W.N.-1: Calculation of depreciation per annum Depreciation p.a. = SOLUTIONS TO ASSIGNMENT PROBLEMS Cost -Scrap Value Life W.N.-2: Calculation of PAT p.a. Problem No.1 80,000 5 10,000 = Rs.14,000 p.a. 2. CAPITAL BUDGETING Year PBDT Depreciation PBT / PAT (PBDT Dep.) 1 20,000 14,000 6,000 2 40,000 14,000 26,000 3 30,000 14,000 16,000 4 15,000 14,000 1,000 5 5,000 14,000 (9,000) Since Income tax rate is not given in the problem, PBT = PAT. Step-1: Calculation of Average Profit after Tax Average Profit after tax= Calculation of ARR 6,000 26,000 16,000 10,000 9,000 5 Step-2: Calculation of Average Investment Average investment = ( 2 1 Initial Cost - Salvage Value) + Salvage Value = ( 2 1 80,000-10,000) + 10,000 = Rs.45,000 = Rs. 8,000 p.a Step-3: Calculation of Accounting Rate of Return (ARR) (Return on Avg. Capital Employed) ARR = AveragePAT x100 8,000 Average investment 45,000 = 17.77% Step-4: Return on Original Capital employed Return on Original Capital employed = 4,000 20,000 X100 Payback reciprocal = 20% Average PAT x100 = x100 Orginal Investment 80, 000,000 Problem No.2 8 = 10% The above payback reciprocal provides a reasonable approximation of the internal rate of return, i.e. 19%. IPCC_34e_F.M_ Capital Budgeting_Assignment Solutions 1
Ph: 98851 25025/26 www.gntmasterminds.com Problem No.3 (i) Payback Period of Projects Particulars C 0 C 1 C 2 C 3 A (10,000) 6,000 2,000 2,000 3 years B (10,000) 2,500 2,500 5,000 3 years C (3,500) 1,500 2,500 1 year and 9.6 months D (3,000) 0 0 3,000 3 years i.e. x2, 000 2,500 12 (ii) If standard payback period is 2 years, Project C is the only acceptable project. But if standard payback period is 3 years, all the four projects are acceptable. (iii) Discounted Payback Period (Cash flows discounted at 10%) A 10,000 + 5,454.6 + 1,652.8 + 1,502.6 + 8,196 3years x,1390 8, 12 = 3 years and 2 months 196 B 10,000 + 2,272.75 + 2,066 + 3,756.5 + 5,122.50 3years 12 x,1904.75= 3 years and 4.6 months 5, 122.55 C 3,500 + 1,363.65 + 2,066 + 375.65 + 3,415 2years x70.35 375 12 =2 years and 2.25 months.65 D 3,000 + 0 + 0 + 2,253.9 + 4,098 3years x746.10 4,098 12 =3 years and 2.18 months If standard discounted payback period is 2 years, no project is acceptable on discounted payback period criterion. If standard discounted payback period is 3 years, Project C is acceptable on discounted payback period criterion. W.N. 1: Calculation of depreciation per annum Depreciation p.a. = Cost -Scrap Value Life Calculation of NPV using Incremental approach = Problem No.4 Step-1: Calculation of Present Value of Cash Outflows: 80,000 5 0 = Rs.16,000 p.a. Particulars Amount Investment in new equipment 80,000 Additional working capital 1,50,000 Total 2,30,000 IPCC_34e_F.M_ Capital Budgeting Assignment Solutions 2
Step-2: Calculation of Present Value of Operating Cash Inflows: Incremental net cash in flow Less: additional wages Depreciation(w.n.1) Incremental PBT Less: Tax @ 40 % Incremental PAT Add: depreciation Incremental CFAT p.a Particulars Amount Rs. Amount Rs. Therefore, Present Value of Operating Cash Inflows = 42,000 X PVAF(13%,5) Step 3: Present Value of Terminal Cash Inflows = = 42,400 X 3.517 = 1,49,120 Gsp or Nsp on sale of initial equipment = 0 Recovery of additional working capital = 1,50,000 1,50,000 PV there off = 1,50,000 * PVF (13%, 5) Step 4: Calculation of NPV NPV = 1,50,000 X 0.543 = 81,450 = PV of cash inflows PV of cash outflows 40,000 16,000 = PV of Operating Cash Inflows +PV of Terminal Cash Inflows PV of cash outflows. = 1,49,120 + 81,450-2,30,000 = Rs.570 Conclusion: Since NPV is positive it is advisable to accept. Problem No.5 To, Guntur 1,00,000 56,000 44,000 17,600 26,400 16,000 42,400 W.N 1: Calculation of depreciation p.a. Depreciation p.a. = Cost -Scrap Value Life 6 1 10 On supplementary equipment = = 1.5 lakhs pa = 140 8 0 = Rs. 17.5 lakhs p.a. (Rs. in Lakhs) Calculation of NPV using Incremental approach Step-1: Calculation of Present Value of Cash Outflows: Cost of initial equipment Cost of additional working capital Less: tax free subsidy from government Particulars Amount 140 15 155 20 135 IPCC_34e_F.M_ Capital Budgeting_Assignment Solutions 3
