Nine Gems Ltd. has just installed MachineR at a cost of Rs. 2,00,000. The machine has a five year life with no residual value. The annual volume of production is estimated at 1,50,000 units, which can be sold at Rs. 6 per unit. Annual operating costs are estimated at Rs. 2,00,000 (excluding depreciation) at this output level. Fixed costs are estimated at Rs. 3 per unit for the same level of production.
Nine Gems Ltd. has just come across another model called MachineS capable of giving the same output at an annual operating cost of Rs. 1,80,000 (exclusive of depreciation).There will be no change in fixed costs. Capital cost of this machine is Rs. 2,50,000 and the estimated life is for five years with nil residual value.
The company has an offer for sale of MachineR at Rs. 1,00,000. But the cost of dismantling and removal will amount to Rs. 30,000. As the company has not yet commenced operations, it wants to sell Machine –R and purchase MachineS.
Nine Gems Ltd. will be a zerotax company for seven years in view of several incentives and allowances available.
The cost of capital may be assumed at 14%. P.V. factors for five years are as follows:
Â Â
Year
P.V. Factors
1
0.877
2
0.769
3
0.675
4
0.592
5
0.519
(i) Advise whether the company should opt for the replacement.
(ii) Will there be any change in your view if MachineR has not been installed but the company is in the process of selecting one or the other machine?
Support your view with necessary workings.
(FinalNov. 1996) (12 marks)
Answer
(i) Replacement of Machine –R
Incremental cash out flow
Â Â
(i)
Cash out flow on Machine –S
Rs. 2,50,000
Less: Sale Value of Machine –R
Less : Cost of dismantling and removal
(Rs. 1,00,000Rs. 30,000)
Rs. 70,000
Net outflow
Rs. 1,80,000
Incremental cash flow from MachineS
Annual cash flow from Machine –S
Rs. 2,70,000
Annual cash flow from Machine –R
Rs. 2,50,000
Net incremental Cash in flow
Rs. 20,000
Present value of incremental cash in flows
= Rs. 20,000 ´ (0.877 +0.769+0.675+0.592+0.519)
= 20,000 ´ 3.432 = Rs. 68,640
NPV of Machine S = Rs. 68,640 – Rs. 1,80,000
= () Rs. 1,11,360
Rs. 2,00,000 spent on Machine –R is a sunk cost and hence it is not relevant for deciding the replacement.
Decision: Since Net present value of Machine –S is in the negative, replacement is not advised.
If the company is in the process of selecting one of the two machines, the decision is to be made on the basis of independent evaluation of two machines by comparing their Netpresent values.
(ii) Independent evaluation of Machine –R and Machine –S:
Â Â
Machine –R
Machine –S
Units produced
1,50,000
1,50,000
Selling price per unit (Rs.)
6
6
Sale value
9,00,000
9,00,000
Less: Operating Cost
(exclusive of depreciation)
2,00,000
1,80,000
Contribution
7,00,000
7,20,000
Less: Fixed Cost
4,50,000
4,50,000
Annual cash flow
2,50,000
2,70,000
Present value of cash flows for five years
8,58,000
9,26,640
Cash Outflow
2,00,000
2,50,000
Net Present Value
6,58,000
6,76,640
As the NPV of cash in flow of Machine –S is higher than that of Machine –R, the choice should fall on machine –S.
Note: As the company is a zero tax company for seven years (Machine life in both cases is only for five years), depreciation and the tax effect on the same are not relevant for consideration.
Question 2
(a) Following are the data on a capital project being evaluated by the management of X Ltd.:
Â Â
Project M
Annual cost saving
Rs. 40,000
Useful life
4 years
I.R.R
15%
Profitability index (PI)
1,064
NPV
?
Cost of capital
?
Cost of project
?
Payback
?
Salvage value
0
Find the missing values considering the following table of discount factor only:
Â Â
Discount factor
15%
14%
13%
12%
1 Year
0.869
0.877
0.885
0.893
2 Years
0.756
0.769
0.783
0.797
3 Years
0.658
0.675
0.693
0.712
4 Years
0.572
0.592
0.613
0.636
2.855
2.913
2.974
3.038
(b) S Ltd. has Rs. 10,00,000 allocated for capital budgeting purposes. The following proposals and associated profitability indexes have been determined.
Â Â
Project
Amount
Profitability Index
1
3,00,000
1.22
2
1,50,000
0.95
3
3,50,000
1.20
4
4,50,000
1.18
5
2,00,000
1.20
6
4,00,000
1.05
Which of the above investments should be undertaken? Assume that projects are indivisible and there is no alternative use of the money allocated for capital budgeting.
(FinalNov. 1998) (12 + 8 marks)
Answer
(a) Cost of Project M
At 15% I.R.R., the sum total of cash inflows = Cost of the project i.e. Initial cash outlay 11 Given:
Annual cost saving
Rs. 40,000
Useful life
4 years
IRR
15%
Now, considering the discount factor table @ 15% cumulative present value of cash inflows for 4 years is 2.855
Therefore,
Total of cash inflows for 4 years for Project M is (Rs. 40,000 ´ 2.855) = Rs. 1,14,200
Hence, cost of the project is = Rs. 1,14,200
Payback period of the Project M
Cost of the project
Annual cost saving
Payback period = =
=
= 2.855 or 2 years 11 months approximately
Cost of Capital
If the profitability index (PI) is 1, cash inflows and outflows would be equal. In this case, (PI) is 1.064. Therefore, cash inflows would be more by 0.64 than outflow.
Probability index (PI) =
or 0.064 =
or 1.064 ´ Rs. 1,14,200 = Rs. 1,21,509
Hence discounted cash inflows =Rs. 1,21,509
Since, Annual cost saving is Rs. 40,000. Hence, cumulative discount factor for 4 years
=
= 3.037725 or 3.038
Considering the discount factor table at discount rate of 12%, the cumulative discount factor for 4 years is 3.038
Hence, the cost of capital is 12%
Net present value of the project
N.P.V. = Total present values of cash inflows – Cost of the project
= Rs. 1,21,509 – Rs. 1,14,200
= Rs. 7,309
(b) Statement showing ranking of projects on the basis of Profitability Index
Â Â
Project
Amount
(Rs.)
P.I.
Rank
1
3,00,000
1.22
1
2
1,50,000
0.95
5
3
3,50,000
1.20
2
4
4,50,000
1.18
3
5
2,00,000
1.20
2
6
4,00,000
1.05
4
Assuming that projects are indivisible and there is no alternative use of the money allocated for capital budgeting on the basis of P.I. , the S Ltd. is advised to undertake investment in projects 1,3 and 5.
However, among the alternative projects the allocation should be made to the projects which adds the most to the shareholders wealth. The NPV method, by its definition, will always select such projects.
Statement showing NPV of the projects
Â Â
Project
(i)
Amount
(Rs.)
(ii)
P.I.
(iii)
Cash inflows of project (Rs.)
(iv)=[(ii) ´ (iii)]
N.P.V. of project
(Rs.)
(v)=[(iv)(ii)]
1
3,00,000
1.22
3,66,000
66,000
2
1,50,000
0.95
1,42,500
() 7,500
3
3,50,000
1.20
4,20,000
70,000
4
4,50,000
1.18
5,31,000
81,000
5
2,00,000
1.20
2,40,000
40,000
6
4,00,000
1.05
4,20,000
20,000
The allocation of funds to the projects 1,3 and 5 (as selected above on the basis of PI) will give NPV of Rs. 1,76,000 and Rs. 1,50,000 will remain unspent.
However, the NPV of the projects 3,4 and 5 is Rs. 1,91,000 which is more than the N.P.V. of projects 1,3 and 5. Further, by undertaking projects 3,4 and 5 no money will remain unspent. Therefore, S Ltd. is advised to undertake investments in projects 3,4 and 5.
Question 3
A large profit making company is considering the installation of a machine to process the waste produced by one of its existing manufacturing process to be converted into a marketable product. At present, the waste is removed by a contractor for disposal on payment by the company of Rs. 50 lacs per annum for the next four years. The contract can be terminated upon installation of the aforesaid machine on payment of a compensation of Rs. 30 lacs before the processing operation starts. This compensation is not allowed as deduction for tax purposes.
The machine required for carrying out the processing will cost Rs. 200 lacs to be financed by a loan repayable in 4 equal installments commencing from the end of year 1. The interest rate is 16% per annum. At the end of the 4^{th} year, the machine can be sold for Rs. 20 lacs and the cost of dismantling and removal will be Rs. 15 lacs.
Sales and direct costs of the product emerging from waste processing for 4 years are estimated as under:
(Rs. In lacs)
Â Â
Year
1
2
3
4
Sales
322
322
418
418
Material consumption
30
40
85
85
Wages
75
75
85
100
Other expenses
40
45
54
70
Factory overheads
55
60
110
145
Depreciation (as per income tax rules)
50
38
28
21
Initial stock of materials required before commencement of the processing operations is Rs. 20 lacs at the start of year 1. The stock levels of materials to be maintained at the end of year 1, 2 and 3 will be Rs. 55 lacs and the stocks at the end of year 4 will be nil. The storage of materials will utilise space which would otherwise have been rented out for Rs. 10 lacs per annum. Labour costs include wages of 40 workers, whose transfer to this process will reduce idle time payments of Rs. 15 lacs in the year 1 and Rs. 10 lacs in the year 2. Factory overheads include apportionment of general factory overheads except to the extent of insurance charges of Rs. 30 lacs per annum payable on this venture. The company’s tax rate is 50%.
Present value factors for four years are as under:
Â Â
Year
1
2
3
4
Present value factors
0.870
0.756
0.658
0.572
Advise the management on the desirability of installing the machine for processing the waste. All calculations should form part of the answer.
(FinalMay 1999) (20 marks)
Answer
Statement of Incremental Profit
(Rs. in lacs)
Â Â
Years
1
2
3
4
Sales :(A)
322
322
418
418
Material consumption
30
40
85
85
Wages
60
65
85
100
Other expenses
40
45
54
70
Factory overheads (insurance)
30
30
30
30
Loss of rent
10
10
10
10
Interest
32
24
16
8
Depreciation (as per income tax rules)
50
38
28
21
Total cost: (B)
252
252
308
324
Incremental profit (C)=(A)(B)
70
70
110
94
Tax (50% of (C))
35
35
55
47
Statement of Incremental Cash Flows
(Rs. in lacs)
Years
0
1
2
3
4
Material stocks
(20)
(35)



