CA IPC ASSIGNMENT CAPITAL BUDGETING & TIME VALUE OF MONEY

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1 CA IPC ASSIGNMENT CAPITAL BUDGETING & TIME VALUE OF MONEY MM: 60 Marks Question No. 1: A Limited is a leading manufacturer of automotive component. It supplies the original equipment to manufacturers as well as the replacement market. Its projects typically have a short life as it introduces new models periodically. You have recently joined A Limited as a financial analyst reporting to Abhishek, the CFO of the company. He has provided you the following information about three projects A, B and C that are being considered by the Executive Committee of A Limited: Project A is an extension of an existing line. Its cash flow will decrease over time. Project B involves a new product. Building its market will take some time and hence its cash flow will increase over time. Project C is concerned with sponsoring a pavilion at a Trade Fair. It will entail a cost initially which will be followed by a huge benefit for one year. However, in the year following that a substantial cost will be incurred to raze the pavilion. The expected net cash flows of the three projects are as follows: Year Project A Project B Project C 0 (15,000) (15,000) (15,000) 1 11,000 3,500 42, ,000 8,000 (4,000) 3 4,800 13, Abhishek believes that all the three projects have risk characteristics similar to the average risk of the firm and hence the firm s cost of capital, viz. 12 percent, will apply to them. You are asked to evaluate the projects. (a) Find the payback periods and the discounted payback periods of Projects A and B. (b) Calculate the NPVs of projects A, B and C. (c) Calculate the IRRs for Projects A, B and C. (d) Calculate the MIRRs for Projects A, B and C assuming that the intermediate cash flows can be reinvested at 12 percent rate of return. (15 Marks) Solution: Computation of P.V.C.I Project A Project B Project C Time PV of ` 12% Inflow flows P.V of P.V.C.I flows P.V of P.V.C.I P.V of ,000 11,000 9,823 9,823 3,500 3,500 3,126 3,126 42,000 37, ,000 18,000 5,579 15,402 8,000 11,500 6,376 9,502 (4,000) (3,188) ,800 22,800 3,418 18,820 13,000 24,500 9,256 18, P.V.C.I 18,820 18,758 34,318 (a) Payback Period = 1 year + 4,000 x 1 year = 1.57 years (Project A) 7,000 Payback Period = 2 years + 3,500 x 1 year = 2.27 years (Project B) 13,000 Discounted Payback Period = 1 year + 5,177 x 1 year = 1.93 years (Project A) 5,579 Discounted Payback Period = 2 years + 5,498 = 2.59 years (Project B) 9,256 (b) Calculation of NPV(`) Particulars A B C P.V.C.I 18,820 18,758 34,318 Less: P.V.C.O (15,000) (15,000) (15,000) NPV 3,820 3,758 19,318 (c) Determination of IRR (Project A) PV factor Total PV (`) Year CFAT (0.25) (0.30) (0.25) (0.30) 1 11, ,800 8, , ,480 4, , ,458 2,184 Total PV 15,738 14,787 Less: Initial outlay (15,000) (15,000)