Ph: 98851 25025/26 Add: cost of supplementary equipment - 10 Present value there off - 10* pvf ( 12%, 2 ) - 10* 0.797 Present value of cash out flows www.gntmasterminds.com 7.97 142.97 Step-2: Calculation of Present Value of Operating Cash Inflows Selling price per unit = 100 Less: - variable cost @ 40% = 40 Contribution per unit = 60 Particulars Y 1 Y 2 Y 3 to 5 Y 6 to 8 a. Sales volume (lakhs of unit) 0.8 1.2 3.0 2.0 b. Total contribution ( a * Rs. 60 per unit) 48 72 180 120 c. Fixed cost 16 16 16 16 d. Advertisement cost 30 15 10 4 e. Depreciation (WN 1) 17.5 17.5 19(17.5+1.5) 19 f. PBF (b-c-d-e) (loss) (15.5) 23.5 135 81 g. Tax @ 50% (7.75) 11.75 67.5 40.5 h. PAT (f-g) (7.75) 11.75 67.5 40.5 i. CFAT (h+e) 9.75 29.25 86.5 59.5 j. PVF @ 12 % 0.893 0.797 1.915 1.363 k. Present value 8.706 23.31 165.64 278.765 Therefore, Present Value of Operating Cash Inflows = Rs.278.765 Present value factor for years 3 to 5 = PVF (12%, 3) + PVF (12%, 4) + PVF (12%, 5) = 0.712+0.636+0.567 = 1.915 (or) PVAF (12%, 5) - PVAF (12%, 2) = 3.605-1.690 = 1.915 Present value factor for years 6 to 8 = PVF ( 12%, 6) + PVF (12%, 7) + PVF (12%, 8) = 0.507+0.452+0.404 = 1.363 (or) PVAF(12%, 8) - PVAF (12%, 5) = 4.968-3.605 = 1.363 Step-3: Present Value of Terminal Cash Inflows = Gsp or Nsp on sale of initial equipment - 0 Gsp or Nsp on sale of supplementary equipment - 1 Recovery of working capital - 15 Pv there off = 16 * PVF (12%, 8) = 16 * 0.404 = 6.464 16 To, Guntur To, Guntur IPCC_34e_F.M_ Capital Budgeting Assignment Solutions 4
Step-4: Calculation of NPV NPV = PV of cash inflows PV of cash outflows = PV of Operating Cash Inflows +PV of Terminal Cash Inflows PV of cash outflows. = 278 + 65 6.464 = Rs. 142.97 Conclusion: Since NPV is positive it is advisable to accept the project. Note: It is given that the company has other profitable businesses and the loss from one business can be set off against profit of other business. Alternatively it can also be assumed that the loss is carried forward and setoff against future profit. Problem No.6 Calculation of NPV a. Step 1: Calculation of Present Value of Cash Outflows: Particulars Amount Cost of machinery 4,00,000 Present Value of Cash Outflows 4,00,000 Step 2: Calculation of Present Value of Operating Cash Inflows: a. Sales volume b. Contribution per unit (10-6) c. Total contribution (axb) d. Fixed cost e. CFAT (c-d) Particulars Amount 40,000 units Rs.4 1,60,000 20,000 1,40,000 p.a PV thereof = 1,40,000 X PVAF(15%,6) = 1,40,000 X 3.784 = 5,29,760 Step-3: Present Value of Terminal Cash Inflows G.S.P/N.S.P on sale of machinery = 20,000 PV thereof = 20,000 X PVF(15%,6) = 20,000 X 0.432 = 8,640 Step-4: Calculation of NPV NPV = PV of cash inflows PV of cash outflows = PV of Operating Cash Inflows +PV of Terminal Cash Inflows PV of cash outflows. = 5,29,760+8,640-4,00,000 = 1,38,400 Conclusion: Since NPV is positive it is advisable to accept the project. b. Let, x represents the sale volume required to justify the project. The project is acceptable if NPV is at least equal to zero Step-1: same as above 4,00,000. IPCC_34e_F.M_ Capital Budgeting_Assignment Solutions 5
Ph: 98851 25025/26 www.gntmasterminds.com Step-2: present value of operating cash inflows Particulars Amount (Rs.) a. Sales volume X unit b. Contribution per unit (10 6) 4 c. Total contribution 4X d. Fixed cost 20,000 e. CFAT (c-d) 4X-20,000 Present value there of = (4X 20,000) * PVAF (15%, 6 years) = (4X 20,000) *3.784 Step-3: same as above 8,640 To, Guntur Step-4: Finding the value of X Since NPV is 0 then present value of cash inflows = present value of cash outflows present value of operating cash inflows + present value of terminal cash inflows = present value of cash out flows (4X 20,000) * 3.784 + 8,640 = 4,00,000 (4X 20,000) = 1,03,424 4X = 1,23,424 X = 30,856 units pa Problem No.7 Given information: Project Investment NPV A 1,00,000 1,25.000 B 1,50,000 45,000 A&B 2,50,000 2,00,000 C 1,50,000 90,000 a. Selection of the projects if the firm has no budget constraint: Given that all the projects have positive NPV therefore it is beneficial to select all the projects I.e A,B & C. b. Selection of projects if there is a budget constraint of 2,50,000: Combination NPV A&B 2,00,000 A&C 2,15,000(1,25,000+90,000) Since NPV is more in case of projects A&C, it is beneficial to invest in project A&C. Problem No.8 W.N - 1: Calculation of depreciation per annum Cost of Machinery 2,50,000 Less: Salvage value 30,000 Depreciable amount 2,20,000 To, Guntur IPCC_34e_F.M_ Capital Budgeting Assignment Solutions 6
