# Solved Problems On Capital Budgeting

56,000 only, the IRR may be taken as slightly lower than 21%. has decided to diversity its production and wants to invest its surplus funds on the most profitable project. The purpose is to find out at which point the present value of inflows are equal to Rs. – 27,000 4,130 16,522 9,562 8,694 11,908 PV (Y) Rs. Two alternatives of promoting the product have been identified: Alternative 1: This will involve employing a number of agents. 5,00,000 will be required to advertise the product. 3,00,000 at the end of the each of the subsequent five years. Required: a) Advise the management as to the method of promotion to be adopted. However, in case, the additional depreciation and capital gain on sale of old machine is also subject to same tax rate @ 40%, then the position would be as follows: Rushi Ahuja 19 FINANCIAL MANAGEMENT 1. The company does not expect to realize any return from scrapping the old machine at the end of 10 years but if it is sold at present to another company in the industry, National Bottling Company would receive Rs. Which proposal be accepted given that the cost of capital of the firm is 8%. Solution In this case, the Annual earnings before depreciation are given for the proposals. -27,000 7,000 7 years i) Calculate NPV of the proposals at different discount rates of 15%, 16%, 17%, 18%, 19% and 20%. B 6,000 7,000 6,000 7,000 PVAF 7 yrs 4.160 4.040 8 yrs 4.487 4.344 P. 2,120 1,280 454 -216 -1,058 -1,765 Calculation of IRR Project A: Since outflow of Rs.

Fixed cost includes (straight line) depreciation of Rs. Assume that tax is 45% and straight line depreciation is allowed for tax purpose. Solution Initial cash outflow Cost of equipments Subsequent cash flows Units sold Sales @ Rs. 6/- Fixed cost (4,50,000 – 30,000 – 70,000) - Depreciation Profit before tax Tax @ 45% Profit after tax Depreciation (added back) Cash flow Rs. 12,00,000 6,00,000 3,50,000 70,000 1,80,000 81,000 99,000 70,000 1,69,000 There is no terminal cash inflow. 20,00 at the end of 5th year in the form of working capital released. 26,000 = 2.692 The PVAF table indicates that for Project X, the PV Factor closest to 2.121 against 5 years is 2.143 at 37% and Project Y, the PV factor closest to 2.692 is 2.689 at 25%. 6,000 3,000 2,000 5,000 5,000 Project 1 3 years 1,000 / 3,000 = 3 1/3 years Calculation of payback period Calculation of accounting rate of return Average cost Average profit after tax Rate of return Project 2 3 years 1,500 / 3,500 = 3 3/7 years Rs. 10,000 3,636 2,065 1,502 2,391 Rushi Ahuja 14 FINANCIAL MANAGEMENT 5 3,500 .621 Net present value Solved Problems 2,173 1,767 Calculation of profitability index PI = PV of inflows / PV of outflows Project 1 PI = Rs. So, the IRR for both the projects are more than 10%.

The company expects to sell 1,00,000 packs of the lotion each year. 20,000 Terminal cash flow: There will be a terminal cash flow of Rs. 4,000 6,500 8,500 12,000 15,000 Project 2: 1 2 3 4 5 Rs. 10,000 4,000 2,500 2,000 3,500 PVF (10%,n) 1,000 .909 .826 .751 .683 PV Rs. In the above calculation of NPV (at 10%), both projects were found to be having positive NPV.

1,100 22% Calculation of NPV (cost of capital 10%) Project 1: Annuity of cash inflows for 5 years PVAF (10%,5y) PV of Annuity (3,000 x 3.791) Less cash outflow Net present value = = = = = Rs. 11,373 10,000 1,373 Project 2: Year 0 1 2 3 4 Cash flow - Rs. 10,000 = 1.177 Calculation of Internal Rate of Return The IRR of a Project is the rate at which the NPV of the project comes to zero.

b) Calculate the internal rate of return for alternative 2. Will it make any difference, if the additional depreciation (on new machine) and gain on sale of old machine is also subject to same tax at the rate of 40%, and the scrap value of the new machines is Rs. Cash inflow (annual) Net savings in variable costs - Tax @ 40% Net benefit 3. Cash inflows (Annual) Net savings in variable costs - Additional depreciation Savings before tax - Tax @ 40% Net benefit Depreciation added back Cash inflows (annual) 3. Problem 16 National Bottling Company is contemplating to replace one of its bottling machines with a new more efficient machine. (It may be noted that there is no tax benefit of depreciation in this case).

Capital budgeting, and investment appraisal, is the planning process used to determine whether an organization's long term investments such as new machinery, replacement of machinery, new plants, new products, and research development projects are worth the funding of cash through the firm's capitalization structure (debt, equity or retained earnings).