2 NPV 738 (213) The IRR is between 25 and 30%. By interpolation, IRR = 28.89%. Determination of IRR (Project B) PV factor Total PV (`) Year CFAT (0.20) (0.30) (0.20) (0.30) 1 3, ,916 2, , ,552 4, , ,527 5,915 Total PV 15,995 13,343 Less: Initial outlay (15,000) (15,000) NPV 995 (1,657) The IRR is between 20 and 30 per cent. By interpolation, IRR = per cent. Determination of IRR (Project C) PV factor Total PV (`) Year CFAT (1.50) (2.00) (1.500) (2.00) 1 42, ,800 13,986 2 (4,000) (640) (444) Total PV 16,160 13,542 Less: Initial outlay (15,000) (15,000) NPV 1,160 (1,458) The IRR is between 150 and 200 per cent. By interpolation, IRR = 172 per cent. (d) Computation of MIRR Terminal Value (A) = 11,000 (1.12) 2 + 7,000 x (1.12) 1 + 4,800 = `26,438 PVF of Re1 at the end of 3 years = 15,000 = ,438 Looking in table A & interpolating we get MIRR = 20.82%. Terminal Value (B) = 3,500 (1.12) 2 + 8,000 x (1.12) ,000 = `26,350 PVF of Re1 at the end of 3 years = 15,000 = ,350 Looking in table A & interpolating we get MIRR = 20.68%. Terminal Value (C) = 42,000 (1.12) 2 + (-4,000) x (1.12) 1 = `48,205 PVF of Re1 at the end of 3 years = 15,000 = ,205 Looking in table A & interpolating we get MIRR = 47.56%. Question No. 2: In the manufacture of a company s range of products, the processes gives rise to two main types of waste material. Type A is the outcome of the company s original process. This wastage is sold at `2 per tonne, but this amount is treated as sundry income and no allowance for this is made in calculating product costs. Type B is the outcome of newer process in the company s manufacturing activity. It is classified as hazardous, has needed one employee costing `9,000 per year specially employed to organise its handling in the factory, and has required special containers whose current resale value is assessed at `18,000. At present the company pays a contractor `14 per tonne for its collection and disposal. Company management has been concerned with both types of waste and after much research has developed the following proposals. Type A waste This could be further processed by installing plant and equipment costing `20,000 and incurring extra direct costs of `2.50 per tonne and extra fixed costs of `10,000 per annum. Extra space would be needed, but this could be obtained by taking up some of the space currently used as a free car park for employees. The apportioned rental cost of that land is `2,500 per annum and a compensation payment totaling `500 per annum would need to be paid to those employees who would lose their car parking facilities. The selling of the processed waste would be `12.50 per tonne and the quantity available would be 2,000 tonnes per annum. Type B waste Using brand new technology, this could be further processed into a non hazardous product by installing a plant costing `1,20,000 on existing factory space whose apportioned rental cost is `12,500 per annum. This plant cost includes a pipeline that would eliminate any special handling of the hazardous waste. Extra direct would be `13.50 per tonne and extra fixed cost of `20,000 per annum would be incurred.

3 This new product would be saleable to a limited number of customers only, but the company has been able to get the option of a contract for two years sales renewable for a further two years. This would be at price of `11 per tonne and the output over the next few years is expected to be 4,000 tonnes per year. For Type A waste project, the board wants to achieve an 8% DCF return over four years. For Type B waste project, it wants a 15% DCF return over six years. You are required to recommend whether the company should invest in either or both of the two projects. Give supporting figures and comments. Ignore taxation. P.V. of an annuity for four 8% is 3.31 and P.V. of an annuity for six 15% is (10 Marks) Solution: Type A Waste Selling Price per tonne after further processing Less: Loss of Selling Price before further processing (per tonne) (2.00) Less: Extra direct cost per tonne (2.50) Additional Contribution per tonne from further processing 8.00 Sale Quantity 2,000 tonnes Annual Additional Contribution Earned `16,000 Less: Extra Fixed Cost (`10,000) Less: Opportunity Cost of Space (compensation to employee) (`500) Net Annual `5,500 P.V.F (8%, 4) 3.31 P.V. of `18,205 P.V of Outflows (Cost of Installing Plant) (`20,000) NPV (`1,795) Advise: Reject the Proposal. Type B Waste Cost of New Plant for Further Processing of type B waste `1,20,000 Less: Scrap of Containers (Scrap Value) (`18,000) P.V of Outflow `1,02,000 Selling Price per tonne `11.00 Add: Saving in disposal cost `14.00 Less: Extra Direct Cost per tonne (`13.50) Contribution per tonne from further processing `11.50 Annual Quantity 4,000 tonnes Contribution `46,000 Less: Extra Fixed Cost (`20,000) Add: Saving in Employees Salary `9,000 Annual Net `35,000 P.V.F. (6.15%) 3.78 P.V of `1,32,300 Less: P.V of Outflows (`1,02,000) NPV `30,300 Question No. 3: (I) Finmin Limited offers a fixed deposit scheme whereby `20,000 matures to `25,250 after two years on a half yearly compounding basis. If the company desires to amend the scheme by compounding interest every quarter, you are required to determine the revised maturity value? (II) You have to pay tuition fees amounting to `12,000 a year at the end of each of the next six years. If the interest rate is 8 percent, how much do you need to set aside today to cover these fees? (4 Marks) Solution: (I) Computation of Revised Maturity Value FVn = PV (1 + r) n Where, Future Value (FVn) = `25,250 Present Value (PV) = `20,000 r = rate of interest half yearly n = 2 years on half yearly basis i.e., 2 x 2 = 4 25,250 = 20,000 (1 + r) 4 (1 + r) 4 =

