interest with Profit after Tax???	
							
ALOK		Absolutely!					
		By adding back, Interest, you will now have return for both the group.	
BIKRANT		Yes!					
		Shall I work out for our example?	
ALOK		Please!					
BIKRANT							
		Profit after Tax			21.00		
		Add: Interest			7.50		
		Profit before Int.			28.50		
ALOK		BIKRANT! I want to take you through an important concept now.	
		What you have done now by adding back interest is right! But please	
		visualise what would have been the Profit after Tax, if there is no Interest	
		expenses.					
BIKRANT		Let me try!					
		We know EBIT was Rs.37.50 Cr. If there is no Interest Expenses, then PBT	
		and PAT would be,					
		EBIT	37.50				
		Less: Interest	Nil				
		PBT	37.50				
		Less: Tax @ 30%	(11.25)				
		PAT	26.25				
		Like this?					
  12

ALOK		Yes! Now please compare your old and new PBT, Tax & PAT.	
								
BIKRANT		Particulars		Old		New		
		PBT		30.00		37.50		
		Tax		(9.00)		(11.25)		
		PAT		21.00		26.25		
ALOK		Now look at your Tax obligation.	
		In your old case, your tax was Rs.9.00 Cr where as in new case (without	
		interest), your tax was Rs.11.25 Cr.	
		You will be forced to pay higher tax if you don’t have interest.	
		Is that right?					
BIKRANT		Yes ALOK!					
		When I have interest, my profit was less and I would be obliged to pay only	
		Rs. 9 Cr. as Tax.					
		When I don’t have interest, my profit will go up and I have to pay more tax	
		in view of higher profits.			
		My additional tax would be 11.25 - 9.00 Cr = 2.25 Cr.	
ALOK		You are right!					
		Presence of Interest has saved you tax of Rs.2.25 Cr	
BIKRANT		Yes ALOK!					
			
ALOK		Now, come back to our example.	
		Your interest obligation was 7.50 Cr [ 50 x 15%]	
		Your Tax rate is 30%					
		Presence of 7.50 Cr expense will directly give you 30% tax benefit.	
BIKRANT		Yes!					
		By claiming Interest Expense of Rs.7.50 Cr, I will save 30% tax on 7.50 Cr	
		which works out of Rs.2.25 Cr.			
		Hey it matches with our recent workings!	
ALOK		Yes! It would match.					
		Get back to track now.			
		You have added back interest to Profit after Tax to find out return out of	
		the project.					
BIKRANT		Yes!					
			
ALOK		Now my question is, what is exact cash outflow on account of interest?	
BIKRANT		Hey!! It is 7.50 Cr less tax benefit. Because, I saved Rs.2.25 Cr tax on account	
		of interest.					
ALOK		So, what amount you should add back now?	
					
BIKRANT		It is Rs.5.25 Cr [7.50 x 70%]			
		But ALOK! We have to add back only what is deducted	
		In our case, we have deducted Rs.7.50 Cr as expense.	
		Then how can I add back Rs.5.25 Cr?	
				13			

ALOK		Your question has logic BIKRANT!			
		You are now adding back Interest with Profit after Tax to know what is the	
		return available for the project.			
		If that is the objective, you should add back or deduct all the items related	
		to interest, right?					
BIKRANT		Yes ALOK!					
							
ALOK		You are going to pay tax of 9 Cr which would have been 11.25 Cr, it there is	
		no interest, right?					
BIKRANT		Yes ALOK?					
ALOK		So, already your tax figure is adjusted to 9.00 Cr from 11.25 Cr due to	
		presence of Interest, right?			
BIKRANT		Yes!					
							
ALOK		So add back that also!					
BIKRANT		Now it makes sense.					
							
ALOK		This tax benefit would be negative figure of – 2.25 and your interest	
		expense will be Rs.7.50 Cr.			
BIKRANT		Yes! so my effective Interest cost is			
		Interest	7.50				
		Less: Tax benefit	2.25				
		Effective cost	5.25				
							
ALOK		Good!					
		Only this cost should be added.			
		Please continue with your table!			
BIKRANT							
		Profit after Tax			21.00		
		Add : Effective Interest (7.50 – 2.25)	5.25		
		Profit after Tax before Interest	26.25		
		Is that correct?					
ALOK		Good!					
		BIKRANT ! I told you !					
		It is not profit but the cash generation is important!	
BIKRANT		Yes!					
ALOK		The profit you have derived now is after providing for non-cash expenses	
		like depreciation					
BIKRANT		So, I should add back that also right?			
							
ALOK		Yes!					
		Go ahead and complete the cash generation.	
			14				

BIKRANT					
		Profit after Tax	21.00		
		Profit after Tax before Interest	26.25		
		Add: Depreciation	12.50		
		Profit after Tax before Interest and Depreciation	38.75		
ALOK		Good! This is the cash that is generated from the project for a year. We call	
		it as flows from operations.			
		If you want to know, whether the project which you have taken up at Rs.100	
		Crs is a viable project, then you have to test, what will be the cash	
		generation for the entire project life.			
		Only then you will have sufficient information on hand, to take a decision	
		whether or not to go ahead with the project.			

Section 5:

ALOK explains how to build projections and derive cash flows for the project life cycle

BIKRANT		Do you mean I have to work out projections?								
																	
ALOK		Yes BIKRANT!															
		You know your project has life of 8 years.								
		You have to see, how much the project can earn over its useful life of 8 years	
		and whether the returns it will generate will match your expectations.			
BIKRANT		Ok! How do we go with the projections?								
ALOK		You need to visualise the Sales and expenses for 8 years					
												
BIKRANT		Ok! Now I have the above information for one year. Should I extrapolate it for	
		8 year?															
ALOK		Yes!															
		But pay attention to growth factors, increase or decrease in expenses, etc.	
BIKRANT		Yes! You are correct.													
		In this eight years,													
		-certain expenses will increase with increase in sales;						
		-certain expenses like interest will come down with the repayment of loans;	
		-certain other expenses like salary & wages will go up since we have to provide	
		increments.															
ALOK		Correct!															
		-Variable expenses will move along with sales!						
		-Fixed Expense would remain fixed and								
		-Expenses like interest would eventually come down.						
		So go ahead with your projection for 8 years assuming sales to grow 5% every	
		year.															
BIKRANT		Ok! How about ALOKfacturing & Operating Expenses.						
ALOK		Assume															
		-60% of your expense are variable. So they will also have 5% increase every	
		year.															
		-Keep 40% of your expenses as fixed.										
BIKRANT		Ok! Let me try. I have to increase sales every year by 5%					
																	
		Particulars	1		2	3		4		5		6	7		8		
		/ Year															
		Sales	150		157.50	165.38		173.64		182.33		191.44	201.01		211.07		
																	
						16											

ALOK	You are going good BIKRANT! For simplicity, let us avoid decimals and round off to	
	next highest number.															
BIKRANT	Ok ALOK!																	
	I’ll rework:																	
	Particulars		1		2		3			4	5	6	7	8		
	/ Year																		
	Sales		150		158		165			174	182	191	201	211		
ALOK	You know your expenses are Rs.100 Crs.									
	As discussed split 60% as Variable and 40% as Fixed Expenses in year 1 and	
	keep providing 5% increase for your variable expenses every year.			
BIKRANT	Ok. I’ll do that!																	
	Particulars /	1		2		3			4	5	6	7	8		
	Year																	
	Sales	150		158		165			174	182	191	201	211		
	Less:																	
	Variable																	
	Expense (60%)	(60)		(63)		(66)			(69)	(72)	(76)	(80)	(84)		
	Fixed Expense																	
	(40%)		(40)		(40)		(40)			(40)	(40)	(40)	(40)	(40)		
	EBDIT	50		55		59			65	70	75	81	87		
ALOK	BIKRANT! You have done very well so far.										
	The EBDIT which you have derived now will be the profits which can be earned	
	without any influence of Debt & Equity structure.							
BIKRANT	Means?																	
ALOK	This is the level of profit which any similar business units can earn in the	
	Industry. Because till this point, your profit is decided by operating income	
	which is your sales and your operating expenses which are basically RM,	
	Labour, Power, other production expenses. If you want you can also consider	
	depreciation. In that case, it would be										
	Particulars /	1		2		3			4		5		6		7	8		
	Year																	
	EBDIT	50.00	55.00	59.00			65.00		70.00		75.00		81.00	87.00		
	Less:	12.50	12.50		12.50			12.50		12.50		12.50		12.50	12.50		
	Depreciation																	
	EBIT	37.50	42.50		46.50			52.50		57.50		62.50		68.50	74.50		
BIKRANT	Yes! I understand.															

ALOK	After EBIT, the profit that is available to owners will be decided by capital structure of business.

If business has more loans, then chunk of EBIT will go for paying interest and you will have very little PBT & PAT.

17

BIKRANT		Yes! I can follow.															
																	
ALOK		Since I have worked out EBIT, you continue the balance.							
		You have to account for Interest, and Tax.									
BIKRANT		Correct.																	
		In our case, whether this 50 Cr Debt will remain for entire 8 Years in the		
		business?																	
ALOK		No BIKRANT!																	
		Debt funds like Term loans are repayable over 3-5-8 years					
		You please assume 8 years repayment.										
BIKRANT		Whether repayment starts from day one?									
																				
