capital expenditure decision

FINANCIAL PATHTHE PACIFIC INSTITUTE OF FINANCIAL STUDIES & RESEARCH

Capital Expenditure Decision

Evaluation Criteria

Discounting Techniques: Non Discounting Techniques:

a) Net present value (NPV) a) Pay back period b) Benefit cost ratio (BCR) OR b) Accounting rate of Return

Profitability index (PI) c) Net benefit cost ratio (NBCR) d) Internal rate of return (IRR)e) Annual capital charge (ACC)

Formulaes:

a) Net present value:- Total PV of cash inflow –Investment Decision criteria:- If NPV is +ve than accept it or vice versa.

b) Benefit cost ratio:- Total PV of cash inflow / InvestmentDecision criteria:- If BCR > 1, accept it or vice versa.

c) Net benefit cash ratio:- (Total PV of cash inflow – Investment) / Investment.OR BCR – 1OR NPV / InvestmentDecision criteria:- If NBCR > 0, than accept it or vice versa.

d) Internal rate of return:- L1 + (L2 – L1) × (H – B) (H – S) If NPV = 0 than use this formulae.Where :-L1=Lower Rate.

L2=Higher Rate.H=highest Value.S=Smallest Value.B=Base Value.

e) Annual capital charge: Investment + total PV of cost / PVIFA (kd,n)

f) Pay back period: Total Investment / Cash Inflow per annum

g) Accounting rate of return: Average annual income / Average InvestmentWhere:Average Investment = (Opening investment + Closing investment) / 2OR Investment /2

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Cash Inflow: = (Increase in profit + Decrease in Cost – Increase in depreciation) × (1-t) + Increase in depreciation + Increase in scrap value.

Scrap value : used in final year cash flow.

Increase in depreciation: Depreciation on new machine – Depreciation on old machine.

Some Numerical Questions Based on Above Formulas

Q1.Zoya Limited is considering 4 projects – A, B, C and D with the following characteristics:Projects Initial Investment Annual net Cash Flow

(Year 1 to 5)A (20) 8.5B (4.5) 2.5C (7) 3.5D (8) 4.5The funds available are limited to Rs.20 lakh and the cost of funds to the firm is 14%. According to Benefit Cost Ratio (BCR), the rank of the projects are(a) A, B, C and D(b) A, D, C and B(c) B, C, A and D(d) C, B, A and D(e) D, B, C and A.

Q2.Anil Enterprises Limited (AEL) has placed two orders to Sunil Enterprises limited (SEL) in order to purchase machines from them. Each machine is sold at a price of Rs.5,00,000 at a profit margin of 20%. It is estimated that the probability of default is 10% for the first order and 5% for the second order. What is the expected profit to SEL from granting the second credit to AEL, assuming that the first order has been paid?(a) Rs.67,500(b) Rs.75,000(c) Rs.85,000(d) Rs.90,000(e) Rs.95,000.

Q3.Calculate the Accounting Rate of Return (ARR) from the following table:Year 0 1 2 3Investment-------------------------- (1,00,000)Sales Revenue-----------------------------------------1,30,000 1,00,000 90,000Operating expenses(excluding depreciation)--------------------------- 64,000 50,000 50,000Depreciation------------------------------------------ 30,000 40,000 20,000Annual income--------------------------------------- 36,000 10,000 20,000




(a) 44%(b) 45%(c) 50%(d) 54%(e) 55%.

Q4.Visual Printers Ltd. (VPL) currently uses a machine, whose book value is Rs.12 lakh with the remaining useful life of 5 years and a salvage value of Rs.2 lakh at the end of the useful life. VPL is proposing to replace the machine by a new machine costing Rs.20 lakh and has a useful life of 5 years and salvage value of Rs.4 lakh at the end of 5 years. The new machine is expected to reduce the annual operating costs by Rs.0.5 lakh and increase the annual income by Rs.1 lakh. The old machine, if sold now, can realise Rs.9 lakh. EPL follows straight-line method of depreciation and is in the tax bracket of 40%. The net incremental cash flows of the new machine during year 0 and year 5 respectively are(a) –Rs.20 lakh, Rs.3.38 lakh(b) –Rs.11 lakh, Rs.3.38 lakh(c) –Rs.11 lakh, Rs.4.10 lakh(d) –Rs.20 lakh, Rs.2.10 lakh(e) –Rs.11 lakh, Rs.2.10 lakh

Q5.The minimum cash flow that must be received at the end of year three, with an initial investment of Rs.40,000 with cash flows for the first and second year of Rs.13,000 each and an opportunity cost of capital of 12.5%, is(a) Rs.18,173(b) Rs.18,275(c) Rs.19,284(d) Rs.25,875(e) Rs.30,565

Q6.If the cost of an investment is Rs.25,000 and it results in a net cash inflow of Rs.1,800 per annum forever. Assuming that the discount rate is 8%, the net benefit cost ratio of that investment is(a) – 0.11(b) – 0.10(c) – 0.09(d) 0.10(e) 0.11

Q7. Bhagerrata construction corporation uses pay back period for the appraisal projects. What is the pay back period of the projects with the following expected cash flows?

