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This part covers Net Present Value Technique (NPV))

Note: This is a third part of earlier articles “Analysis on Capital Budgeting Techniques”. Start reading this Part III article only after reading the Part I &II. Articles available in the following links: 

Part I:
Analysis on capital budgeting techniques

Part II:
Analysis on capital budgeting techniques - Part II

(Watch out for Part IV – VI in the coming weeks)

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

Manu

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.

Vinu

Yes Manu!

Our example Project of Rs.100 Crs has cash flows for 8 years and it’s total is Rs.409.40 Crs.

Manu

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 in Time Value of Money, 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?

Vinu

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%

Manu

Yes Vinu! Already we have calculated WACC as 20%.

But we have not considered effect of tax on Interest while calculating cost of capital!

Vinu

That confuses me!

Manu

Vinu! We know, when we pay interest, we will save tax on interest.

Vinu

Yes!

Manu

In our example, Debt is Rs.50cr, Interest is 15% on debt.

Vinu

Correct!

Manu

We also agreed tax benefit on Interest will reduce interest cost.

Vinu

Yes!

Manu

So please work correct cost of interest.

Vinu

It should be 15% x 70% = 10.50%

Manu

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!

Vinu

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%      

Manu

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%.

Vinu

Correct!

This makes more sense!

WACC has come down due to tax effect.

Manu

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.

Vinu

Yes!!!

Now I understand the link between the two!

Manu

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?

Vinu

Yes! I’ll do that!

Year

Investment

Return@

17.75%

Total

1

2

3

4

5

6

7

8

100.00

117.75

138.65

163.26

192.24

226.36

266.54

313.85

17.75

20.90

24.61

28.98

34.12

40.18

47.31

55.71

117.75

138.65

163.26

192.24

226.36

266.54

313.85

369.56

Manu

Good!

Above table shows, if you invest Rs.100crs @ 17.75%, it should become Rs.369.56 Crs in 8 years.

Vinu

Yes!

Rs.369.56 Crs received after 8 years is equivalent to Rs.100 Cr now, if my return expectation is 17.75%

Manu

Yes! Now total every year cash flows which you have estimated for the project.

Vinu

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.

Manu

Yes! So this answers you that this project will earn more than your expected return of 17.75%.

Vinu

Yes Manu!

Manu

Now we have made this analysis and derived result by thumb rule only. Let us put it in a more professional way.

Vinu

How?

Manu

You please tabulate all the cash flows for 8 years

Vinu

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

Manu

Now you have to find PV of all these year cash flows.

Vinu

How do we calculate that?

Manu

How did you calculated FV of an investment?

Vinu

Future Value is simple.

I have to calculate Interest on principal.

Then I have to add it with principal.

This will give me FV.

Manu

Can you make it as formula?

Vinu

I’ll try.

Future Value = Principal + Interest

Manu

Break down further.

Vinu

FV  = Principal + [Principal x Interest Rate]

      = Principal [1 + Interest]

Manu

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?

Vinu

I’ll calculate that many times.

Manu

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.

Vinu

So, I should have no. of period in power?

Manu

Yes!

Have your formula like this.

FV = PV [1 + i] n

Vinu

Here ‘PV’ Stands for Present Value,

            ‘i’   Stands for Interest &

           ‘n’   Stands for no. of period.

Is that correct?

Manu

Yes! Through ‘PV’ you can find ‘FV’ and vice versa.

Vinu

Ok! But why did you started saying all these?

Manu

I wanted to give you the formula for finding ‘PV’.

Vinu

Ok!

Manu

Now you know,

FV = PV [1 + i] n
So what is the formula for PV?

Vinu

PV  =  FV /[(1+i) n]

Manu

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.

Vinu

I got it!

Manu

Now can you find Present Value of our cash flows for 8 years, at expected rate of return of 17.75% ?

Vinu

Ok!

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

Manu

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

SSo you are correct! It matches with your PV factors in your table.

Vinu

Yeah…../p>

Manu

NNow, multiply this PV Factors with Cash Flows to get Present Value of Cash Flows.

Vinu

Year/p>

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

TOTAL

409.40

197.57

Manu

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

Vinu

True! PV is less than 50% when compared with actual cash flows because of higher expected returns, I believe!

Manu

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.

Vinu

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

Manu

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

Vinu

Yes! This creates greater interest in the Project.

Manu

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.

Vinu

It’s really great!

Does this methodology or analysis has any technical name?

Manu

Yes! It has. It is called “Net Present Value” method to evaluate an investment decision

Vinu

Great!

Manu

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.  

Vinu

Viable?

Manu

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.

Vinu

Yes Manu! 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

Manu

Good! NPV of your project is positive and so it is a viable project.

Vinu

In case of multiple projects, out of which one has to be selected, how we should approach?

Manu

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.

Vinu

Correct! Any Investment Decision should have the objective of creating wealth for the promoters. Thanks for this clarity in NPV concept.

Manu

So, in this example itself you have understood the concept of

  1. Payback period;
  2. Cash flows;
  3. Present Value;
  4. Future Value;
  5. Net Present Value.

Good!

Vinu

Thanks Manu!

Part IV will be continued next week….

Author:
CA N Raja, B.Com.,PGDBA, ACA
Chartered Accountant
nrajca@gmail.com
www.concells.in/elearning

For more such articles from Manu and Vinu, access www.concells.in/elearning


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Category Others, Other Articles by - CA N RAJA 



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