ALOK		That’s a good question.															
		You would need time for project completion & stabilisation in business. So		
		consider one year repayment holiday for principal (which generally bankers		
		would give) and 7 year principal repayment period.							
BIKRANT		So, my interest on loan will coming down year-after-year right?					
ALOK		Yes! It would come down with repayment.									
		Work out repayment schedule and interest schedule for loan before		
		proceeding further.															
BIKRANT		Ok! I’ll assume like this:															
												(Rs. In Cr.)							
		Year		Repayment per year		Total Repayment								
		1			Nil							Nil								
		2-7			7.00							42.00								
		8			8.00							8.00								
							Total					50.00								
ALOK		Ok! Proceed. Assume you take loan in beginning of the year. Also compute		
		average loan balance for all the years.										
BIKRANT																					
		Particulars	1		2		3		4	5		6		7	8			
		/ Year																	
		a)  Opening	50		50		43		36	29		22		15	8			
		Balance	(taken in																
			beginning																
																					
					of the																
					year)																
		b)	Fresh	-		-		-		-	-		-		-	-			
		Loan																			
		c)		Less:	Nil		7		7		7	7		7		7	8			
		Repayment																	
		d)	Closing	50		43		36		29	22		15		8	-			
		Balance																	
									18											

		e)  Average		50				46.50		39.50		32.50		25.50			18.50			11.40		4.00				
		Balance																																	
																													
		Am I correct? And why do you wanted to calculate Average loan balance?		
ALOK		You are correct BIKRANT!																										
		I wanted you to calculate Average loan balance to estimate Interest on loan.		
		You can apply Interest on the average balance for forecasting purposes.		
BIKRANT		Ok! I’ll do that!																														
																												
		Particulars		1			2			3			4			5			6			7		8				
		/ Year																																			
		Average		50.00		46.50		39.50		32.50		25.50		18.50		11.40		4.00				
		Balance																																	
		Interest @		7.50		6.98		5.93			4.89			3.83			2.78			1.73		0.60				
		15%																																			
ALOK		Good!																																			
		Already you have EBIT.																										
		Now deduct this Interest to find profit before Tax & after Tax.						
BIKRANT		Ok I’ll proceed.																														
																							
		Particulars		1		2		3			4		5		6		7		8				
		/ Year																																			
		EBIT			37.50		42.50		46.50			52.50		57.50		62.50		68.50		74.50				
		Less:			(7.50)		(6.98)		(5.93)			(4.89)		(3.83)		(2.78)		(1.73)		(0.60)				
		Interest	@																																		
		15%																																			
		Profit before		30.00		35.52		40.57			47.61		53.67		59.72		66.77		73.90				
		Tax																																			
		Less:			(9.00)		(10.66)		(12.17)		(14.28)		(16.10)		(17.92)		(20.03)		(22.17)				
		Tax @ 30%																																		
		Profit	after		21.00		24.86		28.40			33.33		37.57		41.80		46.74		51.73				
		Tax																																			
ALOK		Great! You have done wonderful job.																					
		But it’s just a starting point for evaluating investment proposals.						
		Now, you have to find out what will be the cash flows from the project.		
		But before that, can you bring you entire projection in one place?						

19

BIKRANT		Let me do that first!												
		Particulars /	1	2		3		4	5	6	7		8		
		Year														
		Sales		150.00	158.00		165.00		174.00	182.00	191.00	201.00		211.00		
		Less:														
		Variable													
		Expense	(60.00)	(63.00)		(66.00)		(69.00)	(72.00)	(76.00)	(80.00)		(84.00)		
		(60%)														
		Fixed Expense													
		(40%)		(40.00)	(40.00)		(40.00)		(40.00)	(40.00)	(40.00)	(40.00)		(40.00)		
		EBDIT		50.00	55.00		59.00		65.00	70.00	75.00	81.00		87.00		
		Less:		12.50	12.50		12.50		12.50	12.50	12.50	12.50		12.50		
		Depreciation													
		EBIT		37.50	42.50		46.50		52.50	57.50	62.50	68.50		74.50		
		Less: Interest	(7.50)	(6.98)		(5.93)		(4.89)	(3.83)	(2.78)	(1.73)		(0.60)		
		@ 15%														
		Profit	before	30.00	35.52		40.57		47.61	53.67	59.72	66.77		73.90		
		Tax														
		Less:		(9.00)	(10.66)		(12.17)		(14.28)	(16.10)	(17.92)	(20.03)		(22.17)		
		Tax @ 30%													
		Profit	after	21.00	24.86		28.40		33.33	37.57	41.80	46.74		51.73		
		Tax														
ALOK	It’s nice to see all in one place.								
		Now only the game starts.										
		You have the information about the earning capacity of your project.		
		Now you know, how much is your sales, expense, interest, tax, etc.			
		Now you have to analyse these number to take a decision.					
BIKRANT		Ok!														
										
ALOK		First compute cash flows from this project for 8 years.					
		Hope you already done it for year 1.								
BIKRANT		Ya! I can!													
		I’ll do it.													
				Cash flow from the project							
		Particulars /	1	2		3		4	5	6	7		8		
		Year														
		Profit	after	21.00	24.86		28.40		33.33	37.57	41.80	46.74		51.73		
		Tax														
		Add:		12.50	12.50		12.50		12.50	12.50	12.50	12.50		12.50		
		Depreciation													
		Add: Interest	7.50	6.98		5.93		4.89	3.83	2.78	1.73		0.60		
		@ 15%														
		Less:	Tax	(2.25)	(2.09)		(1.78)		(1.47)	(1.15)	(0.83)	(0.52)		(0.18)		
		Benefit														
		Cash Inflows	38.75	42.25		45.05		49.25	52.75	56.25	60.45		64.65		
												
ALOK		You are going fantastic BIKRANT!										
							20								

Now you got the critical details for evaluating the investment proposal.

That is ‘cash flows ‘.

Your decision depends on accuracy of these cash flows and now you have it right!

BIKRANT	Thanks ALOK!

Section 6:

ALOK explains Pay Back Period concept and also clears why mere cash flows are not sufficient for Investment Decision Making:

ALOK		Now tell me, what do you infer from those 8 Years cash flows?			
															
BIKRANT		ALOK!													
		The cash flows for 8 year											
		Particulars /	1	2	3		4		5	6	7		8		
		Year													
		Cash Inflows	38.75	42.25	45.05		49.25		52.75	56.25	60.45		64.65		
		Aggregates to Rs.409.40 Crs whereas initial investment is only Rs.100 Crs.	
		Its hell a lot of money!											
ALOK		May be Yes!													
		But don’t look at values grossly.									
		You need to understand the nuance of Present value of Future cash flows.	
		But before that, can you tell me how long this project takes to pay back or say	
		recover the original investment of Rs.100 Crs.							
BIKRANT		Hmmm....													
		First Year - Rs.38.75 Crs											
		Second Year – Rs.42.25 Crs											
		Third year – Rs.45.05 Crs											
		So cumulative cash flows up to year three Rs.126.05 Crs.					
ALOK		It means, between year 2 & 3 you are recovering entire Rs.100 Crs.			
		Can you find out exact period?									
BIKRANT		Recovery up to Year 2 is Rs.81 Crs [38.75 + 42.25]						
		Amount to be recovered in Year 3 is Rs.19 Crs [100-81] for making up Rs.100	
		Crs.													
		Whereas actual recovery in Year 3 is Rs.45.05 Crs.						
		If Rs.45.05 Cr is earned in 12 months, then Rs.19 Crs can be earned in 5.06	
		months [19x 12/45.05]											
ALOK		Exactly!													
		By implementing this project, you can recover your investment of Rs.100 Crs	
		in just 2 Years 5 months.											
BIKRANT		Wow!													
			
ALOK		This is called Pay Back period of the project. This will play crucial role in Project	
		Investments Decisions especially when you raise debts for shorter period.	
					22									

BIKRANT	Correct! If debt have to be repaid in shorter period, then the projects Payback	
	period should also be short.	
ALOK	Business entities would generally prefer projects with shorter payback period.	
	If the payback is long, then risk associated with the projects is also more. Then	
	return expectations from those projects will also be high.	
BIKRANT	True ALOK!	
ALOK	But this ‘Payback period’ alone as a tool to evaluate investment decision would	
	become lopsided.	
BIKRANT	Why?	
ALOK	If you are going to take a decision based only on the project which pays you	
	back early, then you are ignoring the project which pays very well in the later	
	years. You are ignoring the long term profitability of the business.	
BIKRANT	Very True!	
ALOK	You are also ignoring the very important time value of money by placing	
	reliance on payback period only.	
BIKRANT	What is that Time Value of Money?	
		
ALOK	It is the fundamental concept in financial management. You cannot afford to	
	be ignorant of that!	
BIKRANT	Please ALOK! Throw light on that!	
ALOK	The money which you get now is not equal to money which you will get in	
	future.	
BIKRANT	Little more please!	
		
ALOK	If I offer you Rs.1,000/- now and Rs.1,000/- a year after, which one would you	
	prefer?	
BIKRANT	Both are one and the same! Both are same Rs.1000.	
	I don’t find any different between the two!	
ALOK	No! There are differences!	
BIKRANT	Difference?	
		
ALOK	If I give you Rs.1000/- now, you can either consume or invest. Which one	
	would you prefer? Consume or Invest?	
BIKRANT	It depends. If I have immediate requirement, I will consume. If not, I will Invest.	
ALOK	Let’s say you invest in Deposit for 10% for one year.	
		
BIKRANT	So after one year, I will have Rs.1000 + Rs.100 Interest.	
ALOK	Correct!	
	Your present Rs.1000 is equal to Rs.1100 one year later.	
	So, if I offer you either Rs.1000 now	
	(or)	
	One year after the same Rs.1000, you should automatically prefer now,	
	because you can make it as Rs.1100. after one year by investing.	
	23	

		Instead, if you are accepting my offer of Rs.1000 after one year, you are losing	
		Rs.100.							
BIKRANT		Very True!					
		Future value of Rs.1000 now for one year is Rs.1100. So I should accept only if	
		you offer Rs.1100 after one year.			
ALOK		You got that right.					
		Future value of Rs.1000 now is Rs.1100.			
		Or I would say present value of Rs.1100 received after one year is Rs.1000.	
		Does that make sense?			
BIKRANT		Yes very much!					
							
ALOK		Ok! Before we get back to our example, let us do a small calculation.	
		Let’s say, you invest Rs.1000 and you get 10% interest every year on	
		compounding, (meaning interest get accumulated) for a period of 5 years. In	
		that case, what will be the future value of the investment?	
		Please work out its computation.			
BIKRANT		Ok!							
		Year	Principal		Interest @ 10%		Total		
		1	1000		100		1100		
		2	1100		110		1210		
		3	1210		121		1331		
		4	1331		133		1464		
		5	1464		146		1610		
		Is it correct?					
ALOK		Ya!							
		This table shows,					
		-if you invest Rs.1000 in the beginning of the year, its future value at end of	
		year 1 is Rs.1100/-.					
		It means, if you are getting Rs.1100 at end of year 1, it is possible only if you	
		invest Rs.1000 now!					
		If you are getting Rs.1210 at the end of year 2, it is possible only if you invest	
		Rs.1000/- now!					
		Similarly, if you are getting Rs.1610/- at the end of year 5, it is possible only if	
		you invest Rs.1000/-			
BIKRANT		True!							
ALOK		So, we can say, the present value of Rs.1610/- to be received at the end of 5	
		years is Rs.1000/-					
BIKRANT		Yes!							