It is the process of allocating resources for major capital, or investment, expenditures. Problem 19 Rushi Ahuja 23 FINANCIAL MANAGEMENT Solved Problems AP Udyog is considering a new automatic blender. 2,000 iv) Annual inflow 30,000 25,000 1,00,000 25,000 75,000 Cash flow Rs. However, if the life of the Project B extends to 8 years, then as per the IRR method, the Project B becomes acceptable (IRR = 19.83%) as against Project A (IRR = 19.39%). 10,000 Depreciation on new machine = 20,000 / 10 = Rs.Cumulative cash inflows Machine A Machine B 10 5 24 25 40 39 57 53 72 Calculation of Discounted Payback Period (Rs. 15,00,000 17,00,000 32,00,000 5.335 170,72,000 14,00,000 .467 6,53,800 177,25,800 150,00,000 27,25,800 Analysis: Under the NPV analysis of Projects. 9,500 4,000 4,000 4,500 Solved Problems Proposal B Rs. in lacs) Year 1 2 3 4 5 Total PV Less: Initial cash outflow Net present value CF X 100 200 300 450 600 PVF (10%,n) Y 500 400 200 100 100 0.909 0.826 0.751 0.683 0.621 Present value X Y 90.90 454.50 165.20 330.40 225.30 150.20 307.35 68.30 372.60 62.10 1065.50 700.00 700.00 461.35 365.50 Internal Rate of Return (IRR): Project X Year CFX 1 2 3 4 100 200 300 450 5 Total PV Less: Initial cash outflow Net present value 600 PV factor at 27% 28% .787 .781 .620 .610 .488 .477 .384 .373 .303 .291 Present Value 27% 28% 78.70 78.10 124.00 122.00 146.40 143.10 172.80 167.85 181.80 703.70 700.00 3.70 174.60 685.65 700.00 (14.35) IRR = 27 3.70 / 3.70 14.35 x 1 = 27 0.205 = 27.21% Project Y Rushi Ahuja 12 FINANCIAL MANAGEMENT Year CFY 1 2 3 4 5 PV factor at 27% 28% .730 .725 .533 .525 .389 .381 .284 .276 .207 .200 500 400 200 100 100 Total PV Less: Initial cash outflow Net present value Solved Problems Present Value 27% 28% 365.00 362.50 213.20 210.00 77.80 76.20 28.40 27.60 20.70 20.70 705.10 700.00 5.10 697.00 700.00 (3.00) IRR = 37 5.10 / 5.10 3.00 x 1 = 37 0.63 = 37.63% Profitability Index Total Present Value of cash inflow @ 10% PI = Initial cash outlay Rs. In deciding between the two alternatives the Managing Director favors the ‘pay back method’. The new machine will have a greater capacity and annual sales are expected to increase from Rs. The cost of capital is 8% and a 50% tax rate is applicable to both revenue and capital gains. 4,00,000 2,60,000 1,40,000 70,000 70,000 3,30,000 3.993 Rs. 2,00,000 .681 1,36,200 3,890 The replacement decision has a NPV of Rs. The firm may go for replacement of the existing machine. 2,00,000 50,000 10,000 50,000 70,000 10,000 30,000 Proposal II Rs. in lacs) Year 0 1 2 3 4 5 Present value Machine A Machine B -25.00 -40.00 9.10 4.15 11.62 15.00 12.00 9.52 11.56 8.68 9.30 Outflow In 3 years, Payback were Unrecouped oputflow In 4th year, Net present value Thus pay back =3 Cumulative present value Machine A Machine B 9.10 4.15 20.72 19.15 32.72 28.67 44.28 37.35 53.58 Machine A -25.00 19.15 5.85 9.52 5.85 9.52 = 3.614 years =3 Machine B -40.00 32.72 7.28 11.56 7.28 11.56 = 3.629 years Conclusion 1. Profitability index Machine A 12.35 1.494 Machine B 13.58 1.339 Choice B A Rushi Ahuja 8 FINANCIAL MANAGEMENT 3. Discounted payback 3 years 3.614 years 3 years 3.629 years Solved Problems Indifferent A Because of rising demand of Company’s product, Machine B should be the choice as it has higher capacity and its NPV is also higher. 