4 1 + r = 1.06 r = 0.06 i.e., 6% rate half yearly and 12% rate yearly. 2 x 4 If compounded quarterly, revised maturity value = 20, x = 20,000 (1.03) 8 = `25,335.4 (II) The present value of `1 a year for 6 years at 8% is Therefore, you need to set aside 12,000 x = `55,476. Question No. 4. Mr. X wish to get her daughter admitted into a medical college after 15 years from now. He will be required total ` 25,00,000 to get admission into the college. For this he has identified a fund, which pays 9% p.a. In this regard he wanted to know the amount to be invested in each of the following situations: (a) If he decides to make annual payment into the fund at the end of each year; (b) If he decides to invest a lump sum in the fund at the end of the year; (c) If he decides to make annual payment into the fund at the beginning of each year. (6 marks) (FVIF/ CVF (15, 0.09) = 3.642, FVIFA/ CVFA (15, 0.09) = , PVIF/ PVF (15, 0.09) = and PVIFA/ PVFA (15, 0.09) = 8.061). Solution(a) To get `25,00,000 after 15 years from now, Mr. X needs to deposit an amount at the end of each year, which gets p.a. for 15 years to become an amount to `25,00,000. This can be calculated as follows: Future Value = Annual Payment (FVIFA n, r) or Annual Payment (1 + r) n -1 r Future Value = `25,00,000 Rate of interest (r) = 9% p.a. Period (n) = 15 years `25,00,000 = A (FVIFA 15, 0.09 ) `25,00,000 = A ( ) Or, A = `25,00,000 = `85, p.a (b) To get `25,00,000 after 15 years from now, Mr. X needs to deposit a lump sum payment to the fund which gets p.a. for 15 years to become an amount to `25,00,000. This can be calculated as follows Future Value = Amount (FVIF 15, 0.09 ) or Amount ( ) 15 Or, Amount = `25,00,000 = `6,86, (c) To get `25,00,000 after 15 years from now, Mr. X needs to deposit an amount at the beginning of each year which gets p.a. for 15 years to become an amount to `25,00,000. This can be calculated as follows: Future Value = Annual Payment (FVIFA n, r ) (1 + r) `25,00,000 = A (FVIFA 15, 0.09 ) 1.09 `25,00,000 = A ( ) Or, A = `25,00,000 = `78, p.a Question No. 5: An educational institute is planning to install airconditioners for its new computer centre. It has received proposals from 2 manufacturers. The first proposal is for the installation of 6 window `25,000 each. The other is for the installation of split airconditioners of an equal capacity costing `2,00,000. The useful life of window airconditioners is 6 years and that of split airconditioners is 10 years. The cash operating costs associated with each proposal are given below: Year Proposal 1 Proposal 2 1 `20,000 `18, ,000 18, ,000 18, ,000 22, ,000 22, ,000 22, , , , ,000 The salvage value of the window airconditioners at the end of 6 years is expected to be `10,000 and that of the split airconditioners `15,000. Advise the educational institute which proposal should be selected by it if its opportunity cost of funds is 10%. (7 Marks)

5 Solution: Computation of Equivalent Annual Cost (Proposal 1) Particulars Year PV factor (at 10%) Cost (`) PV (`) Purchase cost ,50,000 1,50,000 Operating costs ,000 18, ,000 16, ,000 15, ,000 17, ,000 15, ,000 14,100 Salvage value (10,000) (5,640) Total PV of Outflows 2,40,780 Equivalent Annual PVCO = Total present value of Outflows PV of annuity corresponding to the life of the project at the given cost of capital = `2,40,780/4.355 = `55, (Proposal 2) Particulars Year PV factor (at 10%) Cost(`) PV(`) Purchase cost ,00,000 2,00,000 Operating costs ,000 16, ,000 14, ,000 13, ,000 15, ,000 13, ,000 12, ,000 13, ,000 12, ,000 11, ,000 10,036 Salvage value (15,000) (5,790) Total PV 3,26,594 Equivalent Annual PVCO = `3,26,594/6.145 = `53,148 Advise: Select proposal 2. Question No. 6: Mr. Shanker, an executive in an MNC, is thirty-five years old. He has decided it is time to plan seriously for his retirement. At the end of each per year until he is sixty-five, he will save `10,000 in a retirement account. If the account earns 10 percent per year, how much will Mr. Shanker have saved at the age of sixty-five? (4 Marks) Solution: Computation of Savings of Mr. Shanker Mr. Shanker s savings plan looks like an annuity of `10,000 per year for 30 years. FV = `10,000 x 1 x ( ) 0.10 = `10,000 x = `16,44,940 Question No. 7:Alpha Limited has borrowed `1,000 to be repaid in equal installments at the end of each of the next 3 years. The interest rate is 15 per cent. You are required to prepare an amortisation schedule for Alpha Limited. (4 Marks) Solution: Preparation of Amortisation Schedule Amount of Equal Instalment (A) A = Pn = `1,000 = ` PVIFAi,n