24

ALOK	So this tells you, don’t get carried away by big numbers which you are going	
	to get in future. You have to find its present value to take some meaning full	
	decision.	
BIKRANT	But ALOK, still I am not clear.	
	How it is going to help investment decision by finding the Present Value of	
	Future Cash Flows?	
ALOK	It would help you BIKRANT!	
	Let’s continue with our present case itself.	
	Rs.1000 has been invested @ 10% for 5 years, right?	
BIKRANT	Yes!	
		
ALOK	So by now you know, this Rs.1000 will become Rs.1610/- at the end of 5 Years.	
BIKRANT	Yes!	
		
ALOK	So, if this Rs.1000/- becomes Rs.1610/- in 5 years, it means it means it has	
	earned 10% every year without fail. Am I right?	
BIKRANT	Yes!	
ALOK	And, only if it earns Rs.1610/- its present value would be equivalent to	
	Rs.1000/- Is that correct?	
BIKRANT	Yes! Very much!	
		
ALOK	What would be present value if amount received at the end of 5 years is	
	Rs.1200/- instead of Rs.1610/- ?	
	Will it be equivalent to Rs.1000/-	
BIKRANT	No! Because we know, @ 10% interest rate, present value of Rs.1610/-	
	received after 5 years can be Rs.1000/- only. So it cannot be equivalent to	
	Rs.1,000/- it should be obviously less than Rs.1,000/-	
ALOK	Yes! That’s the point!	
	Now this information would help you to take decision.	
BIKRANT	How?	
ALOK	Let’s see.	
	You are investing Rs.1000 @ 10% for 5 years.	
	You have two options.	
	Option 1 will give Rs.1610 at the end of 5 years.	
	Option 2 will give Rs.1200 at the end of 5 years	
	Which option you will select?	
BIKRANT	Obviously option 1.	
ALOK	Yes! You should because, the present value of Rs.1610 is Rs.1000.	
	In that case, it is equivalent to you give Rs.1000 and take back Rs.1000 now.	
	But in option 2, the present value of Rs.1200 would be less than Rs.1000. It	
	means, you are investing Rs.1000 now and taking back less than Rs.1000/-	
	simultaneously.	
		
	25	

	So you should not think of option 2.	
		
BIKRANT	True!	
ALOK	I’ll also give you third option.	
	Option 3 – You will get Rs.1800/- at the end of year 5.	
	Which option you will prefer?	
BIKRANT	Now I would prefer option 3 because present value Rs.1800/- received at the	
	end of 5 years would be more than Rs.1,000/-	
	It would mean, I invest Rs.1000 now and take back more than Rs.1000	
	simultaneously.	
ALOK	Yes! You got the crux of it.	
	Any investment proposal should be viewed from this angle.	
	You should find present value (PV) of future cash flows from project. If the PV	
	of future cash flows are equal to Initial investment or Total Investment, then	
	the investment is earning expected returns.	
	If PV of future cash flows are greater than the Initial investment or Total	
	Investment, it earns expected + extra. i.e., it earns more than your expected	
	returns.	
BIKRANT	And if PV of future cash flows are less than the Initial investment or Total	
	Investment, it earns less than our expectation.	
ALOK	Hit on the Nail! To put it with some numbers, if you are expecting 10% returns	
	and the project is going to earn 5%, you should be avoiding those projects.	
BIKRANT	Now I understand the Time value concept ALOK! Let us proceed back with our	
	example.	

Section 7:

ALOK takes BIKRANT through Future Value, Present Value and Net Present Value (NPV) Concepts and teaches him how to take Investment Decision using NPV Technique:

ALOK	Good!			
	We have already understood the “Payback period” concept. At that time, I told	
	you, Don’t look merely at cash flows but you should also consider Time Value	
	of Money.			
BIKRANT	Yes ALOK!			
	Our example Project of Rs.100 Crs has cash flows for 8 years and it’s total is	
	Rs.409.40 Crs.			
ALOK	Yes! Here total cash flows doesn’t make much sense. You have to find the	
	present value of the cash flows.			
	If you want to find the present value of the cash flows, you should know what	
	is the expected return?			
	If you recollect our Rs.1000 Example, we were able to find the present value,	
	because of 10% expected rate of return.	
	So, to proceed further, we should know what is the expected return for our	
	project?			
BIKRANT	We have already calculated that.			
	We arrived at Weighted Average cost of capital as 20%.	
		Cost (a)	20.00		
		Total Fund (b)	100.00		
		Cost of Capital (a / b) x 100	20%		
ALOK	Yes BIKRANT! Already we have calculated WACC as 20%.	
	But we have not considered effect of tax on Interest while calculating cost of	
	capital!			
BIKRANT	That confuses me!			
ALOK	BIKRANT! We know, when we pay interest, we will save tax on interest.	
BIKRANT	Yes!			
ALOK	In our example, Debt is Rs.50cr, Interest is 15% on debt.	
BIKRANT	Correct!			
ALOK	We also agreed tax benefit on Interest will reduce interest cost.	
BIKRANT	Yes!			
			27		

ALOK	So please work correct cost of interest.							
BIKRANT	It should be 15% x 70% = 10.50%							
ALOK	Yes! You have to adjust 30% tax rate and only 70% of interest rate is your cost	
	now.													
	Good! Please tabulate your cost of capital table!				
BIKRANT	Let me do that!									
		Source			Amount	Weightage		Cost %			WACC		
		Equity			50 Cr		50%		25%		12.50%		
		Debt			50 Cr		50%		10.50%		5.25%		
		Total	17.75%										
															
ALOK	Good!													
	Your table now shows your funds are in equal proportion.	
	Weightage will change according to the mix. And your WACC is only 17.75%	
	and not 20%.													
BIKRANT	Correct!													
	This makes more sense!									
	WACC has come down due to tax effect.							
ALOK	Yes!													
	You have to do this tax adjustment in cost of capital computation, because	
	your cash flows were arrived after considering tax effect on interest.	
BIKRANT	Yes!!!													
	Now I understand the link between the two!				
ALOK	Good!													
	So now your project should generate a return of 17.75% every year for 8 years.	
	Can you please prepare a table to show what would be the cash that have to	
	be generated for this 8 years?									
BIKRANT	Yes! I’ll do that!									
			Year			Investment	Return@		Total				
								17.75%							
			1		100.00	17.75		117.75				
		2		117.75	20.90		138.65				
		3		138.65	24.61		163.26				
		4		163.26	28.98		192.24				
		5		192.24	34.12		226.36				
		6		226.36	40.18		266.54				
		7		266.54	47.31		313.85				
		8		313.85	55.71		369.56				
ALOK	Good!													

28

	Above table shows, if you invest Rs.100crs @ 17.75%, it should become	
	Rs.369.56 Crs in 8 years.	
BIKRANT	Yes!			
	Rs.369.56 Crs received after 8 years is equivalent to Rs.100 Cr now, if my return	
	expectation is 17.75%	
ALOK	Yes! Now total every year cash flows which you have estimated for the project.	
BIKRANT		Year	Cash Flow		
		1	38.75		
		2	42.25		
		3	45.05		
		4	49.25		
		5	52.75		
		6	56.25		
		7	60.45		
		8	64.65		
		Total	409.40		
	It is Rs.409.40 Crs which is greater than Future Value of Rs.369.56cr.	
ALOK	Yes! So this answers you that this project will earn more than your expected	
	return of 17.75%.	
BIKRANT	Yes ALOK!			
ALOK	Now we have made this analysis and derived result by thumb rule only. Let us	
	put it in a more professional way.	
BIKRANT	How?			
ALOK	You please tabulate all the cash flows for 8 years	
BIKRANT	Ok			
		Year	Cash Flow		
		1	38.75		
		2	42.25		
		3	45.05		
		4	49.25		
		5	52.75		
		6	56.25		
		7	60.45		
		8	64.65		
ALOK	Now you have to find PV of all these year cash flows.	
BIKRANT	How do we calculate that?	
ALOK	How did you calculated FV of an investment?	
BIKRANT	Future Value is simple.	
			29	

	I have to calculate Interest on principal.	
	Then I have to add it with principal.	
	This will give me FV.	
ALOK	Can you make it as formula?	
BIKRANT	I’ll try.		
	Future Value = Principal + Interest	
ALOK	Break down further.	
BIKRANT	FV = Principal + [Principal x Interest Rate]	
	= Principal [1 + Interest]	
ALOK	Fine! But this formula will take you for one year only. What will you do if you	
	have to calculate more number of years. Say 2nd year, 3rd year and so on?	
BIKRANT	I’ll calculate that many times.	
ALOK	Rather raise the number of times to the power in the formula. It means, if you	
	have to calculate many times or for many period, you take it to the power.	
BIKRANT	So, I should have no. of period in power?	
ALOK	Yes!		
	Have your formula like this.	
	FV = PV [1 + i] n	
BIKRANT	Here ‘PV’ Stands for Present Value,	
	‘i’	Stands for Interest &	
	‘n’	Stands for no. of period.	
	Is that correct?	
ALOK	Yes! Through ‘PV’ you can find ‘FV’ and vice versa.	
BIKRANT	Ok! But why did you started saying all these?	
ALOK	I wanted to give you the formula for finding ‘PV’.	
BIKRANT	Ok!		
		
ALOK	Now you know,	
	FV = PV [1 + i] n	
	So what is the formula for PV?	
		
BIKRANT	PV = FV /[(1+i) n]	
ALOK	Good! Now use this formula to find out ‘PV’ of all the cash flows for 8 years. In	
	this formula, the portion “[ 1/(1+i) n]” is called as factor which you will multiply	
	with Cash Flows to derive Present Value.	
BIKRANT	I got it!		
ALOK	Now can you find Present Value of our cash flows for 8 years, at expected rate	
	of return of 17.75% ?	
BIKRANT	Ok!		