5,00,000 7,50,000 7,50,000 12,00,000 12,50,000 10,00,000 8,00,000 The company’s cost of capital is 16% Calculate for each project. (b) Internal rate of return Solution (i) NPV of the two proposals (Figures in Rs. (22.50) 1.000 6.00 0.862 12.50 0.743 10.00 0.641 7.50 0.552 Net present value 0 1 2 3 4 5 6 7 PV Rs. lacs 4.12 5.13 Rushi Ahuja 9 FINANCIAL MANAGEMENT 3 4 5 6 7 Present value Less: Initial outlay NPV 0.564 0.467 0.386 0.319 0.263 10.00 7.50 - 5.64 3.50 22.62 22.50 0.12 7.50 12.50 12.50 10.00 8.00 Solved Problems 4.23 5.83 4.83 3.19 2.10 29.44 30.00 -.56 Project AXE: As the NPV of the proposal AXE at 21% discount rate is Rs. 20,000 8,000 8,000 12,000 Suggest the most attractive proposal on the basis of the NPV method considering that the future incomes are discounted at 12%. Solution Evaluation of investment proposal (net present value method) Year Cash inflows (Rs.) PVF (12%,n) Present value (Rs.) A B A B 0 -9,500 -20,000 1.000 -9,500 -20,000 1 4,000 8,000 0.893 3,572 7,144 2 4,000 8,000 0.797 3,188 6,376 3 4,500 12,000 0.712 3,204 8,544 Net present value (NPV) 464 2,064 NPV is more in proposal B and therefore, it should be accepted. The Chief Accountant, however, thinks that a more specific method should be used and he has calculated for each project: i) ii) iii) The Net Present Value The Profitability Index The Discounted Pay Back Period Having made these calculations, however, he finds himself still uncertain about which project to recommended. The present value interest factor for an annuity for five years at 8% is 3.993 and present value interest factor at the end of five years is 0.681. Solution Rushi Ahuja 20 FINANCIAL MANAGEMENT Cash outflows: Cost of new machine - Disposal value of existing machine 50% Tax on Profit on sale (6,00,000 – 5,00,000) Net outflow Cash inflows (Annual) Incremental Sales Savings in expenses - Incremental depreciation (3,60,000 – 1,00,000) Net profit after tax (incremental) Less tax @ 50% Profit after tax Cash flow (PAT Depreciation) PVAF (8%,5y) Present value of cash inflows (3,30,000 x 3.993) Cash inflow (terminal) Scrap value at the end of 5 th year PVF (8%,5y) Present value (2,00,000 x .681) Net present value (13,17,690 1,36,200 – 14,50,000) Solved Problems Rs. 3,00,000 1,00,000 15,000 65,000 95,000 15,000 15,000 60,000 Life of the Project is 10 years. 6,24,395 64,820 68,9415 4,80,000 2,09,415 Solved Problems Proposal II has higher NPV and so, it may be accepted by the firm. B(8y) 24,960 29,120 31,409 24,240 28,280 30,408 Rushi Ahuja 22 FINANCIAL MANAGEMENT 17 18 19 20 6,000 6,000 6,000 6,000 7,000 7,000 7,000 7,000 3.922 3.812 3.706 3.605 4.207 4.078 3.954 3.837 23,532 22,872 22,235 21,630 27,454 26,684 25,942 25,235 Solved Problems 29,119 28,556 27,678 26,859 Calculation of NPV Dis. 24,960 24,240 23,532 22,872 22,235 21,630 NPV (A) Rs. 2,07,550 Alternative 2 Outflows: Initial expenditure Inflows: Annual Cash inflow Less out of pocket expenses Net inflow PVAF (20%,5y) Present value of inflows (2.991 x 1,00,000) Net present value (2,99,100 – 2,50,000) Rs. 1,50,000 50,000 1,00,000 2.991 2,99,100 49,100 Calculation of internal rate of return for alternative 2: Rs. 1,00,000 x PVAF(r,5Y) 2,50,000  1,00,000 2.5 For 5 years in the PVAF table, the value of 2.5 may be traced between 28% and 29%. At 28% NPV At 29% NPV = = = = (1,00,000 x 2.532) – 2,50,000 Rs. -1,700 The exact IRR may be found by interpolating between 28% and 29% as follows: IRR = 28% 3,200 / (3,200 1,700) = 28.65% Note: The allocated fixed costs in case of Alternative 2 have been ignored because these do not involve any incremental cash outflow. You are required to – i) Identify all the relevant cash flows for this replacement decision. Google(); req('single_work'); \$('.js-splash-single-step-signup-download-button').one('click', function(e){ req_and_ready('single_work', function() ); new c. Rushi Ahuja 18 FINANCIAL MANAGEMENT Solved Problems Problem 15 P. has a machine having an additional life of 5 years which costs Rs. Moreover, in view of the advance tax payments, this assumption seems to be logical.

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