6 Amortisation Schedule Year Payment Interest* Repayment of Principal Balance Outstanding Amount in (`) Amount in (`) Amount in (`) Amount in (`) * = Loan balance at the beginning of the year x interest rate, e.g., year 1 = (`1,000 x 0.15) = `150 Question No. 8: A company is reviewing an investment proposal in a project involving a capital outlay of `90, 00, 000 in plant and machinery. The project would have a life of 5 year at the end of which the plant and machinery could fetch a resale value of `30,00,000. Further the project would also need a working capital of `12, 50, 000, which would be built during the year 1 and to be released from the project at the end of year 5. The project is expected to yield to following cash profits: Year profit (`) 1 35,00, ,00, ,00, ,00, ,00,000 A 25% depreciation for plant and machinery is available on WDV basis as Income Tax exemption. Assume that the Corporate Tax is paid one year in arrear of the periods to which it relates and the first year s depreciation allowance would be claimed against the profits of year 1. The Assistant Management Accountant has calculated NPV of the project using the company s corporate target of 20% pre tax rate of return and has ignored the taxation effect in the cash flows. As the newly recruited Management Accountant, you realise that the project s cash flows should incorporate the effects of tax. The Corporate tax is expected to be 35% during the life of the project and thus the company s rate of return post tax is 13% (65% of 20%). Your Assistant is surprised to note that the difference between discounting the pre tax cash flows at a pre tax DCF rate and post tax cash flows at a post tax rate. Required: (a) Calculate the NPV of the project as the Assistant Management Accountant would have calculated it; (b) Re calculate the NPV of the project taking tax into consideration; (c) Comment on the desirability of the project vis a vis your findings in (b). (10 marks) Solution: Statement showing computation of NPV (ignoring taxation) Particulars Year PV factor (at 10%) Amount (`) PV(`) outflows Cost of Plant & machinery ,00,000 90,00,000 Add: WC outflows ,50,000 10,41,625 P.V.C.O 1,00,41,625 inflows Annual CFBT ,00,000 29,16, ,00,000 20,83, ,00,000 14,46, ,00,000 9,64, ,00,000 8,03,800 Terminal Value (Plant & machinery & WC) , ,08,075 P.V.C.I 99,22,975 NPV (1,18,650) Computation of PVCI Particulars Annual CFBT (1) Less: Annual Depreciation 35,00,000 (22,50,000) 30,00,000 (16,87,500) 25,00,000 (12,65,625) 20,00,000 (9,49,219) 20,00,000 (7,11,914) Annual PBT 12,50,000 13,12,500 12,34,375 10,50,781 12,88,086 Less: 35% (2) - (4,37,500) (4,59,375) (4,32,031) (3,67,773) (4,50,830) Annual CFAT 35,00,000 25,62,500 20,40,625 15,67,969 16,32,227 (4,50,830)

7 Add: Terminal value of Plant & working capital Less: Tax Liability on capital gain (considering 1 year delay) (WN-1) PVF 35,00, ,62, ,40, ,67, ,50,000 58,82, (3,02,490) (7,53,320) ,97,500 20,06,694 14,14,357 9,01,635 31,92,873 (3,61,820) Total PVCI = 1,03,11,239 1,01,06,250 = `2,04,989 Advise: Accept the proposal W.N. 1 Selling price of Plant and machinery = 30,00,000 Less: WDV at end of year 5 = (21,35,742) Capital Gain `8,64,258 Tax Savings = 8,64,258 x 35% = `3,02,490