Sum of the years digits = 1 + 2 + 3 +.. + 10 = 55. Dep. for 1 st year = 2,20,000 x10 x 55 55 000 3 rd year = 2,20 x8 55 000 = Rs. 32,000 4 th year = x7 55 000 5 th year = 2,20 x6 55 000 = Rs.24,000 2 = Rs.40,000 2 nd year = 9 = Rs.36,000 2 = Rs. 8,000 W.D.V at the end of 5th year = Cost depreciation = 2,50,000 1,60,000 = Rs. 90,000 Book value of machine after capital expenditure = 90,000 + 60,000 = Rs. 1,50,000 Depreciable amount from 6th to 10th year = 1,50,000 30,000 = Rs. 1,20,000 Sum of the years digits = 1 + 2 + 3 + 4 + 5 = 15 Dep. for 6 th year = x5,1 20 15, 000 20 = Rs. 40,000 7 th year = x4 15, 000,1 20 x 15, 000 20 = Rs. 24,000 9 th year = x2 15, 000,1 20 x 15, 000 = Rs. 8,000 8 th year = 3 10 th year = 1 Calculation of NPV Step-1: Calculation of Present Value of Cash Outflows,1 = Rs. 32,000,1 = Rs. 16,000 Particulars Cost of Machinery Add: Working capital Add: Cost of Additional equipment [60,000 x PVF (20%, 5y)] Amount 2,50,000 50,000 24,120 Present value of Cash Outflows 3,24,120 Step-2: Calculation of Present Value of Operating Cash Inflows. (Rs. in Lakhs) Particulars Y 1 Y 2 Y 3 Y 4 Y 5 Y 6 Y 7 Y 8 Y 9 Y 10 PBDT Less: Dep.(W.N-1) P.B.T Less: Tax @ 40% P.A.T Add:Depreciation C.F.A.T. X P.V.F (20%, n) 0.4 0.6 L 0.24 L 0.36 0.4 0.76 0.833 0.36 0.64 0.256 0.384 0.36 0.744 0.694 0.32 0.68 0.272 0.408 0.32 0.728 0.579 0.28 0.72 0.288 0.432 0.28 0.712 0.482 0.24 0.76 0.304 0.456 0.24 0.696 0.402 0.40 0.60 0.24 0.36 0.40 0.76 0.335 0.32 0.68 0.272 0.408 0.32 0.728 0.279 0.24 0.76 0.304 0.456 0.24 0.696 0.233 0.16 0.84 0.336 0.504 0.16 0.664 0.194 IPCC_34e_F.M_ Capital Budgeting_Assignment Solutions 7 0.08 0.92 0.368 0.552 0.08 0.632 0.162 P.Value 0.634 0.516 0.422 0.343 0.279 0.255 0.203 0.162 0.128 0.102 Therefore, Present Value of operating cash inflows = Rs.3,04,498 To,
Ph: 98851 25025/26 www.gntmasterminds.com Step-3: Calculation of Present Value of Terminal Cash Inflows (At the end of the project) G.S.P/N.S.P on sale of machinery Add: Recovery of working capital Particulars Amount 30,000 50,000 Total of Terminal Cash Inflows 80,000 Present Value thereof = 80,000 X PVF (20%, 10y) = 80,000 X 0.162 = Rs.12,960 Step-4: Calculation of NPV NPV = PV of cash inflows PV of cash outflows = PV of Operating Cash Inflows + PV of Terminal Cash Inflows PV of Cash Outflows = 3,04,498 + 12,960 3,24,120 = - Rs. 6662 Conclusion: Since NPV is negative it is not advisable for the company to accept the project. Assumptions: Cash flows are assumed to accrue at the end of each year. Interim cash inflows at the end of each year are assumed to be reinvested at the rate of cost of capital. Cash flows given in the problem are assumed to be certain. Problem No.9 Step 1: Calculation of Present value of Net Cash outflows. Machine A: Year Particulars Cash flow PVF @ 14% PV 0 Purchasing Cost 7,50,000 1 7,50,000 1-3 Running Cost p.a. 2,00,000 2.5313 (PVAF@9%, 3y) 5,06,260 PV of Net cash outflows 12,56,260 Machine B: Year Particulars Cash flow PVF @ 14% PV 0 Purchasing Cost 5,00,000 1 6,00,000 1-3 Running Cost p.a. 3,00,000 1.7591 (PVAF@9%, 2y) 5,27,730 PV of Net cash outflows 10,27,730 Step 2: Calculation of Equivalent Present Value of Annual Net Cash outflows. 1. Machine A 2. MachineB 12,56,260 12,56,260 PVAF(9%,3y ) 2.5313 =4,96,290 10,27,730 10,27,730 PVAF(9%,2y ) 1.7591 =5,84,236 To, Conclusion: Since Equivalent Present Value of Net Cash Outflow is less, it is beneficial to purchase Machine A. IPCC_34e_F.M_ Capital Budgeting Assignment Solutions 8