(a) 3.0 years


Year Cash flows(Rs)

0 (2,00,000)1 80,0002 70,0003 30,0004 40,0005 60,000



(b) 3.5 years(c) 4.1 years(d) 3.8 years(e) 5.0 years

Q8. Based on the following data:Year 0 1 2 3

(Investment) (4,00,000)Annual income - 40,000 50,000 30,000

The accounting rate of return is (Assume no salvage value after 3years)a) 10%b) 20%c) 30%d) 40%e) 50%

Q9. A project has an initial cash outflow of Rs 5,00,000 and another outflow of Rs. 2,00,000 at the end of 3rd year. What is the Net Present Value(NPV) of the project with the following cash inflows considering discount rate as 20%? (correct to nearest hundred)

Year 1 2 3 4 5Cash

flows(Rs)2,00,000 3,50,000 3,00,000 2,50,000 2,00,000

a) –Rs 84,300b) Rs 84,300c) Rs 1,68,500d) Rs 6,00,000e) Rs 8,00,000

Q10. Navayuga Pharmaceuticals Ltd, is evaluating system which is expected to have an economic life of six years. The initial outlay and annual operating associated with this system are as follows:

Year 0 1 2 3 4 5 6Costs 15,00,000 1,00,000 1,10,000 1,25,000 1,10,000 1,30,000 2,00,000

If the cost of capital is 12% the annual capital charge associated with the system isa) Rs 3,87,000b) Rs 4,45,400c) Rs 4,89,200d) Rs 5,03,500e) Rs 5,84,600

Q11. Mahavir Engineering Ltd. (MEL) currently uses a machine whose book value is Rs 12lakh and has a remaining useful life of 5years and a salvage value of Rs 2 lakh at the end of useful life. MEL is proposing to replace the machine by a new machine costing Rs 20 lakh and has a useful life of 5 years and salvage value of Rs 4 lakh at the end of 5 years. The new machine is expected to reduce the annual operating costs by Rs 50,000 and increase the annual income by




Rs 1,00,000. The old machine can be sold at Rs 9 lakh. MEL uses straight line depreciation and is in tax bracket of 40%.The net incremental cash flow in the 1st year is:

a) Rs. 0.90 lakhb) Rs. 1.38 lakhc) Rs. 1.50 lakhd) Rs. 3.38 lakhe) Rs. 4.10 lakh

Q12. If the cost of an investment is Rs 2 lakh and it pays Rs 17,500 in perpetuity at an interest rate of 8% p.a., the benefit cost ratio of the investment is

a) -1.29b) -0.09c) 0.70d) 1.09e) 1.22

Q13. Labour Motors Services is considering the purchase of a new bus which requires a cash outlay of Rs. 25,00,000 and has an economic life of five years. If the company provides depreciation of 20% on written down value method, the book value of the asset at the end of 5 th

year isa) Rs. 8.19 lakhb) Rs.10.24 lakhc) Rs.12.80 lakhd) Rs.16.00 lakhe) Rs.16.35 lakh

Q14. M/s Priya Garments and Exports is considering to buy a new piece of equipment, which is expected to cost Rs 4,00,000 and will produce cash flows for the next 6 years (the first cash flow will be exactly one year from today). If the company is able to invest in an upgrade which would cost Rs. 1,20,000 in year 3, it would increase the annual cash flows from 4 th year onwards to Rs.2,00,000. If the discount rate appropriate for the company is 15%, the NPV of the investment is approximately.

a) Rs. 28,765b) Rs. 36,674c) Rs. 45,295d) Rs. 49,672e) Rs. 52,605

Q15. The finance manager of Kargil Engineering Ltd, is analyzing a project with a life of 5 years, which requires an initial investment in equipment and machinery of Rs 80 lakh. The equipment is expected to have a 5-year lifetime and have no salvage value which is to be depreciated on straight line basis. The project is expected to generate revenues of Rs 40 lakh each year for the 5 years and have operating expenses (not including depreciation) amounting to 30% of revenues. The tax rate is 40%. What is the Internal Rate of Return (IRR) of the project?