30

		Year	Cash Flow	PV Factor			
			1		38.75	0.849			
			2		42.25	0.721			
			3		45.05	0.612			
			4		49.25	0.520			
			5		52.75	0.442			
			6		56.25	0.374			
			7		60.45	0.318			
			8		64.65	0.270			
ALOK	You have done it beautifully.				
	Let me check your PV Factor calculation for year 1	
	__1__  =  ______1____				
	(1+i) n	(1+17.75%) 1				
	=		_____1____				
			(1+0.1775) 1				
	=	0.849.				
	You got that right!				
	Let me also check on random, say, PV factor for year 5.	
	__1__  =  ______1____				
	(1+i) n	(1+17.75%) 5				
	=	_____1____				
			(1+0.1775) 5				
	=		__1__				
				2.2636				
	=	0.442				
	So you are correct! It matches with your PV factors in your table.	
BIKRANT	Yeah…..							
ALOK	Now, multiply this PV Factors with Cash Flows to get Present Value of Cash	
	Flows.							
BIKRANT		Year	Cash Flow	PV Factor	PV of Cash Flows		
			1		38.75	0.849	32.89		
			2		42.25	0.721	30.46		
			3		45.05	0.612	27.57		
			4		49.25	0.520	25.61		
			5		52.75	0.442	23.32		
			6		56.25	0.374	21.04		
			7		60.45	0.318	19.22		
			8		64.65	0.270	17.46		
						31			

			TOTAL		409.40			197.57		
ALOK		Now look at your table.					
		You are earning Rs.409.40 Crs cash flows over a period of 8 years but its	
		present value is only Rs.197.57crs					
BIKRANT		True! PV is less than 50% when compared with actual cash flows because of	
		higher expected returns, I believe!					
ALOK		Yes! You are correct. If you expect high returns, PV of future cash flows will be	
		low. But what is important is you have to compare the PV of future cash	
		inflows with PV of cash outflow.					
BIKRANT		Ok! In our case, PV of cash out flow is Rs.100Crs. I think we need not make any	
		special workings because it is being spent now.	
		PV of cash inflows is Rs.197.57cr					
ALOK		Look at it! It sounds like great deal.					
		It’s like you give Rs.100 Cr now and simultaneously taking back Rs.197.57cr	
		You not only get back your Rs.100crs but also get additional Rs.97.57cr	
BIKRANT		Yes! This creates greater interest in the Project.	
ALOK		Yes and it would!							
		Because you have brought your 8 years future picture compressed into single	
		value and you can compare that with your investment amount to take a	
		decision.							
BIKRANT		It’s really great!							
		Does this methodology or analysis has any technical name?	
ALOK		Yes! It has. It is called “Net Present Value” method to evaluate an investment	
		decision							
BIKRANT		Great!							
ALOK		In this method, you will Find ‘PV’ of cash inflows and compare it with ‘PV’ of	
		cash out flows.							
		If ‘PV’ of Inflows is greater than or equal to ‘PV’ of cash out flow then those	
		projects are viable projects.					
BIKRANT		Viable?							
ALOK		Yes! Because those projects not only generates profits, but their profits also	
		matches the expected level.					
		If PV of cash inflow matches PV of out flow, it generates expected return and	
		you know the rest, I believe.					
BIKRANT		Yes ALOK! I understand. Let me tabulate our example.	
		PV of Cash inflows			=	197.57cr		
		Less: PV of Cash outflows	= (100.00cr)			
		NPV of the Project			=	97.57cr			
			
ALOK		Good! NPV of your project is positive and so it is a viable project.	
					32					

BIKRANT	In case of multiple projects, out of which one has to be selected, how we	
	should approach?	
ALOK	In case of multiple projects, select the project with highest NPV.	
	Because highest NPV means, your project earns more than the expected	
	returns.	
	When the project earns more than the expected returns, it will result in	
	creation of wealth for the owners of the company.	
BIKRANT	Correct! Any Investment Decision should have the objective of creating wealth	
	for the promoters. Thanks for this clarity in NPV concept.	
ALOK	So, in this example itself you have understood the concept of	
	a)	Payback period;	
	b)	Cash flows;	
	c)	Present Value;	
	d) Future Value;	
	e) Net Present Value.	
	Good!		
BIKRANT	Thanks ALOK!	

33

Section 8:

ALOK explains Internal Rate of Return (IRR) Concept and how to take Investment Decisions using IRR Technique:

ALOK		BIKRANT, Let me ask you one more question.	
BIKRANT		Please ALOK!			
ALOK		What was the return earned by the project, which we discussed in the example	
		(Rs.100 Crs Project)?			
BIKRANT		We have already calculated. It is 17.75% after factoring tax effect on interest.	
ALOK		I am sorry BIKRANT!			
		That was the Expected Return.			
		My question is			
		“What is the actual return?” that can be earned by the Project?	
BIKRANT		Actual Return???			
		I never gave a thought on that			
		I was focusing only on cash flows.			
		Should we calculate Actual Return?			
ALOK		Yes BIKRANT!			
		You should calculate IRR for the projects!	
		Because it would make more sense, and communicate with more clarity, when	
		you say the return in %.			
		And moreover, it will communicate exact return which may be more or less	
		than expected return.			
BIKRANT		Ok!			
		So this would act as Yardstick, I believe.			
		If Actual Return is greater than Expected Return, we can select the project and	
		if not, reject the project.			
ALOK		Yes!  Let  us  take  one  simple  example  before  we  make  use  of  our	
		comprehensive one.			
BIKRANT		Ok!			
ALOK		Let’s say you have invested Rs.100 now and it generates Rs.110 at the end of	
		the year.			
		Now can you calculate the actual return earned by this investment?	
BIKRANT		Very simple.			
		a) Return (110-100)		10		
		b) Investment		100		
		c) Return on Investment		10%		
		[(a/b) x 100]				
ALOK		Good! You have done it!			
	34				

		This actual return is called as “Internal Rate of Return” Usually called as IRR.	
		In this case, you have calculated it very simply, because, it was straight	
		number.				
		Let’s us modify the example a bit.	
BIKRANT		Ok!				
ALOK		Let’s say, you want to invest Rs.100 with an expected return of 10% for 5 years	
BIKRANT		Ok!				
ALOK		The actual cash flows by investing is, say	
		Year		Cash Flows			
		1		20			
		2		35			
		3		40			
		4		50			
		5		50			
BIKRANT		Let me try to find IRR	
ALOK		Please Proceed.	
BIKRANT		Year		Cash Flows			
		1		20			
		2		35			
		3		40			
		4		50			
		5		50			
		Hmm……????	
		I couldn’t make it out	
ALOK		Yes! You can’t make out this on look!	
		Because it you calculate as earlier, you would get varied returns	
		In year 1, it would be _20 x 100 = 20%	
				100		
		Year 2, it would be  35 x 100 = 35%	
					100		
		Again Time value concept should also be considered.	
BIKRANT		Yes! It throws confusion!	
		Then how to find a solution for this?	
ALOK		We have to go by Trial & Error (T&E) method only. Because we don’t have	
		constant cash flow to predict the IRR easily.	
BIKRANT		What is that ‘Trial & Error Method’ (T&E)?	
ALOK		In T&E Method, you will try to find IRR through Trials.	
		Let us assume IRR for our current Example is 20%	
BIKRANT		20%? How can we do that arbitrarily?	
				35	

ALOK	That’s why, it is T&E Method.				
	You please find the PV of cash flows, assuming Expected Return is 20%	
BIKRANT	Ok						
		Year	Cash Flow		PV Factor@ 20%	PV of Cash Flows		
		1	20		0.833	16.67		
		2	35		0.694	24.29		
		3	40		0.579	23.16		
		4	50		0.482	24.10		
		5	50		0.402	20.10		
					TOTAL	108.32		
						
ALOK	You are correct BIKRANT!				
	Look at the PV of cash flows. It is 108.32.			
	Whereas PV of Outflow is Rs.100.00.			
	So your NPV is 8.32.				
BIKRANT	Correct. But we have to find IRR – right?			
ALOK	Yes!						
	Remember, when NPV is Positive at a particular return rate, the project is	
	earning more than that rate of return.			
BIKRANT	Yes!						
ALOK	When NPV is Negative at a particular return rate, the project is earning less	
	than that rate of return.				
BIKRANT	Correct!						
ALOK	When NPV is equal to Zero, at a particular rate, the project is earning a	
	particular rate of return and that rate of return is called as Internal Rate of	
	Return.						
BIKRANT	Yaa!!!!						
	When NPV is zero, PV of Project Inflows will be equal to PV of outflows.	
ALOK	So you should target for that rate of return where your NPV will be zero.	
	Now at 20% rate, your NPV is positive.			
	So you should reduce your NPV now for which you have to increase rate of	
	return.						
	Make it as 25% and work out your NPV.			
BIKRANT	Ok:						
		Year	Cash Flow		PV Factor@ 25%	PV of Cash Flows		
		1	20		0.800	16.00		
		2	35		0.640	22.40		
		3	40		0.512	20.48		
		4	50		0.410	20.50		
		5	50		0.328	16.40		
					TOTAL	95.78		
					36			

ALOK		Good!					
		Now calculate your NPV @ 25%.	
BIKRANT		PV of Inflows		95.78		
		PV of Outflows		100.00		
		NPV		-4.22		
ALOK		Watch out!					
		It is negative 4.22.	
BIKRANT		Yes!					
ALOK		At 20% your NPV is 8.32.	
		At 25% your NPV is -4.22	
		But for finding IRR, your NPV should be zero.	
BIKRANT		So NPV lies between 20% and 25% right?	
ALOK		Yes! You can find IRR, by using Interpolation Method.	
BIKRANT		What’s that? Is it too complicated?	
ALOK		No! It’s Simple.					
		You Know @ 20% NPV is 8.32 &	
		@ 25% NPV is -4.22.	
BIKRANT		Yes.					
ALOK		The difference between the two rate is 5% i.e.,(25%-20%)and the difference	
		the two NPV is 12.54 i.e., [8.32 – (–4.22)]	
BIKRANT		Correct!					
ALOK		Since you know NPV is +8.32 @ 20%, and – 4.22 @ 25%, you have options to	
		start either from 20% or 25%.	
BIKRANT		Ok! Let me start from 20%.	
ALOK		Now you know the difference between NPV at both the rate of returns.	
BIKRANT		Yes! It is 12.54.					
ALOK		If you are starting from 20%, how much you should add to rate of return to	
		make NPV as zero?	
BIKRANT		At 20%, NPV is 8.32. So, I should subtract 8.32 to make NPV as zero from 12.54	
		(difference between two NPVs).	
ALOK		Good!					
		12.54 is for 5%.					
		You have to find % applicable for 8.32.	
BIKRANT		Yes! Let me do that!	
		12.54 = 5%						
		8.32 = ?						
		Is that correct?					
ALOK		Yes! Proceed.					
BIKRANT		So, it should be	8.32 x 5% = 3.32%	
				12.54			
				37	