Problem No. 10 Step-1: Calculation of CFAT p. a Particulars Machine X Machine Y Estimated savings in cost Estimated savings in Wages 500 6,000 800 8,000 Less: Additional cost of maintenance Additional cost of supervision 800 1,200 1,000 1,800 CFAT p.a 4,500 6,000 Step-2: Calculation of Pay back period Payback period = Particulars Machine X Machine Y Investment 18000 = 3 yrs. Initial CFAT Assumption: The two machines are mutually exclusive. 9000 = 2yrs. 4500 6000 Conclusion: It is beneficial to select the machine with least pay back period i.e. Machine X. Calculation of IRR: (Single out flow & multiple even cash inflows) From the given information, PVA = 36,000 We know that, PVA Problem No.11 periodic payment = 11,200 term of annuity = 5 years = P.P X PVAF (r%, 5 yrs) 36,000 = 11,200 X PVAF PVAF = 3.214 Trace the PVAF in the PVAF table against 5 years Therefore IRR = 17% approximately Calculation of NPV & IRR: Year Using interpolation, Cash flow IRR = l 1 1 (l 2l1 ) NPV@l 1NPV@l 2 Problem No.12 NPV at the rate of 12% NPV at the rate of 13% PVF @12% PV PVF @13% PV 0 (35,00,000) 1 (35,00,000) 1 (35,00,000) 1-4 10,00,000 3.037 30,37,000 2.974 29,74,000 5 5,00,000 0.567 2,83,500 0.543 2,71,500 6 5,00,000 0.507 2,53,500 0.48 2,40,000 NPV 74,000 (14,500) NPV@l = 12% + (13% 12%) 88 74,500, 000 = 12.836% Since NPV is positive, it is beneficial for the company to accept the proposal. Since IRR is > cost of capital, it is beneficial for the company to accept the proposal. IPCC_34e_F.M_ Capital Budgeting_Assignment Solutions 9
Ph: 98851 25025/26 www.gntmasterminds.com Problem No.13 1. Computation of Net Present Values of Projects: Year Project A Rs. (1) Cash flows Project B Rs. (2) (3) Discounting Factor @ 16% Project A Rs. (3) x (1) Discounted Cash flow Project B Rs. (3) x (2) 0 1,35,000 2,40,000 00 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 Cumulative PV of Cumulative inflows PV 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: Excess PV of cash inflows over the Project A Project B 18,270 34,812 Project cost (Rs.) (Rs.1,53,270 Rs.1,35,000) (Rs.1,53,270 Rs.1,35,000) Computation of period required To recover excess amount of cumulative PV over project cost (Refer to Working note2) (Rs.18,270 / Rs.46,368) 0.39 year 0.81 years (Rs.34,812 / Rs.42,840) Discounted payback period 3.61 year 4.19 years (4 0.39 years (5 0.81) years IPCC_34e_F.M_ Capital Budgeting Assignment Solutions 10
(ii) Profitability Index : = Sumofdisco untcash inflows initiancas houtlay Rs.,193,254 Rs.,135,000 Rs.2,74,812 Rs.2,40,000 Profitability Index (for Project A) = Profitability Index (for Project B) = (iii) Net present value (for Project A) = Rs.58,254 (Refer to Working note 1) Net present value (for Project B) = Rs.34,812 = 1.43 = 1.15 Problem No.14 Advise to the Hospital Management: Sales Revenue Less: Operating Cost Less: Depreciation (80,000 6,000)/8 Net Income Tax @ 30% Earnings after Tax (EAT) Add: Depreciation Cash inflow after tax per annum Less: Loss of Commission Income Net Cash inflow after tax per annum In 8th Year : New Cash inflow after tax Add: Salvage Value of Machine Net Cash inflow in year 8 Calculation of Net Present Value (NPV): 1 to 7 8 Determination of Cash inflows Year CFAT PV Factor @10% Less: Cash Outflows 13,525 19,525 NPV 4.867 0.467 Amount 40,000 7,500 32,500 9,250 23,250 6,975 16,275 9,250 25,525 12,000 13,525 13,525 6,000 19,525 Present Value of Cash inflows 65,826.18 9,118.18 74,944.36 80,000.00 (5,055.64) Profitabil ity Index Sumofdiscounted cashinflows Present value ofcashoutflows 74 80,944,000. 36 =0.937 Advise: Since the net present value is negative and profitability index is also less than 1, therefore, the hospital should not purchase the diagnostic machine. Note: Since the tax rate is not mentioned in the question, therefore, it is assumed to be 30 percent in the given solution. Problem No.15 Recommendations regarding Two Alternative Proposals: (i) Net Present Value Method: Computation of Present Value IPCC_34e_F.M_ Capital Budgeting_Assignment Solutions 11
Ph: 98851 25025/26 www.gntmasterminds.com Project A = Rs.4,00,000 x 3.791 = Rs.15,16,400 Project B = Rs.5,80,000 x 3.791 = Rs.21,98,780 Computation of Net Present Value: Project A = Rs.15,16,400 12,00,000 = Rs.3,16,400 Project B = Rs.21,98,780 18,00,000 = Rs.3,98,780 Advise: Since the net present value of Project B is higher than that of Project A, therefore, Project B should be selected. (ii) Present Value Index Method: Present Value Index = Project A = Project B = PresentValue ofcash inflow InitialInv estment 15, 16,400 = 1.264 12,00,000 18 21,98,00,,000 780 = 1.222 Advise: Since the present value index of Project A is higher than that of Project B, therefore, Project A should be selected. (iii) Internal Rate of Return (IRR): Project A: P.V. Factor = InitialInv estment 12,00,000 AnnualCash Inflow 4,00,000 PV factor falls between 18% and 20% = 3 Present Value of cash inflow at 18% and 20% will be: Present Value at 18% = 3.127 x 4,00,000 = 12,50,800 Present Value at 20% = 2.991 x 4,00,000 = 11,96,400 12,50,80012,00,000 IRR = 18 + x(20 18) 12,50,80011,96,400 50,800 x 54,400 = 18 + 2 = 18 + 1.8676 = 19.868% Project B: 18,00,000 P.V. Factor = 3. 