a) 13.82%b) 13.94%c) 14.16%d) 15.25%e) 18.00%

Q16. Based on the following data of a project:

And the cost of capital is 10%, the discounted payback period is:a) 2.34 yearsb) 2.71 yearsc) 3.15 yearsd) 3.82 yearse) 4.46 years

Q17. Palaniappa Tools & Spares Ltd., is planning to purchase a purchasing machine with the following features:Cost of machine Rs, 3,00,000Annual cost of operations Rs, 2,50,000 for the first four years Rs, 3,00,000 for the subsequent yearsUseful life 10 yearsThe annual capital charge of the machine, if cost of capital is 10 percent, is

a) Rs. 5,06,236b) Rs. 6,54,558c) Rs. 7,62,382d) Rs. 8,29,780e) Rs. 9,42,732

ANSWERS OF THE QUESTION

1- Ans. (e) The NPV of the 4 projects are:Project Present value of future BCR(PV/I) RANK


Year Cash flow (Rs)0 (1,42,000)1 50,0002 65,0003 80,0004 90,0005 92,000



Cash flows (Rs.in lakh)A 8.5 PVIFA(14%,5)=29.18 29.18/20=1.459 IB 2.5 PVIFA(14%,5)=8.583 8.583/4.5=1.907 IIC 3.5 PVIFA(14%,5)=12.016 12.016/7=1.717 IIID 4.5 PVIFA(14%,5)=15.449 15.449/8=1.931 IV

2- Ans. (a) The expected profit from granting the second credit to AEL, assuming the payment for the first order has been made by AEL ,is0.90{0.95 × 100000 - 0.05 × 400000} = Rs.67,500

3- Ans (a) Accounting rate of Return = Average profit after tax/average book value of investmentAverage annual income =36,000+10,000+20, 000

3= 22,000

Average net book value of investment = (1,00,000+0) ÷ 2 = 50,000Accounting Rate of return = (22,000÷50,000 ) × 100=44%.

4- Ans (b)Net incremental cash flow during year 0 is= - (Investment for new machine – Present realizable value of old machine)= - (20 - 9) = -Rs 11 lakhNet incremental cash flow during year 5 is= Incremental PAT + Incremental Depreciation + Incremental Scrape realizable value.Depreciation of old machine = (12 – 2) / 5 = Rs 2,00,000Depreciation of old machine = (20 – 4) / 5 = Rs 3,20,000Incremental depreciation = Rs 3,20,000 – 2,00,000 = Rs 1,20,000.Net incremental cash flow during year 5= (50,000 + 1,00,000 – 1,20,000) (1-0.4) + 1,20,000 + 2,00,000 = Rs 3,38,000

5- Ans (d) 40,000 = 13,000÷(1.125)1 + 13,000÷(1.125)2 + X ÷ (1.125)3

or, 40,000 = 11,555.55+ 10,271.60 + X÷(1.125)3

or, X÷(1.125)3= 18,172.84or, X = 18,172.84 x(1.125)3

= Rs. 25,875.00

6- Ans (b)

The present value of cash flow will be = Rs .18000.08

=Rs .22,500

NPV of that investment = Rs. 22,500 – Rs. 25,000 = - Rs 2500.




Hence, the net profit cost ratio for that investment = −Rs.2500Rs25000

=−0.1

7- Ans (b)Initial outlay = Rs.2,00,000Amount receivables in 3 years = 80000 + 70000 + 30000 = 1,80,000.Hence, the number of years required to recover the initial outlay will be = 3years + (2,20,000 – 2,00,000) ÷ 40,000 = 3.5 yrs.Hence, answer is 3.5 years.