Compensation for contract
(30)




Contract payment saved

50
50
50
50
Tax on contract payment

(25)
(25)
(25)
(25)
Incremental profit

70
70
110
94
Depreciation added back

50
38
28
21
Tax on profits

(35)
(35)
(55)
(47)
Loan repayment

(50)
(50)
(50)
(50)
Profit on sale of machinery (net)




5
Total incremental cash flows
(50)
25
48
58
48
Present value factor
1.00
0.870
0.756
0.658
0.572
Net present value of cash flows
(50)
21.75
36.288
38.164
27.456
Net present value
= Rs. 123.658 – Rs. 50 = 73.658 lacs.
Advice: Since the net present value of cash flows is Rs. 73.658 lacs which is positive the management should install the machine for processing the waste.
Notes:
1. Material stock increases are taken in cash flows.
2. Idle time wages have also been considered
3. Apportioned factory overheads are not relevant only insurance charges of this project are relevant.
4. Interest calculated at 16% based on 4 equal instalments of loan repayment.
5. Sale of machinery Net income after deducting removal expenses taken. Tax on Capital gains ignored.
6. Saving in contract payment and income tax there on considered in the cash flows.
Question 4
ABC Company Ltd. has been producing a chemical product by using machine Z for the last two years. Now the management of the company is thinking to replace this machine either by X or by Y machine. The following details are furnished to you:
Z
X
Y
Book value (Rs.)
1,00,000


Resale value now (Rs.)
1,10,000


Purchase price (Rs.)