	Is it correct?	
ALOK	Yes! It is!	
	Since you started with 20%, you should add 3.32%. Because IRR lies between	
	20% and 25%. So your IRR would be 23.32%	
BIKRANT	Great! So you mean to say, PV of cash Inflows @ 23.32% would be equal to PV	
	of cash outflows.	
ALOK	Yes! NPV would be zero at this level.	
BIKRANT	That’s great! What would have been the effect if I had started with 25% for	
	arriving at IRR?	
ALOK	Let’s see that also.	
	At 25%, your NPV is – 4.22	
	How much you should add to make it as zero?	
BIKRANT	+4.22	
ALOK	Good	
	12.54 is the difference between NPVs at 5%.	
	You have to find Return% applicable for 4.22	
BIKRANT	Let me do that!	
	12.54 = 5%	
	4.22 = ?	
	It should be 4.22 x 5% = 1.68%	
	12.54	
ALOK	Correct!	
	You have now started with 25%	
	You know IRR lies between 20% - 25%	
	So what you have to do with this 1.68%?	
BIKRANT	I should subtract it from 25%	
ALOK	Please do it!	
BIKRANT	IRR  = 25% – 1.68% = 23.32%	
	In both the approaches, it is same.	
ALOK	It will be and should be.	
	If you have taken up this project with an expectation of 15%, then you should	
	be happy because you will earn 23.32%	
BIKRANT	Yes! Now I understand!	
	IRR will convey the actual return that can be earned by the project.	
	In NPV calculations, we start with known or Expected Rate of Return.	
	Whereas in IRR, we derive the Actual Rate of Return.	
ALOK	Yes! You are Correct!	
	IRR would be used as Tool to judge the acceptance of the project.	

38

	You might work out NPV of the project with your expected cost of capital (or)	
	Expected Return whereas IRR calculations will throw as to what is the actual	
	return that can be generated!		
	You can compare IRR and Expected Return to take a decision on going ahead	
	with the project!				
BIKRANT	That’s really great! Can we compress our IRR understanding as a single	
	formula?					
ALOK	Yes!					
	IRR = Lower Rate +	NPV at Lower Rate	Difference	
			-------------------------------------------------------	x  between	
			(NPV at Lower Rate – NPV at Higher Rate)	Lower	
						Rate and	
						Higher Rate	
	Lower Rate and higher rate are finalised only when we reach positive and	
	negative NPV.					
BIKRANT	What’s that?					
ALOK	In the example, we took two rates 20% and 25%.		
	We started with 20%, reached positive NPV. So we took higher rate and	
	reached negative NPV.				
	At times, our initial rate may also give negative NPV. In such cases, we have to	
	next assume, lower rates to derive positive NPV.		
BIKRANT	Yes! I understand that!				
	Is there any tool to predict arbitrary rate? Like we selected 20% in this	
	example?					
ALOK	That’s a valid question. Because, if arbitrary rate is far away from IRR, then it	
	would become time consuming process to find IRR.		
	We have a supporting tool for selecting Arbitrary Rate.		
BIKRANT	Is it? Thank God!				
ALOK	It is called Investment Factor.		
BIKRANT	How do you find that?				
ALOK	You have to find average cash inflows of the project and divide it from	
	Investment amount. It would give you a value which have to be traced and	
	located from PVIFA Table.		
BIKRANT	My God! This is going above my head. Can you explain it through our example?	
ALOK	Yes! What are your cash inflows in the example?		
BIKRANT	These are the cash flows:		
		Year	Cash Flow			
		1		20			
		2		35			
				39		

				3		40						
				4		50						
				5		50						
ALOK		Now, find average of the cash flows.	
BIKRANT			a. Total Cash Flows			195				
			b. No. of Years			5				
			c. Average Cash Flow (a/b)	39				
ALOK		Now divide the Average Cash Flow from Investment Amount and call it as	
		Investment Factor.							
BIKRANT			a. Total Cash Flows			195			
			b. No. of Years			5			
			c. Average Cash Flow (a/b)	39			
			d. Investment			100			
			e. Investment Factor (d/c)	2.564			
ALOK		This 2.564 is called as Investment Factor and it will help you to assume a rate	
		which will be some extent close to your IRR.	
BIKRANT		Ok!							
ALOK		For this exercise, you have make use of Present Value Interest Factor Annuity	
		Table.							
BIKRANT		What is that?							
ALOK		This table will tell you, at what rate of return, you will achieve Investment	
		Factor of 2.564 in 5 Years.					
BIKRANT		Ok! Please show me how to use the table.	
ALOK		This is the table. You should ensure you are taking the correct table with	
	following title. Because there are four different kind of tables for finding	
	Interest factors.							

												
BIKRANT		Ok!							
ALOK		You have to trace 2.564 in the table across 5 Years.	
BIKRANT												
		Hmmm…I could not trace here.					
								40				

ALOK	You will not. Check in the next band of rates. 11% to 20%.	
BIKRANT	Ok.	

Table is available only up to 20%.

How do I proceed further?

ALOK	This is enough. Look at 5 years period across 20%. The Factor has touched 2.991. Whereas Investment Factor which we were looking for is 2.564. So, we can infer, rate of return would be more than 20% to touch Investment Factor of 2.564.

This would help us to select the arbitrary rate as 20% and the rest is based on how NPV goes.

BIKRANT	That’s great!

41

Section 9:

ALOK and BIKRANT works out IRR for their Project Investment for Rs.100 Crs:

BIKRANT		ALOK! Now, I have grip on IRR Concept. Shall we work out IRR for our Rs.100	
		Crs Project?								
ALOK		I am glad that you didn’t forget IRR for our project. Let’s work out IRR. First,	
		write all the cash flows of our project.	
BIKRANT		These are the cash flows:					
			Year	Cash Flow				
			1		38.75				
			2		42.25				
			3		45.05				
			4		49.25				
			5		52.75				
			6		56.25				
			7		60.45				
			8		64.65				
			TOTAL		409.40				
ALOK		Good! You have to find IRR for this project. First find Investment Factor.	
BIKRANT		Ok.								
		Average Cash = Total cash flows / No. of Years	
								
		a. Total Cash Flows			409.40			
		b. No. of Years				8			
		c. Average Cash Flows		51.175			
		(a/b)								
ALOK		Now, divide this cash flow from Investment Amount.	
BIKRANT		Ok.								
		a. Investment Amount	100.00			
		b. Average Cash Flows	51.175			
		c. Investment Factor	1.9324			
		(a/b)								
ALOK		Good!								
		Now, trace this 1.9324 in PVIFA Table across 8 Years.	
BIKRANT		Ok!								

42

												
		Hmmm…even at 20% for 8 Years, factor is only 3.837 whereas our requirement		
		is 1.9324. It means IRR is above 20%. So, shall I assume 30% to start with?		
ALOK		Yes BIKRANT! Get started.					
BIKRANT				Cash		Disc.					
			Year			Factor	PV				
				Flow							
					@ 30%						
											
		1	38.75	0.769		29.81				
												
		2	42.25	0.592		25.00				
												
		3	45.05	0.455		20.51				
												
		4	49.25	0.35		17.24				
												
		5	52.75	0.269		14.21				
												
		6	56.25	0.207		11.65				
												
		7	60.45	0.159		9.63				
												
		8	64.65	0.123		7.93				
												
			TOTAL	409.4				135.98				
												
		Is it Correct?								
ALOK		Yes BIKRANT! Find Net Present Value also.		
BIKRANT			a. PV of Inflows		135.98						
			b. PV of Outflow		100.00						
			c. NPV			35.98						
ALOK		So, 30% is not your IRR, since you are getting positive NPV.		
BIKRANT		Yes, at IRR, NPV should be Zero. Right?		
ALOK			Yes BIKRANT. Try for next rate.					

43

BIKRANT		Ok. Now, I want NPV to come down. So, I should assume higher rate. Ill		
		assume 50%.								
ALOK		Ok! Go ahead.								
BIKRANT			Cash			Disc.						
		Year				Factor		PV				
			Flow									
					@ 50%						

		1	38.75		0.667		25.83				
												
		2	42.25		0.444		18.78				
												
		3	45.05		0.296		13.35				
												
		4	49.25		0.198		9.728				
												
		5	52.75		0.132		6.947				
												
		6	56.25		0.088		4.938				
												
		7	60.45		0.059		3.538				
												
		8	64.65		0.039		2.523				
												
		TOTAL	409.4					85.63				
												
ALOK		Find NPV.										
BIKRANT		a. PV of Inflows		85.63					
		b. PV of Outflow		100.00					
		c. NPV				-14.37					
		NPV @ 50% is negative.					
ALOK		So, you have positive NPV @ 30% and negative NPV @ 50%.			
BIKRANT		It means, IRR lies between 30% and 50%.			
ALOK		Find IRR through Interpolation.			
BIKRANT		Ok. I’ll make use of the formula.			
		IRR = Lower Rate +		NPV at Lower Rate	Difference		
			-------------------------------------------------------  x	between		
			(NPV at Lower Rate – NPV at Higher Rate)	Lower		
										Rate and		
										Higher Rate		
					
ALOK		Define each and every item of the formula.			
BIKRANT		Ok!										
		Lower Rate = 30%								
		Higher Rate = 50%								
		NPV at Lower Rate = 35.98					
		NPV at Higher Rate = -14.37					
								44				

	Difference between Lower Rate and Higher Rate = 20%	
ALOK	Good!		
	Now compute IRR.	
BIKRANT	IRR = 30 +	35.98	
		------------------------ x 20	
		35.98 – (-14.37)	
	= 30% +	35.98	
		----------------------- x 20	
		50.35	
	IRR=44.29%	
ALOK	BIKRANT! I just want to interrupt here.	
	Interpolation formula works best when the difference between rates are	
	narrow. When you have wide gap between two assumed rates, the IRR which	
	you get may only be an approximate one and not accurate.	
	So, try to reduce the gap between two rates.	
BIKRANT	Now, the gap between two rates are 20%.	
	Do you mean to say, I should reduce it further?	
ALOK	Yes BIKRANT!		
	Your IRR formula derivation says, it is 44.29%. So it is an indication that IRR is	
	in that range. So select two rates which will be close to that.	
BIKRANT	Ok. Ill select 40% and 43%	
ALOK	Ok BIKRANT. Please rework.	