103 5,80,000 Present Value of cash inflow at 18% and 20% will be: Present Value at 18% = 3.127 x 5,80,000 = 18,13,660 Present Value at 20% = 2.991 x 5,80,000 = 17,34,780 18, 13,66018,00,000 IRR = 18 + x(20 18) 18, 13,66017,34,780 13,660 x 78,880 = 18 + 2 = 18 + 0.3463 = 18.346% To, Guntur To, Guntur Advise: Since the internal rate of return of Project A is higher than that of Project B, therefore, Project A should be selected. IPCC_34e_F.M_ Capital Budgeting Assignment Solutions 12
Working notes: Depreciation on machine. X = Depreciation on machine. Y = Annual savings: Wages Scrap Total savings(a) Problem No.16 Cost -Scrap Value Life Cost -Scrap Value Life = =,150,000 5 2,40,000 6 = Rs.30,000 = Rs.40,000 Particulars Machine X Machine Y 90,000 10,000 1,00,000 1,20,000 15,000 1,35,000 Annual estimated cash cost: Indirect material Supervision Maintenance Total cash cost(b) 6,000 12,000 7,000 25,000 8,000 16,000 11,000 35,000 Annual cash savings(a-b) Less: depreciation Annual savings before tax Less: tax @ 30 % Annual profit after tax Add: depreciation Annual cash in flows 75,000 30,000 45,000 13,500 31,500 30,000 1,00,000 40,000 60,000 18,000 42,000 40,000 61,500 82,000 Evaluation of alternatives: (i) ARR = average annual net savings Average 31, investment Machine X = x100= 42% 75,000 500 42,000 x,120,000 Machine Y = 100= 35% Decision: Machine X is better. To, Guntur [Note: ARR can be computed alternatively taking initial investment as the basis forcomputation (ARR = Average Annual Net Income/Initial Investment). The value ofarr for Machines X and Y would then change accordingly as 21% and 17.5%respectively] (ii) Present Value Index Method Present Value of Cash Inflow = Annual Cash Inflow x P.V. Factor @ 10% Machine X = 61,500 x 3.79 = Rs.2,33,085 Machine Y = 82,000 x 4.354 P.V index = Rs.3,57,028 = present value of cash inflow Investment IPCC_34e_F.M_ Capital Budgeting_Assignment Solutions 13
Ph: 98851 25025/26 2,1,33 50,000, 085 1. 2 3,40,57,,000 028 Machine X = 1. 5539 Machine Y = 4876 Decision: Machine X is better. www.gntmasterminds.com Project Present Value of Cash Inflows Problem No.17 PART A Initial cash outlay IPCC_34e_F.M_ Capital Budgeting Assignment Solutions 14 NPV P.I Ranking as per NPV Ranking as per P.I A 1,87,600 x PVAF (12%, 2y ) = 317044 3,00,000 17,044 57 IV V B 66,000 x PVAF (12%, 5y ) = 2,37,930 2,00,000 37,930 1.19 III III C 1,00,000 x PVAF (12%, 3y) = 2,40,200 2,00,000 40,200 1.201 II II D 20,000 x PVAF (12%, 9y) = 1,06,560 1,00,000 6,560 66 V IV E 66,000 x PVAF (12%, 10y) = 3,72,900 3,00,000 72,900 1.243 I I PART B All the projects have positive NPV. So, we can accept all the projects subject to availability of funds. It is also given that the company is having limited funds of Rs.4,00,000 and we need Rs.11,00,000 to invest in all the projects. So, it is required to do capital rationing. Capital Rationing, assuming that the projects are divisible Project Cash Outflow NPV Surplus funds E 3,00,000 72,900 1,00,000 C 1,00,000 20,100 x,100,000 2 40,00, 200 -,000 Total 93,000 - PART - C All the projects have positive NPV. To accept all the projects we need initial investment of Rs.11,00,000. But the available funds are just Rs.5,00,000. Therefore, it is necessary to do capital rationing. Assumptions: Capital Rationing, assuming that the projects are divisible Project Cash outlay NPV Surplus funds E 3,00,000 72,900 2,00,000 C 2,00,000 40,200 --- Total 1,13,100 Perfect linear relationship is assumed to exist between inflows and outflows. In other words, NPV changes proportionately to changes in investment. It is assumed that there is scarcity of funds in the current year only. In other words, there is no scarcity of funds in subsequent years. The given projects are mutually independent.