1,80,000
2,00,000
Annual fixed costs
(including depreciation)(Rs.)
92,000
1,08,000
1,32,000
Variable running cost
(including labour) per unit (Rs.)
3
1.50
2.50
Production per hour (unit)
8
8
12
You are also provided the following details:
Selling price per unit
(Rs.) 20
Cost of materials per unit
(Rs.) 10
Annual operating hours
2,000
Working life of each of the three machines (as from now)
5 years
Salvage value of machines Z is Rs. 10,000, X is Rs. 15,000 and Y is Rs. 18,000
The company charges depreciation using straight line method. It is anticipated that an additional cost of Rs. 8,000 per annum would be incurred on special advertising to sell the extra output of machine Y. Assume tax rate of 50% and cost of capital 10%. The present value of Rs. 1 to be received at the end of the year at 10% is as under:
Â Â
Year
1
2
3
4
5
Present value
.909
.826
.751
.683
.621
Required: Using NPV method, you are required to analyse the feasibility of the proposal and make recommendations. (FinalNov.1999) (14 marks)
Answer
ABC Company Ltd.
Computation of yearly cash inflow
Machine
Z
X
Y
Sales (units)
16,000
16,000
24,000
Selling price per unit (Rs.)
20
20
20
Sales: (A)
3,20,000
3,20,000
4,80,000
Less: Costs
Variable running costs
48,000
24,000
60,000
Material cost
1,60,000
1,60,000
2,40,000
Annual fixed cost
92,000
3,00,000
1,08,000
2,92,000
1,32,000
4,32,000
Additional cost (special advertising)


8,000
Total Cost: (B)
3,00,000
2,92,000
4,40,000
Profit befor tax: (A)(B)
20,000
28,000
40,000
Less: Tax ( @ 50%)
10,000
14,000
20,000
Profit after tax
10,000
14,000
20,000
Add: Depreciation
20,000
33,000
36,400
Cash inflow
30,000
47,000
56,400
Computation of Cash Inflow in 5^{th} Year
Machine
Z
X
Y
Cash inflow
30,000
47,000
56,400
Add: Salvage value of machines
10,000
15,000
18,000
Cash inflow
40,000
62,000
74,400
Computation of Net Present Value
Year
Machine
Z
X
Y
Discounting factor
Cash inflow Rs.
P.V. of Cash inflow Rs.
Cash inflow Rs.
P.V. of Cash inflow Rs.
Cash inflow Rs.
P.V. of Cash inflow Rs.
1
0.909
30,000
27,270
47,000
42,723
56,400
51,267.60
2
0.826
30,000
24.780
47,000
38,822
56,400
46,586.40
3
0.751
30,000
22,530
47,000
35,297
56,400
42,356.40
4
0.683
30,000
20,490
47,000
32,101
56,400
38,521.20
5
0.621
40,000
24,840
62,000
38,502
74,400
46,202.40
1,19,910
1,87,445
2,24,934.00
Less: Purchase price
1,10,000
1,80,000
2,00,000.00
Net present value
9,910
7,445
24,934.00
Recommendations:
The net present value is higher in the case of machine Y. Therefore, it is advisable that the company should replace machine Z with machine Y.
However, as the cost of investment is not same for all machines, it would be better to base the decision on profitability index which is as under:
P.I. =
Machine Z = = = 1.09
Machine X = = 1.041
Machine Y = = 1.12
Since the profitability index of machine Y is the highest therefore machine Z should be replaced by machine Y.
Question 5
(a) Company X is forced to choose between two machines A and B. The two machines are designed differently, but have identical capacity and do exactly the same job. Machine A costs Rs. 1,50,000 and will last for 3 years. It costs Rs. 40,000 per year to run. Machine B is an ‘economy’ model costing only Rs. 1,00,000, but will last only for 2 years, and costs Rs. 60,000 per year to run. These are real cash flows. The costs are forecasted in rupees of constant purchasing power. Ignore tax. Opportunity cost of capital is 10 per cent. Which machine company X should buy?
(b) Company Y is operating an elderly machine that is expected to produce a net cash inflow of Rs. 40,000 in the coming year and Rs. 40,000 next year. Current salvage value is Rs. 80,000 and next year’s value is Rs. 70,000. The machine can be replaced now with a new machine, which costs Rs. 1,50,000, but is much more efficient and will provide a cash inflow of Rs. 80,000 a year for 3 years. Company Y wants to know whether it should replace the equipment now or wait a year with the clear understanding that the new machine is the best of the available alternatives and that it in turn be replaced at the optimal point. Ignore tax. Take opportunity cost of capital as 10 percent. Advise with reasons. (FinalMay 2000) (12 + 8 marks)
Answer
(a) Statement showing the Evaluation of Two Machines
Â Â
Machines
A
B
Purchase cost (Rs.): (i)
1,50,000
1,00,000
Life of machines (years)
3
2
Running cost of machine per year (Rs.): (ii)
40,000
60,000
Cumulative present value factor for 13 years @ 10%: (iii)
2.486

Cumulative present value factor for 12 years @ 10%: (iv)