8- Ans (b)Average annual income for 3 years = (50,000 + 40,000 + 30,000) ÷ 3= Rs. 40,000Average net book value of investments = (4,00,000 + 0) ÷ 2 = Rs 2,00,000Accounting rate of return = (40,000 ÷ 2,00,000) ×100 = 20%

9- Ans (c)Present value of cash outflows = 5,00,000 + (2,00,000 × PVIF20%, 3 yrs) = Rs.6,15,741Present value of cash inflows = (2,00,000× PVIF20%, 1 yrs) + (3,50,000× PVIF20%, 2 yrs) + (3,00,000× PVIF20%, 3 yrs) + (2,50,000×PVIF20%, 4 yrs) + (2,00,000× PVIF20%, 5 yrs) = Rs.7,84,265NPV = Total Present Value of Cash inflow – Total InvestmentRs.7,84,265 – Rs.6,15,741 = Rs 1,68,524

10- Ans (c)

Annual capital charge = Cost+Total PV o f Cost

PVIFAPV of costs associated with the system = (1,00,000× PVIF12%,1yrs) + (1,10,000× PVIF12%,2yrs) + (1,25,000× PVIF12%,3yrs) + (1,10,000×PVIF12%,4yrs) + (1,30,000× PVIF12%,5yrs) + (2,00,000× PVIF12%,6yrs) =

Annual capital charge =Cost+PV of AnnualCost

PVIFA = 4,89,200.

11- Ans (b)Net incremental cash flow during year 0 is = -(Investment for new machine – present realizable value of old machine)= -(20 – 9) = -11 lakhs.Net incremental cash flow during year 5 is:= Incremental PAT + Incremental Depreciation + Incremental realizable value Depreciation of old machine = (12,00,000 – 2,00,000) ÷ 5 = Rs.2,00,000 Depreciation of new machine = (20,00,000 – 4,00,000) ÷ 5 = Rs.3,20,000 Incremental depreciation = Rs 3,20,000 – 2,00,000 = Rs 1,20,000 Net incremental cash flow during year= (50,000 + 1,00,000 – 1,20,000) ×(1 - 0.4) + 1,20,000 = Rs.1,38,000 = 1.38 lakh.

12- Ans (d)Present value of cost = Rs 2,00,000Present value of Perpetuity = Rs.17,500 ÷ .08 = Rs 2,18,750




BCR = Total Present Value of Benefit ÷ Investment = Rs.2,18,750 ÷ 2,00,000 = 1.09

13- Ans (a)Year Book value of

asset (Rs)Depreciation

(Rs)Remaining

book value (Rs)1 25,00,000 5,00,000 20,00,0002 20,00,000 4,00,000 16,00,0003 16,00,000 3,20,000 12,80,0004 12,80,000 2,56,000 10,24,0005 10,24,000 2,04,800 8,19,000

14- Ans (d)In the scenario given, the cash flow would look like this:

YEAR 0 1 2 3 4 5 6Out Flow -4L - - -1.2 - - -In flow 1L 1L 1L 2L 2L 2L

Total Out Flow = - 4L - (1.2L ×PVIF15%,3Yrs) = -4.789LTotal Inflow = (1L ×PVIFA15%,3Yrs) + 2L ×(PVIFA15%,6Yrs - PVIFA15%,3Yrs) = 5.285LNPV = Total Inflow – Total Out flow = 5.285L – 4.789L = Rs 49,672

15- Ans (a)Year 0 Year (1-5)

Rs (lakh)Initial invsestment 80Revenue 40Operating expenses 12Depreciation (80/5) 16Earning before tax 12Tax @ 40% 4.8Profit after tax 7.2Operating cash flow = PAT + Depreciation

23.2

80 = 23.8 × PVIFA(k,5yrs)

K = 13% RHS = 23.2 × 3.517 = 81,59,440K = 14% RHS = 23.2 × 3.433 = 79,64,560By Interpolation Method.

13 %+ (14 %−13 % )× (81,59,440 – 80,00,000 )(81,59,440– 79,64,560 )

=13.8181∨13.82 %

16- Ans (b)Calculation of discounted payback period:

Year Cash PVIF @ Present value




flows(Rs.) 10% cash flows1 50,000 0.909 45,4502 65,000 0.826 53,6903 80,000 0.751 60,0804 90,000 0.683 61,4705 92,000 0.621 57,132

Sum of first two year is = 45,450 + 53,690 = Rs.99,1401,42,000 – 99,140 = 42,860 =2 + (1,42,000 – 99,140) ÷60,080 = 2.71Discounted payback period is 2.71 years.

17- Ans (c)Present value of the costs associated with the machine will beRs.30,00,000 + Rs.2,50,000 * PVIFA(10%,4years) + Rs.3,00,000 * PVIFA(10%,6years) * PVIF(10%,4years)= Rs.30,00,000 + Rs.2,50,000 * 3.170 + Rs.3,00,000 * 4.355 * 0.683= Rs.46,84,839.50The required annual capital charge will be = ( Cost + Total PV of Annual Cost ) ÷ PVIFA(10%,10years) = Rs.7,62,382(approx).



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