45

BIKRANT			Cash		Disc.			Disc. Factor					
		Year			Factor @		PV			PV			
			Flow					@ 43%					
					40%								

		1	38.75		0.714		27.68	0.699		27.10			
													
		2	42.25		0.510		21.56	0.489		20.66			
													
		3	45.05		0.364		16.42	0.342		15.41			
													
		4	49.25		0.260		12.82	0.239		11.78			
													
		5	52.75		0.186		9.81	0.167		8.82			
													
		6	56.25		0.133		7.47	0.117		6.58			
													
		7	60.45		0.095		5.73	0.082		4.94			
													
		8	64.65		0.068		4.38	0.057		3.70			
													
		TOTAL	409.4				105.87			98.98			
													
		Invest-					100.00			100.00			
		ment											
													
		NPV					5.87			-1.02			
										
ALOK		Great! It looks like you are now closer to IRR. Calculate through Formula.		
BIKRANT		Ok!											
		IRR = Lower Rate +	NPV at Lower Rate	Difference		
			-------------------------------------------------------	x  between		
			(NPV at Lower Rate – NPV at Higher Rate)	Lower		
										Rate and		
										Higher Rate		
		Lower Rate = 40%									
		Higher Rate = 43%									
		NPV at Lower Rate = 5.87								
		NPV at Higher Rate = -1.02								
		Difference between Lower Rate and Higher Rate = 3%				
ALOK		Great! Please go ahead.								
BIKRANT		IRR = 40 +	5.87								
			------------------------	x 3						
			5.87 – (-1.02)								
		IRR = 42.56%									
ALOK		Now, this looks like your IRR.								
		You can also cross check your IRR.						
BIKRANT		Yes, I know, at IRR, NPV should be Zero.						
						46						

ALOK	Correct! If you find present value of cash flows at 42.56%, it will be close to	
	Rs.100 Crs and NPV will be almost zero.	
	I used the word “almost” because we have used lot of decimals and there	
	may be approximation effect.	
BIKRANT	I understand ALOK!	
	So, this is how we calculated IRR. It’s a very lengthy process.	
ALOK	Yes! ALOKally it’s a very lengthy process. But, Excel worksheet will do all these	
	computations in no minute.	
BIKRANT	Is it?	
ALOK	Yes BIKRANT!	
	I’ll teach you that later on.	
BIKRANT	Ok ALOK!	

47

Section 10:

ALOK explains other tools available for evaluating Investment Decisions and starts with Discounted Pay Back Period:

BIKRANT		ALOK, So far you have explained me three tools for evaluating Investment	
		Decision.															
ALOK		Yes BIKRANT. We have discussed about									
		a) Payback period;													
		b) Net Present Value Technique;									
		c) Internal Rate of Return Technique.								
BIKRANT		Are there any other tools and techniques for evaluating Investment Decisions?	
ALOK		Yes BIKRANT. There are other tools like									
		a) Discounted Payback period;									
		b) Profitability Index Method;									
		c) Modified Internal Rate of Return Method.						
		d) Average Rate of Return											
BIKRANT		Oh! Four more? Can you explain me one by one?						
ALOK		Yes BIKRANT. First let’s look into Discounted Payback Period.				
BIKRANT		Ok.															
ALOK		This is an extension of Pay Back Period concept by including Time Value of	
		Money.															
BIKRANT		Ok. How do we understand the difference between Payback and Discounted	
		Payback period?													
ALOK		For that, let’s bring our Payback period working for our Rs.100 Crs Project	
		example.															
BIKRANT		Ok. We had the following Cash Flows									
		Particulars /		1		2		3		4	5		6		7	8		
		Year																
		Cash Inflows		38.75		42.25		45.05		49.25	52.75		56.25		60.45	64.65		
		And we calculated the Payback period as 2 Years 5 Months.				
ALOK		Good! But this Payback period is actually misleading. Do you know why?	
BIKRANT		Yes! I think because it ignores Time Value of Money.						
ALOK		Exactly.															
		Cash flows generated at the end of year 2 is not equal to cash flows at the end	
		of year 1. Same the case for year 3-8. But Payback period treats all the cash	
		flows equally.															
BIKRANT		I got it. So, if we want to find the real value of cash flows, we should find its	
		Present Value.															
								48									

ALOK		Exactly. Cash flows should be discounted to present value by using cost of		
		capital rate.							
BIKRANT		Ok.								
ALOK		The period at which the Present Value of Cash Flows matches your Present		
		Value of Investment will be called as Discounted Payback Period.		
BIKRANT		Ok. Let me try.							
ALOK		Do you remember what’s your cost of capital is?		
BIKRANT		Yes! We have calculated it as 17.75%.				
ALOK		Good! Use that rate for discounting the cash flows.		
BIKRANT		Ok ALOK!								
ALOK		It is not necessary that you should work out discounted cash flows for all the		
		8 years. It would be sufficient if you just work up to discounted payback period.		
BIKRANT		But how	do I	know, whether the discounted cash flow is approaching		
		Investment amount.					
ALOK		I would suggest you to have additional column for cumulative cash flows which		
		will help you to track cumulative cash flows.		
BIKRANT		Ok. Let me try for the first 5 years cash flows.		
		Year		Cash		Disc. Factor	PV				
				Flow		@ 17.75%					

		1		38.75		0.849	32.91				
		2		42.25		0.721	30.47				
											
		3		45.05		0.613	27.59				
											
		4		49.25		0.520	25.62				
											
		5		52.75		0.442	23.30				
									
ALOK		Good! Now as said, add a column for PV of cumulative cash flows.		
BIKRANT		Ok.								
		Year		Cash		Disc. Factor	PV	Cumulative			
				Flow		@ 17.75%		Cash Flow			

		1		38.75		0.849	32.91	32.91			
											
		2		42.25		0.721	30.47	63.38			
											
		3		45.05		0.613	27.59	90.97			
											
		4		49.25		0.520	25.62	116.59			
											
		5		52.75		0.442	23.30	139.90			
									
ALOK		Good! Look at your Cumulative Cash Flow Position.		
		In Year 3, it is Rs.90.97 Cr whereas in Year 4 it is Rs.116.59 Cr.		
							49				

BIKRANT		Yes. So, investment of Rs.100 Crs is recovered in between 3rd and 4th year –	
		Right?					
ALOK		Yes! Please try and find out exact Discounted Payback period.			
BIKRANT		Ok.					
		a. Cumulative PV of cash inflows up to 3rd Year	90.97	
		b. PV of cash flows required in 4th Year to make up Rs.100 Crs	9.03	
		(100-90.97)					
		c. Actual PV of Cash flows in 4th Year			25.62	
		d. Time taken in 4th Year to generate Rs.9.03 Cr.	4.23	
		[Rs.9.03 x 12 months / Rs.25.62 Cr]			Months	
		Discounted Payback Period =3 Years, 4.23 Months			
			Or			
		3 Years, 4 Months, 7 days			
ALOK		Great!					
		You have done it.					
		Now look at the difference between Payback and Discounted Payback period.	
BIKRANT		Payback Period – Traditional		2 Years, 5 Months			
		Payback Period - Discounted		3 Years, 4.23 Months			
		Almost difference of One year.					
ALOK		Yes BIKRANT!					
		Traditional Payback period method assumes cash flows will not earn further	
		and it ignores the Time Value of Money. Hence, Traditional method can used	
		only for thumb rules purposes and it cannot be a used as a criterion for	
		decision making.					
		If we are very particular about payback period, then we should use Discounted	
		Payback Period tool for correct decision making.			
BIKRANT		Fine ALOK!					
		Now, I have clarity on Discounted Pay Back Period tool.			
		Shall we move on to the next tool?					

50

Section 11:

ALOK explains Profitability Index Tool for evaluating Investment Decisions:

ALOK		Let us now focus on Profitability Index Tool.	
BIKRANT		Ok!			
ALOK		It is also called as Desirability Factor.	
BIKRANT		How it is calculated?			
ALOK		I can say, it is an extension of NPV Method.	
		Here, you would use PV of Inflows and Outflows for arriving at the desirability	
		factor.			
BIKRANT		Do we have any specific formula?	
ALOK		Yes!			
		Profitability Index (PI) = PV of Inflows / PV of Outflows	
BIKRANT		As simple as that?			
ALOK		Yes! Can you calculate PI for our Rs.100 Crs example?	
BIKRANT		a. PV of Cash Inflows	197.57		
		b. PV of Cash Outflows	100.00		
		c. Profitability Index	1.98		
ALOK		Good!			
BIKRANT		How to interpret this result?	
ALOK		If PI is greater than 1, then that project is earning above your expected returns.	
BIKRANT		It means we should have positive NPV?	
ALOK		Yes! When you have positive NPV, your numerator will be higher than the	
		denominator and hence the result will be greater than 1.	
BIKRANT		So, if it is less than 1?			
ALOK		If it is less than 1, then PV of Inflows are less than that of Outflows. It means,	
		those projects will have negative NPV.	
BIKRANT		So, we can select a project when its PI is greater than 1 and reject, when it is	
		less than 1?			
ALOK		Yes!			
BIKRANT		ALOK, I have a doubt!			
ALOK		Please ask.			
BIKRANT		When we can conclude, Whether to invest or not in a project using NPV	
		Method, why there is a need for additional method like PI, which also serves	
		the same purpose?			
ALOK		No BIKRANT!			
		Profitability Index method has a purpose.	
		This method is used when we have Capital Rationing.	
			51		

BIKRANT		Capital Rationing?						
ALOK		Yes BIKRANT! There may be circumstances, when you have to take up investment	
		projects when the resources are limited. You may have to select a project from	
		various options.						
		At that time, NPV method will favour the project with highest NPV. But you	
		may not be able to take those projects due to capital limitation.	
BIKRANT		Can you explain that with some example?			
ALOK		Yes BIKRANT.							
		Assume you have Rs.120 Lakhs with you which you can invest in the following	
		projects for the given NPVs :						
		Project	Cost of the Project		NPV				
		A	50		15				
		B	40		18				
		C	25		10				
		D	30		11				
		E	35		19				
		Which project you would be selecting? Can you rank the projects for selecting	
		the best?							
BIKRANT		Hmmm….I would give first rank to Project E because it has highest NPV of 19	
		Lakhs. Then, Second Rank to Project B with NPV of 18 Lakhs……..	
ALOK		Can you please tabulate that?						
BIKRANT		Ok!							
		Project	Cost of the Project		NPV		Ranking		
		E	35		19		1		
		B	40		18		2		
		A	50		15		3		
		D	30		11		4		
		C	25		10		5		
ALOK		As per your ranking, you would first invest in Project E, followed by Project B.	
		Then you should select Project A, but because of capital limitation, you may	
		not be able to take it. So, you may have to think of 4th ranked project next.	
BIKRANT		Why?							
ALOK		Because your resources are limited to Rs.120 Lakhs.	
		By Investing in Project E & B, you would have consumed Rs.75Lakhs and	
		balance left would be only Rs.45 Lakhs. Whereas, 3rd Ranked Project would	
		require Rs.50Lakhs.						
		So, you may have to skip 3rd Ranked Project and look for 4th Ranked Project.	
		Can you tabulate this combination of Project Selection?	
				52				

BIKRANT		Ok.										
												