1.735
Present value of running cost of machines (Rs.): (v)
99,440
1,04,100
[(ii) ´ (iii)]
[(ii) ´ (iv)]
Cash outflow of machines (Rs.): (vi)=(i) +(v)
2,49,440
2,04,100
Equivalent present value of annual cash outflow
1,00,338
1,17,637
[(vi)÷(iii)]
[(vi) ÷(iv)]
Decision: Company X should buy machine A since its equivalent cash outflow is less than machine B.
(b) Statement showing Present Value of Cash inflow of New Machine when it replaces Elderly Machine Now
Â Â
Cash inflow of a new machine per year
Rs. 80,000
Cumulative present value for 13 years @ Rs. 10%
2.486
Present value of cash inflow for 3 years (Rs. 80,000 ´ 2,486)
Rs.
1,98,880
Rs.
Less: Cash Outflow
Purchase cost of new machine
1,50,000
Less: Salvage value of old machine
80,000
70,000
N.P.V of cash inflow for 3 years
1,28,880
Equivalent annual net present value of cash
inflow of new machine
51,842
Statement showing Present Value of Cash inflow of New machine when it replaces Elderly Machine Next Year
Cash inflow of new machine per year
Rs. 80,000
Cumulative present value of 13 years @ 10%
2.486
Rs.
Present value of cash inflow for 3 years (Rs. 80,000 ´ 2,486)
1,98,880
Rs.
Less: Cash outflow
Purchase cost of new machine
1,50,000
Less: Salvage value of old machine
70,000
80,000
N.P.V. of cash inflow for 3 years
1,18,880
Advise: Since the equivalent annual cash inflow of new machine now and next year is more than cash inflow (Rs. 40,000) of an elderly machine the company Y is advised to replace the elderly machine now.
Company Y need not wait for the next year to replace the elderly machine since the equivalent annual cash inflow now is more than the next year’s cash inflow.
Question 6
X Ltd. an existing profitmaking company, is planning to introduce a new product with a projected life of 8 years. Initial equipment cost will be Rs. 120 lakhs and additional equipment costing Rs. 10 lakhs will be needed at the beginning of third year. At the end of the 8 years, the original equipment will have resale value equivalent to the cost of removal, but the additional equipment would be sold for Rs. 1 lakh. Working capital of Rs. 15 lakhs will be needed. The 100% capacity of the plant is of 4,00,000 units per annum, but the production and salesvolume expected are as under:
Â Â
Year
Capacity in percentage
1
20
2
30
35
75
68
50
A sale price of Rs. 100 per unit with a profit volume ratio of 60% is likely to be obtained. Fixed Operating Cash Cost are likely to be Rs. 16 lakhs per annum. In addition to this the advertisement expenditure will have to be incurred as under:
Â Â
Year
1
2
35
68
Expenditure in Rs. lakhs each year
30
15
10
4
The company is subjected to 50% tax, straightline method of depreciation, (permissible for tax purposes also) and taking 12% as appropriate after tax cost of Capital, should the project be accepted? (FinalMay 2002) (14 marks)
Answer
Computation of initial cash outlay
Â Â
(Rs. in lakhs)
Equipment Cost (0)
120
Working Capital (0)
15
135
Calculation of Cash Inflows:
Â Â
Years
1
2
35
68
Sales in units
80,000
1,20,000
3,00,000
2,00,000
Rs.
Rs.
Rs.
Rs.
Contribution @ Rs. 60 p.u.
48,00,000
72,00,000
1,80,00,000
1,20,00,000
Fixed cost
16,00,000
16,00,000
16,00,000
16,00,000
Advertisement
30,00,000
15,00,000
10,00,000
4,00,000
Depreciation
15,00,000
15,00, 000
16,50,000
16,50,000
Profit /(loss)
(13,00,000)
26,00,000
1,37,50,000
83,50,000
Tax @ 50%
NIL
13,00,000
68,75,000
41,75,000
Profit/(Loss) after tax
(13,00,000)
13,00,000
68,75,000
41,75,000
Add: Depreciation
15,00,000
15,00,000
16,50,000
16,50,000
Cash inflow
2,00,000
28,00,000
85,25,000
58,25,000
Computation of PV of CIF
Â Â
Year
CIF
Rs.
PV Factor
@ 12%
Rs.
1
2,00,000
.893
1,78,600
2
28,00,000
.797
22,31,600
3
85,25,000
.712
60,69,800
4
85,25,000
.636
54,21,900
5
85,25,000
.567
48,33,675
6
58,25,000
.507
29,53,275
7
58,25,000
.452
26,32,900
8
58,25,000
.404
29,99,700
WC
15,00,000
SV
1,00,000
__________
2,73,21,450
PV of COF 0
1,35,00,000
Additional Investment
= Rs. 10,00,000 ´ .797
7,97,000
1,42,97,000
NPV
1,30,24,450
Recommendation: Accept the project in view of positive NPV.
Question 7
A company proposes to install a machine involving a Capital Cost of Rs.3,60,000. The life of the machine is 5 years and its salvage value at the end of the life is nil. The machine will produce the net operating income after depreciation of Rs.68,000 per annum. The Company’s tax rate is 45%.
The Net Present Value factors for 5 years are as under:
Discounting Rate
:
14
15
16
17
18
Cumulative factor
:
3.43
3.35
3.27
3.20
3.13
You are required to calculate the internal rate of return of the proposal.
(PEIINov. 2002) (4 marks)
Answer
Computation of cash inflow per annum Rs.
Net operating income per annum
68,000
Less: Tax @ 45%
30,600
Profit after tax
37,400
Add: Depreciation
72,000
(Rs.3,60,000 / 5 years)
Cash inflow
1,09,400
The IRR of the investment can be found as follows:
A company has to make a choice between two projects namely A and B. The initial capital outlay of two Projects are Rs.1,35,000 and Rs.2,40,000 respectively for A and B. There will be no scrap value at the end of the life of both the projects. The opportunity Cost of Capital of the company is 16%. The annual incomes are as under:
Year
Project A
Project B
Discounting
factor @ 16%
1

60,000
0.862
2
30,000
84,000
0.743
3
1,32,000
96,000
0.641
4
84,000
1,02,000
0.552
5
84,000
90,000
0.476
You are required to calculate for each project:
(i) Discounted payback period
(ii) Profitability index
(iii) Net present value (PEIINov. 2002) (6 marks)
Answer
(1) Computation of Net Present Values of Projects
Year
Cash flows Discounting Discounted
factor @ 16 % Cash flow
Project A
Project B
Project A
Project B
Rs.
Rs.
Rs.
Rs.
(1)
(2)
(3)
(3) ´ (1)
(3) ´ 2)
0
1,35,000
2,40,000
1.000
1,35,000
2,40,000
1