A project can be accepted only once. A project can either be accepted now or rejected. In other words, there is no question of postponement. Problem No. 18 Part: A Calculation of NPV Step 1:Calculation of Present Value of Cash Outflows a) Initial investment b) Working capital Particulars Amount 600 80 Present Value of Cash Outflows 680 Step 2:Calculation of Depreciation p.a. Depreciation cos t life scrap 6,00,000 5 0 =1,20,000 Step 3:Calculation of Present Value of Operating cash inflows Particulars Y 1 Y 2 Y 3 Y 4 Y 5 a) PBDT 240 275 210 180 160 b) Depreciation (120) (120) (120) (120) (120) c) PBT 120 155 90 60 40 d) Tax @35% (42) (54.25) (31.5) (21) (14) e) PAT 78 100.75 58.5 39 26 f) CFAT (e+b) 198 220.75 178.5 159 146 g) Pvf@12% 0.8929 0.7972 0.7118 0.6355 0.5674 h) PV of cashinflow 176.7942 175.98 127.0563 10445 82.8404 Therefore, Present Value of Operating Cash Inflows = Rs.663.71 Step 4: Calculation of PV of Terminal Cash inflows PV of TMCI = 80 x PVF (12%, 5y) = 80 x 0.5674 = 45.39 Step 4: Calculation of NPV NPV = PV of Operating Cash Inflows + PV of Terminal Cash Inflows PV of Cash Outflows = 663.71+ 45.39 680 = 29.1 Part: B Calculation of IRR year Cash flow PVF @ 12% Present Value PVF @ 14% Present Value 0 (680) 1 (680) 1 (680) 1 198 0.8929 176.7 0.8772 173.68 2 220.75 0.7972 175.9 0.7695 169.86 3 178.5 0.7118 127.6 0.6750 120.48 4 159 0.6355 101.5 0.5921 94.1 5 226 0.5674 123.24 0.5195 117.38 NPV29.1 (4.43) IPCC_34e_F.M_ Capital Budgeting_Assignment Solutions 15
Ph: 98851 25025/26 www.gntmasterminds.com Using interpolation IRR L1 NPV@L 1 (L 2L) 1 NPV@L 1NPV @L 2 12 (2) 29.1 29. 4.43 1 12 (2) 33 29.5. 1 13.735% Part: C Discounted payback period Year Discounted cash flow Cumulative 1 176.7 176.7 2 175.9 352.6 3 127.6 480.2 4 101.2 581.4 5 128.24 709.6 Discounted payback period 4 709 128.6.24 581. 4 4 128 128.24. 19 4.9years Part: D Payback period Year Discounted cash flow Cumulative 1 198 198 2 220.75 418.75 3 178.5 597.25 4 159 756.25 5 226 982.25 Payback period 3 756.25 597 159. 25 3 159 159= 4 Problem No.19 (a) Payback Period Method: A = 5 + (500/900) = 5.5 years B = 5 + (500/1200) = 5.4 years C = 2 + (1000/2000) = 2.5 years Net Present Value: NPV= A (- 5000) + (900-6.145) = (5000) + 5530.5 = Rs.530.5 NPV B is calculated as follows: IPCC_34e_F.M_ Capital Budgeting Assignment Solutions 16
Year Cash flow (Rs.) 10% discount factor Present value (Rs.) 0 (5,000) 00 (5,000) 1 700 0.909 636 2 800 0.826 661 3 900 0.751 676 4 1,000 0.683 683 5 1,100 0.621 683 6 1,200 0.564 677 7 1,300 0.513 667 8 1,400 0.467 654 9 1,500 0.424 636 10 1,600 0.386 618 1591 NPV C = (-5000) + (2000 2.487) + (1000 0.683) = Rs.657 Internal Rate of Return If NPV= A 0, present value factor of IRR over 10 years = 5000/900 = 5.556 From tables, IRR A = 12 per cent. IRR B Year Cash flow (Rs.) 10% discount factor Present value (Rs.) 20% discount factor Present value (Rs.) 0 (5,000) 00 (5,000) 00 (5,000) 1 700 0.909 636 0.833 583 2 800 0.826 661 0.694 555 3 900 0.751 676 0.579 521 4 1,000 0.683 683 0.482 482 5 1,100 0.621 683 0.402 442 6 1,200 0.564 677 0.335 402 7 1,300 0.513 667 0.279 363 8 1,400 0.467 654 0.233 326 9 1,500 0.424 636 0.194 291 10 1,600 0.386 618 0.162 259 1,591 (776) Interpolating: IRR B = IRR C Year 10,1591 x10 (,1591776 ) Cash flow (Rs.) = 10+6.72 = 16.72 per cent 15% discount factor Present value (Rs.) 18% discount factor Present value (Rs.) 0 (5,000) 00 (5,000) 00 (5,000) 1 2,000 0.870 1,740 0.847 1,694 2 2,000 0.756 1,512 0.718 1,436 3 2,000 0.658 1,316 0.609 1,218 4 1,000 0.572 572 0.516 516 140 136 IPCC_34e_F.M_ Capital Budgeting_Assignment Solutions 17
Ph: 98851 25025/26 Interpolating: IRR C = 15 140x3 15 1. 52 (140136 ) Accounting Rate of Return ARR A : Average capital employed = Average accounting profit = ARR A = (400x100) 2,500 = 16 per cent ARR B : Average accounting profit = ARR B = (650x100) 2,500 = 26 per cent ARR C = Average accounting profit = ARR C = (500x100) 2,500 = 20 per cent 5,000 = Rs.2,500 2 ( 9,000 5,000 ) = Rs.400 10 ( 11,5005,000 ) 10 ( 7,000 5,000 ) 4 = 16.52 per cent = Rs.650 = Rs.500 www.gntmasterminds.com (b) Summary of Results Project A B C Payback (years) 5.5 5.4 2.5 ARR (%) 16 26 20 IRR (%) 12.4 16.7 16.5 NPV (Rs.) 530.5 1,591 657 Comparison of Rankings Method Payback ARR IRR NPV 1 C B B B 2 B C C C 3 A A A A Step-1: Calculation of Pay Back Period Problem No. 20 (Rs. In Lakhs) Year 1 2 3 4 5 Machine A Machine B CFAT Accumulated CFAT CFAT Accumulated CFAT 1.5 2.0 2.5 1.5 Pay Back Period 2 + 1.5 3.5 6.0 7.5 8.5 0.5 1.5 2.0 3.0 2.0 5.0 = 2.6 Years 3 + 2.5 3.5 0.5 2.0 4.0 7.0 9.0 5.0 = 3.33 years 3.0 4. 0 Since Pay Back Period is less for Machine A, it is beneficial to purchase Machine A. IPCC_34e_F.M_ Capital Budgeting Assignment Solutions 18