		Project	Cost of the Project		NPV	Ranking					
		E	35		19	1					
		B	40		18	2					
		D	30		11	4					
		TOTAL	105		48							
ALOK		Going by NPV Method, you would be able to select only three Projects E, B		
		and D and your Total Investment would be Rs.105 Lakhs and NPV would be		
		Rs.48 Lakhs. You will have unused resources for Rs.15 Lakhs.		
BIKRANT		Correct.										
ALOK		This is the scenario which you may have to accept when your Projects are not		
		divisible. You have to go by NPV.									
BIKRANT		What we will do when our Projects are divisible?					
ALOK		There comes the role of Profitability Index. When the Projects are divisible in		
		nature and you have limitation in Capital, PI Method will be the best method		
		in selecting the projects. It would even change the ranking of the projects.		
BIKRANT		How’s is that possible?									
ALOK		Let’s try. Can you find PI for the example which we have discussed?		
BIKRANT		This one?										
		Project	Cost of the Project		NPV							
		A	50		15							
		B	40		18							
		C	25		10							
		D	30		11							
		E	35		19							
ALOK		Yes.										
BIKRANT		We don’t have PV of Cash Inflows.							
ALOK		We know										
		NPV = PV of Inflows – PV of Outflows							
		You have information about NPV and PV of Outflows (Cost of Project).		
		Then finding PV of Inflows shouldn’t be a problem.					
BIKRANT		Ok. I’ll do that.									
		(a)	(b) PV of Outflow		(c)		(d)			
							PV of Inflow			
		Project	(Cost of the Project)		NPV					
							=(b)+(c)			
												
		A	50				15		65			
				53							

		B	40			18				58			
		C	25			10				35			
		D	30			11				41			
		E	35			19				54			
ALOK		Good! Now find Profitability Index										
BIKRANT		(a)		(b)		(c) PV of			(d)					
		Project	PV of Inflow		Outflow			PI					
		A	65		50		1.30					
		B	58		40		1.45					
		C	35		25		1.40					
		D	41		30		1.37					
		E	54		35		1.54					
ALOK	Good! Now, please rank the projects according to PI Factor.				
BIKRANT		(a)		(b)		(c) PV of			(d)		Ranking		
		Project	PV of Inflow		Outflow			PI					
		A	65		50		1.30		5			
		B	58		40		1.45		2			
		C	35		25		1.40		3			
		D	41		30		1.37		4			
		E	54		35		1.54		1			
ALOK		Did you noticed the difference in ranking of the Projects?				
BIKRANT		No.													
ALOK		Prepare a Table and list the ranking of projects based on NPV and PI.	
BIKRANT		Ok.													
		Rank		NPV Method			PI Method				
		1		E					E				
		2		B					B				
		3		A					C				
		4		D					D				
		5		C					A				
		Yes! There is a difference in ranking between NPV Method and PI method for	
		Projects A and C.										
ALOK		Under NPV method, Project A is given 3rd Rank whereas PI method ranks it in	
		5th Position and vice versa for Project C.								
BIKRANT		Why did this happen?										
ALOK		Profitability index method measures benefit for every Rupee Invested whereas	
		NPV just looks at value as a whole.										

54

		As per PI Method, for every Re.1 you invest in Project C, you would get Inflow	
		of Rs.1.40. It is higher than inflows expected from Project D (Rs.1.37) and	
		Project A (Rs.1.30). That’s why, PI method favoured Project C in third position.	
BIKRANT		Do you mean to say, Profitability Index method is superior to NPV Method.	
ALOK		Yes it is, when you have capital rationing and divisible projects. In other cases,	
		it is the NPV that is best, because it only enhances the value of the investors.	
BIKRANT		Ok.													
ALOK		Now, work out how you can make best use of divisible projects and enhance	
		value to the owners. Tell me how you will be investing your Rs.120 Lakhs in	
		these projects?											
BIKRANT		I’ll go by ranking:											
															
		(a)			(b) PV of Outflow		Ranking							
		Project		(Cost of the Project)									
		A				50		5							
		B				40		2							
		C				25		3							
		D				30		4							
		E				35		1							
		I’ll first invest in Project E, B and C. This would consume Rs.100 Lakhs. I would	
		still have resources for Rs.20 Lakhs. I have to select either Project D or A.	
ALOK		Yes! Since part project is possible, you select part project of either D or A but	
		ensure, it gives maximum NPV.									
BIKRANT		Ok. I’ll do that.											
															
		Project			Cost		NPV		Possible			Proportionate		
		(a)			(b)		(c)		Investment (d)			NPV		
													e=d x c / b		
		A		50		15		20				6.00		
		D		30		11		20				7.33		
		Project D gives higher NPV. So, I can use the remaining resources of Rs.20	
		Lakhs for investing in Project D.									
ALOK		Good! Now, prepare a table showing selected projects under PI Method and	
		total NPV benefit.											
BIKRANT		Ok.													
		(a)			(b) PV of Outflow		NPV				
		Project			(Cost of the Project)							
		E			35				19.00				
								55								

		B		40	18.00		
		C		25	10.00		
		D		20	7.33		
		Total		120	54.33		
ALOK		Look at the total NPV – it is Rs.54.33 Lakhs when you selected projects	
		according to PI Method. If you had sticked to NPV method, you would have	
		achieved total NPV of only Rs.48 Lakhs against investment of Rs.105 Lakhs.	
BIKRANT		True ALOK.				
		PI Method works best when we have capital rationing and divisible projects.	
ALOK		Yes BIKRANT.				
		So whenever you have divisible projects and capital rationing, evaluate the	
		projects through PI Method.				
BIKRANT		Sure ALOK.				

56

Section 12:

ALOK explains short comings of IRR and introduces Modified Internal Rate of Return

ALOK		Now we’ll understand Modified Internal Rate of Return.	
BIKRANT		Modified?			
ALOK		Yes BIKRANT.			
BIKRANT		But why?			
ALOK		It’s because, IRR method by itself has certain shortcomings. To overcome	
		those short comings, Modified IRR is used.	
BIKRANT		What are those short comings?	
ALOK		The major short coming of IRR is its assumption. It assumes, cash flows are	
		reinvested at IRR rate. But in reality it may not happen that easily. While	
		computing project cash flows, it is always best to estimate the reinvestment	
		at cost of capital rate.	
BIKRANT		True!			
ALOK		That’s why we use Modified IRR.	
BIKRANT		How, it is modified?	
ALOK		In modified IRR, we will assume cash flows are invested at cost of capital every	
		year. Then we will compare the future value of cash flow with Investment	
		amount to know the rate of return and that rate will be called as MIRR.	
BIKRANT		Do we have any formula for this?	
ALOK		Yes!			
		Investment x (1 + i)n = Future Value of Investment;	
BIKRANT		Here, “I” is the MIRR Rate right?	
ALOK		Yes!			
		‘n’ is the no. of years.	
		Future Value of Investment have to be found by investing the cash flows at	
		cost of capital rate.	
BIKRANT		Can we try finding MIRR for our Rs.100 Crs example?	
ALOK		Yes Please! and here is the cash flows:	
		Year		Cash Flow		
						
		1		38.75		
						
		2		42.25		
						
		3		45.05		
						
				57	

		4		49.25					
										
		5		52.75					
										
		6		56.25					
										
		7		60.45					
										
		8		64.65					
										
		TOTAL		409.4					
									
BIKRANT		So, I should calculate as if cash flows are invested at Cost of Capital rate – right?		
ALOK		Yes! Assume, you make the investment at the end of the year, because only at		
		the end, you will have all the cash flows.		
BIKRANT		Ok. So, cash flow generated in Year 1 will be invested at the end of year 1,		
		meaning it is invested for 7 Years only.		
ALOK		Yes. Proceed in that way. How do you calculate Future Value of Cash Flows?		
BIKRANT		I know the formula						
		FV = PV x (1+i)n						
ALOK		Good!								
		Cash flows are your PV every year.		
		Cost of Capital of 17.75% and it is “i”		
		“n” will change every year.				
		In year 1, n will be 7.				
		In year 2, n will be 6.				
		In year 3, n will be 5						
		…………………………..						
		…………………………….						
		In year 8, n will be 0.				
BIKRANT		Correct!								
ALOK		Go ahead!								
BIKRANT		Year		Cash		FV Factor	FV			
				Flow		@17.75%				
										