60,000
0.862

51,720
2
30,000
84,000
0.743
22,290
62,412
3
1,32,000
96,000
0.641
84,612
61,536
4
84,000
1,02,000
0.552
46,368
56,304
5.
84,000
90,000
0.476
39,984
42,840
Net present value 58,254 34,812
(2) Computation of Cumulative Present Values of Projects Cash inflows
Project A
Project B
Year
PV of
cash inflows
Cumulative
PV
PV of Cumulative
cash inflows PV
Rs.
Rs.
Rs.
Rs.
1


51,720
51,720
2
22,290
22,290
62,412
1,14,132
3
84,612
1,06,902
61,536
1,75,668
4
46,368
1,53,270
56,304
2,31,972
5
39,984
1,93,254
42,840
2,74,812
(i) Discounted payback period: (Refer to Working note 2)
Cost of Project A = Rs.1,35,000
Cost of Project B = Rs.2,40,000
Cumulative PV of cash inflows of Project A after 4 years = Rs.1,53,270
Cumulative PV of cash inflows of Project B after 5 years = Rs.2,74,812
A comparison of projects cost with their cumulative PV clearly shows that the project A’s cost will be recovered in less than 4 years and that of project B in less than 5 years. The exact duration of discounted pay back period can be computed as follows:
Project A
Project B
Excess PV of cash inflows over the
18,270
34,812
project cost (Rs.)
(Rs.1,53,270  Rs.1,35,000)
(Rs.2,74,812  Rs.2,40,000)
Computation of period required
0.39 year
0.81 years
to recover excess amount of cumulative PV over project cost
(Rs.18,270 / Rs.46,368)
(Rs.34,812 / Rs.42,840)
(Refer to Working note 2)
Discounted payback period
3.61 year
4.19 years
(4  0.39) years
(5  0.81) years
(ii) Profitability Index: =
(iii) Net present value = Rs.58,254
(for Project A)
(Refer to Working note 1)
Net present value = Rs.34,812
(for Project B)
Question 9
The cash flows of projects C and D are reproduced below:
Cash Flow
NPV
Project
C_{0}
C_{1}
C_{2}
C_{3}
at 10%
IRR
C
 Rs.10,000
+ 2,000
+ 4,000
+ 12,000
+ Rs.4,139
26.5%
D
 Rs.10,000
+ 10,000
+ 3,000
+ 3,000
+ Rs.3,823
37.6%
(i) Why there is a conflict of rankings?
(ii) Why should you recommend project C in spite of lower internal rate of return?
Time
1
2
3
Period
PVIF_{0.10, }t
0.9090
0.8264
0.7513
PVIF_{0.14, }t
0.8772
0.7695
0.6750
PVIF_{0.15,} t
0.8696
0.7561
0.6575
PVIF_{0.30, }t
0.7692
0.5917
0.4552
PVIF_{0.40, }t
0.7143
0.5102
0.3644
(PEIIMay. 2003) (8 marks)
Answer
(i) Net Present Value at different discounting rates
Project
0%
10%
15%
30%
40%
Rs.
Rs.
Rs.
Rs.
Rs.
C
8,000
4,139
2,654
632
2,158
{Rs.2,000
{Rs.2,000 ´ 0.909
{Rs.2,000 ´ 0.8696
{Rs.2,000 ´ 0.7692
{Rs.2,000 ´0.7143
+Rs.4,000
+Rs.4,000 ´ 0.8264
+ Rs.4,000 ´ 0.7561
+ Rs.4,000 ´ 0.5917
+ Rs.4,000 ´ 0.5102
+Rs.12,000
+Rs.12,000 ´ 0.7513
+ Rs.12,000 ´ 0.6575
+Rs.12,000 ´ 0.4552
+ Rs.12,000 ´ 0.3644
Rs.10,000}
Rs.10,000}
 Rs.10,000}
 Rs.10,000}
 Rs.10,000}
Ranking
I
I
II
II
II
D
6,000
3,823
2,937
833
 233
{Rs.10,000
{Rs.10,000 ´ 0.909
{Rs.10,000 ´ 0.8696
{Rs.10,000 ´ 0.7692
{Rs.10,000 ´ 0.7143
+Rs.3,000
+Rs.3,000 ´ 0.8264
+Rs.3,000 ´ 0.7561
+ Rs.3,000 ´ 0.5917
+Rs.3,000 ´ 0.5102
+Rs.3,000
+Rs.3,000 ´ 0.7513
+Rs.3,000 ´ 0.6575
+ Rs.3,000 ´ 0.4552
+Rs.3,000 ´ 0.3644
Rs.10,000}
 Rs.10,000}
 Rs.10,000}
 Rs.10,000}
 Rs.10,000}
Ranking
II
II
I
I
I
The conflict in ranking arises because of skewness in cash flows. In the case of Project C cash flows occur more later in the life and in the case of Project D, cash flows are skewed towards the beginning.
At lower discount rate, project C’s NPV will be higher than that of project D. As the discount rate increases, Project C’s NPV will fall at a faster rate, due to compounding effect.
After break even discount rate, Project D has higher NPV as well as higher IRR.
(ii) If the opportunity cost of funds is 10%, project C should be accepted because the firm’s wealth will increase by Rs.316 (Rs.4,139  Rs.3,823)
The following statement of incremental analysis will substantiate the above point.
Cash Flows (Rs.)
NPV at
IRR
Project
C_{0}
C_{1}
C_{2}
C_{3}
10%
12.5%
Rs.
Rs.
Rs.
Rs.
CD
0
8,000
1,000
9,000
316
0
{8,000 ´ 0.909
{8,000 ´ 0.88884
+1,000 ´ 0.8264
+ 1,000 ´ 0.7898
+ 9,000 ´ 0.7513}
+ 9,000 ´ 0.7019}
Hence, the project C should be accepted, when opportunity cost of funds is 10%.
Question 10
Beta Company Limited is considering replacement of its existing machine by a new machine, which is expected to cost Rs.2,64,000. The new machine will have a life of five years and will yield annual cash revenues of Rs.5,68,750 and incur annual cash expenses of Rs.2,95,750. The estimated salvage value of the new machine is Rs.18,200. The existing machine has a book value of Rs.91,000 and can be sold for Rs.45,500 today.
The existing machine has a remaining useful life of five years. The cash revenues will be Rs.4,55,000 and associated cash expenses will be Rs.3,18,500. The existing machine will have a salvage value of Rs.4,550, at the end of five years.
The Beta Company is in 35% tax bracket, and write off depreciation at 25% on writtendown value method.
The Beta Company has a target debt to value ratio of 15%. The Company in the past has raised debt at 11% and it can raise fresh debt at 10.5%.
Beta Company plans to follow dividend discount model to estimate the cost of equity capital. The Company plans to pay a dividend of Rs.2 per share in the next year. The current market price of Company’s equity share is Rs.20 per equity share. The dividend per equity share of the Company is expected to grow at 8% p.a.
Required:
(i) Compute the incremental cash flows of the replacement decision.
(ii) Compute the weighted average cost of Capital of the Company.
(iii) Find out the net present value of the replacement decision.
(iv) Estimate the discounted payback period of the replacement decision.
(v) Should the Company replace the existing machine ? Advise.
(PEIINov. 2003) (12 marks)
Answer
(i) Incremental Cash Flows Statements of the replacement decision
Descriptttion
0
1
2
3
4
5
Rs.
Rs.
Rs.
Rs.
Rs.
Rs.
(a) Incremental sales (cash)