Step-2: Present Value of Cash Out flows Cost of Machinery Present Value of Cash Outflows Particulars Amount 5,00,000 5,00,000 Step-3: Present Value of Operating Cash Inflows Year Machine A Machine B CFAT PVF @ 10% PV Y 1 Y 2 Y 3 Y 4 Y 5 Y 1 Y 2 Y 3 Y 4 Y 5 2.0 2.5 1.5 0.5 1.5 2.0 3.0 0.826 0.751 0.683 0.621 0.909 0.826 0.751 0.683 1.652 1.8775 245 0.621 0.4545 1.239 1.502 2.049 1.5 0.909 1.3635 2.0 0.621 1.242 Present Value there of for Machine A= 6.5385 Present Value there of for Machine B= 6.4865 Step-4: Present Value of Terminal Cash Inflows - Nil Step-5: Calculation of NPV and Profitability Index Particulars Machine A Machine B Present Value of cash inflows Present Value of cash outflows 6.5385 (5.0) 6.4865 (5.0) NPV @ 10% 1.5385 1.4865 Profitability Index (P.V of Cash Inflows / Cash Outflows) 1.31 1.30 Since NPV and P.I. are higher for Machine A, it is beneficial to purchase Machine A. Step-6: Calculation of I.R.R for Machine A Year 0 1 2 3 4 5 Cash flow 5.0 1.5 2.0 2.5 1.5 NPV @ 20% NPV @ 24% PVF P V PVF P V (5.0) (5.0) 0.833 1.25 0.806 1.21 0.694 1.39 0.650 1.30 0.579 1.45 0.524 1.31 0.482 0.72 0.423 0.63 0.402 0.40 0.341 0.34 NPV 0.21 (0.21) Using Interpolation IRR = L l + NPV@ L NPV@ L 1 NPV@ 1 L 2 0.21 (L 2 L 1 ) = 20 + 4 0.210.21 = 22%. Step-7: Calculation of IRR for Machine B Year 0 1 2 3 4 5 Cash flow 5.0 0.5 1.5 2.0 3.0 2.0 NPV @ 18% NPV @ 20% PVF P V PVF P V 0.847 0.718 0.609 0.516 0.437 (5.0) 0.42 8 1.22 1.55 0.87 0.833 0.694 0.579 0.482 0.402 (5.0) 0.42 4 1.16 1.45 0.80 0.14 (0.13) IPCC_34e_F.M_ Capital Budgeting_Assignment Solutions 19
Ph: 98851 25025/26 www.gntmasterminds.com Using Interpolation IRR = L l + = 18 + = 19.04% NPV@ L NPV@ L 1 NPV@ 1 L 2 0.14 0.14 0.13 (L 2 L 1 ) 2 = 18 + 12 = 19.04% To, Since IRR is high for Machine A, it is beneficial to purchase Machine A. Step-8: Calculation of Average Rate of Return 1. Depreciation CostScrap Life 2. Average Investment = 1 2 Particulars Machine A Machine B Initial Investment Scrap Scrap Add.W/cap 3. Average PAT. p.a. (Avg CFAT Depreciation) 1,00,000 1,00,000 2,50,000 2,50,000 70,000 1.5 22.5 1.5 1 1 5 80,000 0.5 1.5 232 1 5 4. Average Rate of Return (3) / (2) 0.28 (70,000/2,50,000) 0.32 (80,000/2,50,000) Since machines are mutually exclusive and A.R.R. is high for Machine B, it is beneficial to purchase Machine B. Conclusion: In all the above cases except in the case of A.R.R - purchase of Machine - A is beneficial. Assumptions: 1. For Pay back period: Cash flows are assumed to accrue evenly throughout the year. 2. For NPV Cash flows are assumed to accrue at the end of each year. Interim cash inflows at the end of each year are assumed to be reinvested at the rate of cost of capital. Cash flows given in the problem are assumed to be certain. 3. For IRR Cash flows are assumed to accrue at the end of each year. Interim cash inflows at the end of each year are assumed to be reinvested at the rate of IRR. Cash flows given in the problem are assumed to be certain. Problem No.21 To, (a) (i) Payback Period Project A: 10,000/10,00 = 1 year IPCC_34e_F.M_ Capital Budgeting Assignment Solutions 20
Project B: 10,000/7,500 Project C: 2 years + Project D: 1 year. = 1 1/3 years. 10,0006, 2 12,000 000 3 1 years (ii) ARR (10,00010,0001) /2 Project A: 0 (10,0001) /2 (15,00010,0001) /2 50 (10,0001) /2 5 2,,000 500 (18,00010,0001) /3 53 (10,0001) /2 5 2,,000 667 (16,00010,0001) /3 40 (10,0001) /2 5 2,,000 000 Project B: % Project C: % Project D: % To, Guntur Note: This net cash proceed includes recovery of investment also. Therefore, net cash earnings are found by deducting initial investment. (iii) IRR Project A: Project B: Project C: The net cash proceeds in year 1 are just equal to investment. Therefore, r = 0% This project produces an annuity of Rs.7,500 for two years. Therefore, the required PVAF is: 10,000/7,500 = 1.33. This factor is found under 32% column. Therefore, r = 32% Since cash flows are uneven, the trail and error method will be followed. Using 20% rate of discount