		1		38.75		3.139	121.62			
										
		2		42.25		2.665	112.61			
										
		3		45.05		2.264	101.98			
										
		4		49.25		1.922	94.68			
										
		5		52.75		1.633	86.12			
										
		6		56.25		1.387	77.99			
										
		7		60.45		1.178	71.18			
										
		8		64.65		1.000	64.65			
											
								58			

		TOTAL	409.4			730.83		
								
ALOK		That’s fantastic.			
		So, the above table shows, if your cash flows are invested year after year at	
		17.75%, it would fetch a Future Value of Rs.730.83 Crs.	
BIKRANT		Is this Rs.730.83 Crs is the terminal value?	
ALOK		Exactly. This is the Terminal Value of the cash flow and you have to bring this	
		cash flow to the zeroth year to know the MIRR.	
BIKRANT		Shall I apply the formula?			
ALOK		Please!			
BIKRANT		Investment x (1 + i)n = Future Value of Investment;	
ALOK		Explain each items in the formula.	
BIKRANT		Investment = Rs.100 Crs;			
		n=8 years;			
		Future Value or Terminal Value of Investment = Rs.730.83 Crs	
		i= MIRR – which we have to find.			
ALOK		Good! Please calculate.			
BIKRANT		100 x (1+i)8 = 730.83			
		(1+i)8 = 730.83 / 100			
		(1+i)8 = 7.3083			
		(1+i) = 7.30831/8			
		(1+i) = 1.2823			
		i = 1.2823 – 1			
		i= 0.2823			
		MIRR = 28.23%			
ALOK		Fantastic!			
		You have done it clearly BIKRANT!			
		MIRR = 28.23%			
BIKRANT		Thanks ALOK!			
		How do we use this rate for decision making?	
ALOK		If MIRR is greater than or equal to your Cost of Capital, accept the project	
		and if it is less than your Cost of Capital, reject the project.	
BIKRANT		Ok! Now, I have clarity on MIRR.			
						59		

Section 13:

ALOK explains Accounting (Average) Rate of Return Method (ARR) in Capital Budgeting:

ALOK	Shall we move on to Accounting or Average Rate of Return method?			
BIKRANT	Ok.														
ALOK	This method is mostly used for evaluating performance rather than taking	
	investment decisions.											
BIKRANT	But, why?													
ALOK	Because, this method focuses on Accounting Profit.						
BIKRANT	So, what?													
ALOK	Accounting Profits are not cash flows. In Investment Decisions, if you don’t	
	factor cash flows for decision making, it would be a grave mistake.			
BIKRANT	Then why we have to understand this tool?							
ALOK	We have to understand this tool, because it helps in evaluating the	
	performance of the management in Investment Projects.					
BIKRANT	Ok. How it is calculated?										
ALOK	For calculating ARR, we need two information:						
	a)	Annual Average Earnings after Tax;							
	b) Average Investment.										
BIKRANT	Ok. How do we find “Annual Average Earnings After Tax”?					
ALOK	This is nothing but average of Profit after Tax for the Project Life Period.	
BIKRANT	Ok. How about the “Average Investment”?							
ALOK	You can find Opening and Closing Balance of Investment during the Project Life	
	period and derive average every year. Then find average of average balances	
	of all years by dividing it by Project Life. It would be the Average Investment.	
BIKRANT	Shall we try ARR for our Rs.100 Crs Example?							
ALOK	For that, you need information on Profit after Tax. I’ll give you that:			
	Particulars /	1		2	3	4		5	6	7		8		
	Year														
	Profit	after	21.00		24.86	28.40	33.33		37.57	41.80	46.74		51.73		
	Tax														
BIKRANT	Thanks ALOK. I’ll calculate average profit:

a)	Total Profit (8 Years)	285.43	
b)	Project Life Period	8 Years	
c)	Average Profit (a/b)	35.68	

60

ALOK		Good! Now, please calculate Average Investment also. For that, you have to		
		calculate Opening and Closing Balance of Investment every year.					
BIKRANT		Ya! I know. We have to subtract depreciation for deriving closing balance –		
		right?																		
ALOK		Yes! Go ahead.															
BIKRANT		Ok																		
		Year		1		2		3	4		5	6		7	8		
		Opening																	
		Balance		100.00		87.50		75.00	62.50		50.00	37.50		25.00	12.50		
		Depreciation	12.50		12.50		12.50	12.50		12.50	12.50		12.50	12.50		
		Closing		87.50		75.00		62.50	50.00		37.50	25.00		12.50	-		
ALOK		Good! Now, calculate average balance for each year.							
BIKRANT		Ok.																		
		Year		1		2		3	4		5	6		7	8			
		a. Opening																	
		Balance		100.00		87.50		75.00	62.50		50.00	37.50		25.00	12.50			
		b.																		
		Depreciation	12.50		12.50		12.50	12.50		12.50	12.50		12.50	12.50			
		c. Closing	87.50		75.00		62.50	50.00		37.50	25.00		12.50	-			
		d. Average																	
		Balance		93.75		81.25		68.75	56.25		43.75	31.25		18.75	6.25			
		(a+c)/2																		
															
ALOK		Good! Now, derive average of average balances by totalling all the balances		
		and dividing it by project life period.												
BIKRANT		Ok.																		
		a)	Total Average Balance			400.00									
		b)	Project Life Period			8 Years									
		c)	Average Investment (a/b)		50.00									
ALOK		Good. Now, you have Average Profit and Average Investment. Please calculate		
		ARR.																		
BIKRANT		a)	Average Profit					35.68									
		b) Average Investment			50.00									
		c) Accounting Rate of Return		71.36%									
ALOK		Good! Now, you know how to calculate ARR.									
		With this you know how to evaluate the Investment Projects.					
BIKRANT		Yes ALOK!																	
		Thank you very much.															

61

Section 14: BIKRANT raises his concern about too many techniques and which one to use for decision making:

BIKRANT		ALOK, now I have overall knowledge of all the tools available for evaluating	
		Investment Projects. But, I feel we have lot many tools and I am not sure,	
		which tool we should be using for taking correct decisions.	
ALOK		That’s a very valid observation. Because each tool may give different results	
		and at times give different direction also. To understand that, let’s summarise	
		all the results for our Rs.100 Crs Project.	
BIKRANT		I’ll do that.			
		Tool	Result		
		Payback period	2 Years 5 Months		
		Discounted Payback Period	3 Years, 4.23 Months		
		Net Present Value	Rs.97.57cr		
		Profitability Index	1.98		
		Internal Rate of Return	42.56%		
		Modified Internal Rate of Return	28.23%		
		Accounting Rate of Return	71.36%		
			
ALOK		Good! Our Project example has very comfortable numbers for 8 years period.	
		So, I would say, all the tools have given very favourable results.	
		Each and every tool has some purpose and that should be given appropriate	
		weightage. If you are hard pressed for repaying loan taken for the project in	
		short period, then Payback Period is an important Tool.	
		If you are particular about ensuring wealth maximisation for the shareholders,	
		then NPV is right tool.			
		If you have capital limitation and divisible projects, Profitability Index will help	
		you.			
		If you want to ensure, you returns are more than your cost of capital, IRR will	
		help you.			
		If you are not convinced with IRR, then MIRR is available.	

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	If you want to evaluate the performance of the management, then ARR	
	method is available.	
BIKRANT	Great Yaar!	
ALOK	But sometimes, two tools may give results in opposite direction. At that point,	
	we have to take calculated decision.	
BIKRANT	Like?	
ALOK	Conflict between NPV and IRR.	
BIKRANT	When it can happen?	
ALOK	Let’s say you have to select only one project out of three projects – A B & C. It	
	is called as Mutually exclusive projects. Because selection of one will lead to	
	rejection of the other projects.	
BIKRANT	Ok.	
ALOK	In such cases, it may so happen NPV method favour one project, say Project A	
	and IRR method may favour Project B or C.	
BIKRANT	Conflict starts! But why such conflict arises?	
ALOK	It may be due to various factors.	
	a) There may be differences in Cash Flows of the Projects. i.e., Cash flow	
	pattern of all the projects are different.	
	b) There may be differences in timing of the Cash Flows of the Projects.	
	i.e., Some projects may have lower cash flows in the beginning / end	
	and some may have higher cash flow in the beginning /end.	
	c) There may be differences in life of the Project. i.e., all projects having	
	different life periods.	
	d) There may be differences in Reinvestment rate assumptions.	
BIKRANT	Ok.	
ALOK	If the conflict is due to different life period of the projects, then we can sort	
	out the conflict.	
BIKRANT	How?	
ALOK	We can make use of ‘Annualised NPV’ Tool.	
BIKRANT	How does it work?	
ALOK	We have to find Annualised NPV for all the projects and select the project	
	which has highest Annualised NPV.	
BIKRANT	How do we calculate?	
ALOK	Annualised NPV = NPV / PVIFA for Project Life Period at Cost of Capital.	
BIKRANT	What is that?	
ALOK	You should divide the NPV of each project by Present Value Interest Factor	
	Annuity.	
	This value should be picked up from PVIFA Table, across project life period’s	
	cost of capital.	
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BIKRANT	Ok. I got it.	
ALOK	In this way, you have to calculate for all the project and select the highest one.	
	So, understand, when you have conflict between NPV and IRR due to life	
	period of the projects, you can sort out through Annualised NPV.	
BIKRANT	Yes! That’s clear. But, how about the other cases when there is a dispute	
	between NPV and IRR.	
ALOK	In such cases, you should think from Owners / Shareholders angle. The very	
	objective of running the business is to maximise the shareholders wealth. Out	
	of many tools available, only NPV result will help in maximising the wealth of	
	the shareholders.	
BIKRANT	So, you mean to say, we should select the project with highest NPV.	
ALOK	Yes! If Shareholders wealth optimisation is the objective, then you should go	
	with NPV in case of dispute between NPV and IRR.	
BIKRANT	Ok!	
ALOK	Every business, which takes up investment project for	
	-New Activity;	
	-Expansion;	
	-Diversification;	
	-Modernisation;	
	Should carefully evaluate the viability of the project using the tools we have	
	discussed.	
BIKRANT	Very True. If they evaluate correctly, they will know in advance whether they	
	are taking up a viable project or not.	
ALOK	Yes! They have to take evaluation or Capital Budgeting exercise very seriously	
	because it will affect long term growth and future direction of the business.	
BIKRANT	Yes ALOK! A wrong investment in projects will even collapse a business.	
ALOK	True! Moreover, Capital Investment Projects requires huge investment of	
	money. So, we are taking a big risk by investing huge resources. So, it should	
	be made only after careful evaluation, because amount once invested cannot	
	be easily taken back. It’s almost an irreversible decision.	
BIKRANT	Yes ALOK! I have understood the Capital Budgeting Tools and concepts	
	comprehensively. Thank you very much.	
ALOK	Welcome BIKRANT!	

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