1,13,750
1,13,750
1,13,750
1,13,750
1,13,750
(b) Incremental cash

Operating cost
(22,750)
(22,750)
(22,750)
(22,750)
(22,750)
Depreciation
 New machine
66,000
49,500
37,125
27,844
20,883
 Old machine
22,750
17,063
12,797
9,598
7,198
(c) Incremental depreciation
43,250
32,437
24,328
18,246
13,685
(d) EBIT (abc)
93,250
1,04,063
1,12,172
1,18,254
1,22,815
(e) Tax 35% of (d)
32,638
36,422
39,260
41,389
42,985
(f) NOPAT : (de)
60,612
67,641
72,912
76,865
79,830
(g) Free operating
1,03,862
1,00,078
97240
95,111
93,515
cash in flows: (f+c)
(h) Capital expenditure
(2,18,500)





(i) Incremental salvage value
13,650
(Rs.18,200  Rs.4,550)
(j) Tax saving incremental
9,591
(On loss of sale of machines
(Rs.44,448Rs.17,045) ´.35%
Incremental cash flows of
the replacement decision
(2,18,500)
1,03,862
1,00,078
97,240
95,111
1,16,756
(ii) Computation of weighted average cost of capital of the company (WACC): K_{e} = + g
= + 8% = 18%
K_{d} = 10.5% * ( 1 0.35) = 6.825%
WACC = K_{d}´
= 6.825% * 15% + 18% ´ 85%
= 16.32% or 16.32375%
(iii) Computation of net present value of the replacement decision:
(ii) Estimation of internal rate of return (IRR) of the Project ‘ P ‘ and ‘ J ‘
Internal rate of return r (IRR) is that rate at which the sum of cash inflows after discounting equals to the discounted cash out flows. The value of r in the case of given projects can be determined by using the following formula:
CO_{o }=_{ }
Where Co = Cash flows at the time O
CF_{t }= Cash inflow at the end of year t
r = Discount rate
n = Life of the project
SV & WC = Salvage value and working capital at the end of n years.
In the case of project ‘P’ the value of r (IRR) is given by the following relation:
40,000 =
r = 19.73%
Similarly we can determine the internal rate of return for the project ‘J’ . In the case of project ‘J’ it comes to:
r = 25.20%
(iii) The conflict between NPV and IRR rule in the case of mutually exclusive project situation arises due to reinvestment rate assumption. NPV rule assumes that intermediate cash flows are reinvested at k and IRR assumes that they are reinvested at r. The assumption of NPV rule is more realistic.
(iv) When there is a conflict in the project choice by using NPV and IRR criterion, we would prefer to use “Equal Annualized Criterion”. According to this criterion the net annual cash inflow in the case of Projects ‘P’ and ‘J’ respectively would be:
Project ‘P’ = (Net present value/ cumulative present value of Re.1 p.a
@ 15% for 6 years)
= (Rs.5,375.65 / 3.7845)
= Rs.1,420.44
Project ‘J’ = (Rs.3807.41/2.2832)
= Rs.1667.58
Since the cash inflow per annum in the case of project ‘J’ is more than that of project ‘P’, so Project J is recommended.
Question 12
(a) PQR Limited has decided to go in for a new model of Mercedes Car. The cost of the vehicle is Rs.40 lakhs. The company has two alternatives:
(i) taking the car on finance lease; or
(ii) borrowing and purchasing the car.
LMN Limited is willing to provide the car on finance lease of PQR Limited for five years at an annual rental of Rs.8.75 lakhs, payable at the end of the year.
The vehicle is expected to have useful life of 5 years, and it will fetch a net salvage value of Rs.10 lakhs at the end of year five. The depreciation rate for tax purpose is 40% on writtendown value basis. The applicable tax rate for the company is 35%. The applicable before tax borrowing rate for the company is 13.8462%.
What is the net advantage of leasing for the PQR Limited?
The values of present value interest factor at different rates of discount are as under:
Â Â
Rate of discount
t_{1}
t_{2}
t_{3}
t_{4}
t_{5}
0.138462
0.8784
0.7715
0.6777
0.5953
0.5229
0.09
0.9174
0.8417
0.7722
0.7084
0.6499
(PEIIMay. 2004) (8 marks)
Answer
Cash flow of lease contract is shown below:
(Rs. in lakhs)
0
1
2
3
4
5
Cost of car
40
Depreciation
16
9.6
5.76
3.456
2.0736
Loss of depreciation
tax shield
(Dep ´ tax rate)
5.6
3.36
2.016
1.2096
0.7258
Lease payment
8.75
8.75
8.75
8.75
8.75
Tax shield on
lease payment
3.0625
3.0625
3.0625
3.0625
3.0625
Loss of salvage value
10
Cash flow of lease
40
11.2875
9.0475
7.7035
6.8971
16.4133
Present value cash flow of lease = Rs.39.47 lakhs
10.3551
7.61528
5.9486
4.8859
10.667
(11.2875
´ 0.9174)
(9.0475
´ 0.8417)
(7.7035
´ 0.7722)
(6.8971
´ 0.7084)
(16.4133
´ 0.6499)
Net Advantage of Leasing (K_{d} = 9%) = Rs.0.53 lakhs (Rs.40 lakhs  Rs.39.47 lakhs)
Question 13
PQR Ltd. is evaluating a proposal to acquire new equipment. The new equipment would cost Rs. 3.5 million and was expected to generate cash inflows of Rs. 4,70,000 a year for nine years. After that point, the equipment would be obsolete and have no significant salvage value. The company’s weighted average cost of capital is 16%.
The management of the PQR Ltd. seemed to be convinced with the merits of the investment but was not sure about the best way to finance it. PQR Ltd. could raise the money by issuing a secured eightyear note at an interest rate of 12%. However, PQR Ltd. had huge taxloss carry forwards from a disastrous foray into foreign exchange options. As a result, the company was unlikely to be in a position of taxpaying for many years. The CEO of PQR Ltd. thought it better to lease the equipment than to buy it. The proposals for lease have been obtained from MGM Leasing Ltd. and Zeta Leasing Ltd. The terms of the lease are as under:
MGM Leasing Ltd.
Zeta Leasing Ltd.
Lease period offered
9 years
7 years
Number of lease rental payments with initial lease payment due on entering the lease contract
10
8
Annual lese rental
Rs. 5,44,300
Rs. 6,19,400
Lease terms equivalent to borrowing cost (Claim of lessor)
11.5% p.a.
11.41% p.a.
Leasing terms proposal coverage
Entire
Entire
Rs. 3.5 million cost of equipment
Rs. 3.5 million cost of equipment
Tax rate
35%
35%
Both the Leasing companies were in a taxpaying position and write off their investment in new equipment using following rate:
Year
1
2
3
4
5
6
Depreciation rate
20%
32%
19.20%
11.52%
11.52%
5.76%
Required:
(i) Calculate the NPV to PQR Ltd. of the two lease proposals.
(ii) Does the new equipment have a positive NPV with (i) ordinary financing, (ii) lease financing ?
(iii) Calculate the NPVs of the leases from the lessors’ view points. Is there a chance that they could offer more attractive terms ?
(iv) Evaluate the terms presented by each of the lessors. (PEIINov. 2004) (16 marks)