the NPV is + Rs.1,389. At 30% rate of discount, the NPV is Rs.633. The true rate of return should be less than 30%. At 27% rate of discount it is found that the NPV is Rs.86 and at 26% + Rs.105. Through interpolation, we find r = 26.5% Project D: In this case also by using the trail and error method, it is found that at 37.6% rate of discount NPV becomes almost zero. Therefore, r = 37.6% (iv) NPV Project A: at 10% -10,000+10,000x0.909 = -910 at 30% -10,000+10,000x0.769 = -2,310 Project B: at 10% -10,000+7,500(0.909+0.826) = 3,013 at 30% -10,000+7,500(0.769+0.592) = +208 Project C: at 10% -10,000+2,000x0.909+4,000x0.826+12,000x0.751 = +4,134 at 30% -10,000+2,000x0.769+4,000x0.592+12,000x0.455 = -633 Project D: at 10% -10,000+10,000x0.909+3,000x(0.826+0.751) = +3,821 at 30% -10,000+10,000x0.769+3,000x(0.592+0.4555) = +831 IPCC_34e_F.M_ Capital Budgeting_Assignment Solutions 21
Ph: 98851 25025/26 www.gntmasterminds.com The Project are ranked as follows according to the various methods: Ranks Projects PB ARR IRR NPV (10%) NPV (30% A 1 4 4 4 4 B 2 2 2 3 2 C 3 1 3 1 3 D 1 3 1 2 1 (b) Payback and ARR are theoretically unsound method for choosing between the investment projects. Between the two time-adjusted (DCF) investment criteria, NPV and IRR, NPV gives consistent results. If the projects are independent (and there is no capital rationing), either IRR or NPV can be used since the same set of projects will be accepted by any of the methods. In the present case, except Project A all the three projects should be accepted if the discount rate is 10%. Only Projects B and D should be undertaken if the discount rate is 30%. If it is assumed that the projects are mutually exclusive, then under the assumption of 30% discount rate, the choice is between B and D (A and C are unprofitable). Both criteria IRR and NPV give the same results D is the best. Under the assumption of 10% discount rate, ranking according to IRR and NPV conflict (except for Project A). If the IRR rule is followed, Project D should be accepted. But the NPV rule tells that Project C is the best. The NPV rule generally gives consistent results in conformity with the wealth maximization principle. Therefore, Project C should be accepted following the NPV rule. PROBLEM NO. 22 Step 1:Calculation of Present Value of Cash Outflows Particulars Machine -1 Machine -2 Cost of Machine 15,00,000 20,00,000 Step 2:Calculation of Depreciationp.a Depreciation cos t life scrap 15,00 5, 000 20,00 5, 000 a) Machine 1 = 3,00,000 b) Machine 2 =4,00,000 Step 3:Calculation of Present Value of Operating Cash inflow Particulars Machine 1 Machine 2 a) PBDT 6,25,000 8,75,000 b) Depreciation 3,00,000 4,00,000 c) PBT 3,25,000 4,75,000 d) Tax @30% 97,500 1,42,500 e) PAT 2,27,500 3,32,500 f) CFAT (e+b) 5,27,500 7,32,500 P.V of operating cashinflow Machine 1 = 5,27,500 x PVAF (12%, 5y) Machine 2 = 7,32,500 x PVAF (12%, 5y) = 5,27,500 x 3.605 = 7,32,500 x 3.605 = 19,01,637.5 = 26,40,662.5 IPCC_34e_F.M_ Capital Budgeting Assignment Solutions 22
Step 4: Present Value of Terminal Cash inflow = 0 Part A: Calculation of NPV NPV =PV of Operating Cash Inflows + PV of Terminal Cash Inflows PV of Cash Outflows a) Machine 1 NPV = 19,01,637 + 0 15,00,000 = 4,01,637.5 b) Machine 2 NPV = 26,40,662.5 20,00,000 Profitability index =6,40,664 PV ofcashinflows PV ofcashoutflows a) Machine 1 Profitability index 19,01,639 1. 268 Part B: Calculation of Profitability Index 15,00,000 b) Machine II Profitability index 26,40,664 1. 320 15,00,000 Step:1 Calculation of cumulative cash inflows Part C: Calculation of Discounted Pay Back Period Machine I Machine II Year PVF @ 2% Cash flow PV Cumulative PV Cash flow PV Cumulative PV 1 0.893 5,27,500 4,71,058 4,71,058 7,32,500 6,54,123 6,54,123 2 0.797 5,27,500 4,20,418 8,91,476 7,32,500 5,83,803 12,37,926 3 0.712 5,27,500 3,75,580 12,67,056 7,32,500 5,21,540 17,59,466 4 0.636 5,27,500 3,35,490 16,02,546 7,32,500 4,65,870 22,25,336 5 0.567 5,27,500 2,99,093 19,01,639 7,32,500 4,15,328 26,40,664 Step 2: Calculation of Discounted Pay Back Period Machine 1 Discounted Pay Back Period Machine II 3 (15,00,00012,67,056) 3,35,490 3 3 2,32,35,490, 944 = 3+0.6943 = 3.69 years Discounted payback period3 (20,00,000 17,59,466) 4,65,870 3 2,40 4,65,,870 534 = 3 + 0.5163 = 3.52 years or 3 years 6.24 months THE END IPCC_34e_F.M_ Capital Budgeting_Assignment Solutions 23