Answer
(i) NPV to PQR Ltd of MGM Leasing Ltd lease proposal.
Investment decision: Present value of Operating cash inflows
Present Value at 16% = Rs 4,70,000 ´ 4.6065 = Rs 21,65,055 (A)
Financing decision : Present value of cash outflows
Present value at 12 % = Rs 5,44,300 + Rs 5,44,300 ´ 5.3282
= Rs 34,44,439 (B)
Hence Net Present Value = (A) – (B) =(Rs 12,79,384)
NPV to PQR Ltd of Zeta Leasing Ltd lease proposal.
Investment decision :Present value of Operating cash inflows
Present Value at 16% = Rs 4,70,000 ´ 4.6065 = Rs 21,65,055 (A)
Financing decision : Present value of cash outflows
Present value at 12 % = Rs 6,19,400 + Rs 6,19,400 × 4.5638
= Rs 34,46,218. (B)
Hence Net Present Value = (A) – (B) = (Rs 12,81,163)
(ii) NPV of new equipment with ordinary financing
Investment decision :Present value of Operating cash inflows
Present Value at 16% = Rs 4,70,000 ´ 4.6065 = Rs 21,65,055 (A)
Financing decision : Present value of cash outflows
Rs 35,00,000 (B)
Hence Net Present Value = (A) – (B) = (Rs 13,34,945)
Conclusion : The company has a negative NPV with ordinary financing as well as lease financing.
(iii) NPV to MGM Leasing Ltd.
(Rs, 000)
Year
Equipment cost
Dep’n
Dep’n tax shield
After tax lease payment
After tax CFs
Present value factor at 7.8%
After tax CFs(Present Value)
0
( 3,500)
700
245
353.795
(2,901.21)
1
(2,901.21)
1
1,120
392
353.795
745.795
0.928
692.0978
2
672
235.2
353.795
588.995
0.861
507.1247
3
403.2
141.12
353.795
494.915
0.798
394.9422
4
403.2
141.12
353.795
494.915
0.74
366.2371
5
201.6
70.56
353.795
424.355
0.687
291.5319
6
353.795
353.795
0.637
225.3674
7
353.795
353.795
0.591
209.0928
8
353.795
353.795
0.548
193.8797
9
353.795
353.795
0.509
180.0817
Total
7.299
159.1502
Discount rate = 12% x(1.35) =7.8%
NPV = Rs 159.1502
MGM Lease Ltd’s NPV is positive. They could reduce the lease terms by Rs 1,59,150 divided by cumulative PV factor at 7.8% (7.299) divided by (1 – 0.35) i.e. Rs 33,545.16 to make their proposal more attractive.
NPV to Zeta Leasing Ltd.
(Rs 000)
Year
Equipment cost
Dep’n
Dep’n tax shield
After tax lease payment
After tax CFs
Present value factor at 7.8%
After tax CFs (Present Value)
0
(3,500)
700
245
402.61
(2,852.39)
1
(2852.39)
1
1,120
392
402.61
794.61
0.928
737.3981
2
672
235.2
402.61
637.81
0.861
549.1544
3
403.2
141.12
402.61
543.73
0.798
433.8965
4
403.2
141.12
402.61
543.73
0.74
402.3602
5
201.6
70.56
402.61
473.17
0.687
325.0678
6
402.61
402.61
0.637
256.4626
7
402.61
402.61
0.591
237.9425
6.242
89.8921
NPV (7.8%) = Rs. Rs 89,892
Zeta Ltd could improve the proposal by reducing the lease terms by Rs 89,892 divided by cumulative PV factor at 7.8% (6.242) divided by (1 – 0.35) i.e. Rs 22,155.62 to make their proposal more attractive.
(iv) From PQR Ltd’s point of view the leasing terms offered by MGM Leasing gives the least Net Present Value. PQR Ltd is not getting tax shield on leasing, depreciation and interest because of heavy losses incurred in the earlier years. With proper negotiations , the leasing terms can be reduced marginally.
Question 14
MNP Limited is thinking of replacing its existing machine by a new machine which would cost Rs. 60 lakhs. The company’s current production is Rs. 80,000 units, and is expected to increase to 1,00,000 units, if the new machine is bought. The selling price of the product would remain unchanged at Rs. 200 per unit. The following is the cost of producing one unit of product using both the existing and new machine:
Unit cost (Rs.)
Existing Machine (80,000 units)
New Machine (1,00,000 units)
Difference
Materials
75.0
63.75
(11.25)
Wages & Salaries
51.25
37.50
(13.75)
Supervision
20.0
25.0
5.0
Repairs and Maintenance
11.25
7.50
(3.75)
Power and Fuel
15.50
14.25
(1.25)
Depreciation
0.25
5.0
4.75
Allocated Corporate Overheads
10.0
12.50
2.50
183.25
165.50
(17.75)
The existing machine has an accounting book value of Rs. 1,00,000, and it has been fully depreciated for tax purpose. It is estimated that machine will be useful for 5 years. The supplier of the new machine has offered to accept the old machine for Rs. 2,50,000. However, the market price of old machine today is Rs. 1,50,000 and it is expected to be Rs. 35,000 after 5 years. The new machine has a life of 5 years and a salvage value of Rs., 2,50,000 at the end of its economic life. Assume corporate Income tax rate at 40%, and depreciation is charged on straight line basis for Incometax purposes. Further assume that book profit is treated as ordinary income for tax purpose. The opportunity cost of capital of the Company is 15%.
Required:
(i) Estimate net present value of the replacement decision.
(ii) Estimate the internal rate of return of the replacement decision.
(iii) Should Company go ahead with the replacement decision? Suggest.
Â Â
Year (t)
1
2
3
4
5
PVIF_{0.15,t}
0.8696
0.7561
0.6575
0.5718
0.4972
PVIF_{0.20,t}
0.8333
0.6944
0.5787
0.4823
0.4019
PVIF_{0.25,t}
0.80
0.64
0.512
0.4096
0.3277
PVIF_{0.30,t}
0.7692
0.5917
0.4552
0.3501
0.2693
PVIF_{0.35,t}
0.7407
0.5487
0.4064
0.3011
0.2230
(PEIINov. 2005) (8+3+1=12marks)
Answer
(i) Net Cash Outlay of New Machine
Purchase Price Rs. 60,00,000
Less: Exchange value of old machine
[2, 50,000 0.4(2,50,0000)] 1,50,000
Rs. 58,50,000
Market Value of Old Machine: The old machine could be sold for Rs. 1,50,000 in the market. Since the exchange value is more than the market value, this option is not attractive. This opportunity will be lost whether the old machine is retained or replaced. Thus, on incremental basis, it has no impact.
Depreciation base: Old machine has been fully depreciated for tax purpose.
Thus the depreciation base of the new machine will be its original cost i.e. Rs. 60,00,000.
Net Cash Flows: Unit cost includes depreciation and allocated overheads. Allocated overheads are allocations from corporate office therefore they are irrelevant. The depreciation tax shield may be computed separately. Excluding depreciation and allocated overheads, unit costs can be calculated. The company will obtain additional revenue from additional 20,000 units sold.
Thus, aftertax saving, excluding depreciation, tax shield, would be
After adjusting depreciation tax shield and salvage value, net cash flows and net present value is estimated.
Calculation of Cash flows and Project Profitability
Rs. (‘000)
0
1
2
3
4
5
1
Aftertax savings

1824
1824
1824
1824
1824
2
Depreciation (Rs. 60,00,000 – 2,50,000)/5

1150
1150
1150
1150
1150
3
Tax shield on depreciation (Depreciation × Tax rate )

460
460
460
460
460
4
Net cash flows from operations (1+3)

2284
2284
2284
2284
2284
5
Initial cost
(5850)
6
Net Salvage Value
(2,50,000 – 35,000)





215
7
Net Cash Flows
(4+5+6)
(5850)
2284
2284
2284
2284
2499
8
PVF at 15%
1.00
0.8696
0.7561
0.6575
0.5718
0.4972
9
PV
(5850)
1986.166
1726.932
1501.73
1305.99
1242.50
10
NPV
Rs. 1913.32
(ii)
Â Â
Rs. (‘000)
0
1
2
3
4
5
NCF
(5850)
2284
2284
2284
2284
2499
PVF at 20%
1.00
0.8333
0.6944
0.5787
0.4823
0.4019
PV
(5850)
1903.257
1586.01
1321.751
1101.57
1004.35
PV of benefits
6916.94
PVF at 30%
1.00
0.7692
0.5917
0.4550
0.3501
0.2693
PV
(5850)
1756.85
1351.44
1039.22
799.63
672.98
PV of benefits
5620.12
IRR = 20% + 10% ×
= 28.23%
(iii) Advise: The company should go ahead with replacement project, since it is positive NPV decision.
Question 15
A Company is considering a proposal of installing a drying equipment. The equipment would involve a Cash outlay of Rs. 6,00,000 and net Working Capital of Rs. 80,000. The expected life of the project is 5 years without any salvage value. Assume that the company is allowed to charge depreciation on straightline basis for Incometax purpose. The estimated beforetax cash inflows are given below:
Beforetax Cash inflows (Rs. ‘000)
Year
1
2
3
4
5
240
275
210
180
160
The applicable Incometax rate to the Company is 35%. If the Company’s opportunity Cost of Capital is 12%, calculate the equipment’s discounted payback period, payback period, net present value and internal rate of return.