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FM09-CH 10....IM PANDEY

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SOLUTIONS OF NUMERICALS
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  Ch. 10: Determining Cash Flows for Investment Analysis 1 CHAPTER 10 DTERMINING CASH FLOWS FOR INVESTMENT ANALYSIS Problem 1 Assumption: (1) It is assumed that the given annual  c ash inflows are after-tax. (2) ARR is calculated as average cash profit divided by srcinal investment. Alternatively, average investment (srcinal investment/2) can be used for calculation. Required rate 10% Tax rate 35% Projects A B C D E Outlay -500,000 -120,000 -92,000 -5,750 -40,000 Annual inflows 125,000 12,000 15,000 2,000 6,000 Life 8 15 20 5 10 PVAF @10% 5.3349 7.6061 8.5136 3.7908 6.1446 PV of NCF 666,865.8 91,273.0 127,703.5 7,581.6 36,867.4 NPV 166,865.8 -28,727.0 35,703.5 1,831.6 -3,132.6 IRR 18.6% 5.6% 15.4% 21.8% 8.1% PB (years) 4.00 10.00 6.13 2.88 6.67 ARR 25.0% 10.0% 16.3% 34.8% 15.0% Rank Project NPV IRR PB ARR A 1 2 2 2 B 5 5 5 5 C 2 3 3 3 D 3 1 1 1 E 4 4 4 4 Problem 2 Cost of capital 10% Tax rate 43% Cost of project X 20,000 Life of project X 5 Straight line depreciation 4,000 Cost of project Y 15,000 Life of project Y 5 Straight line depreciation 3,000 PROJECT X Year 0 1 2 3 4 5 BT cash flows -20,000 4,200 4,800 7,000 8,000 2,000 AT cash flows (T = 35%) 2,730 3,120 4,550 5,200 1,300 Add: DTS (Dep. × T = 4,000 × .35 ) 1,400 1,400 1,400 1,400 1,400 NCF -20,000 4,130 4,520 5,950 6,600 2,700 PVF 1.000 0.909 0.826 0.751 0.683 0.621 PV (Rs) -20,000 3,755 3,736 4,470 4,508 1,676 NPV (Rs) -1,855 PI 0.91  I. M. Pandey, Financial Management, 9 th  Edition, New Delhi: Vikas. 2 IRR 6.29% Accumulated cash flows -20000 -15870 -11350 -5400 1200 3900 Payback (years) 4 PROJECT Y Year 0 1 2 3 4 5 BT cash flows -15,000 4,200 4,500 4,000 5,000 1,000 AT cash flows (T = 35%) 2,730 2,925 2,600 3,250 650 Add: DTS (Dep. × T = 3,000 × .35 ) 1,050 1,050 1,050 1,050 1,050 NCF -15,000 3,780 3,975 3,650 4,300 1,700 PVF 1.000 0.909 0.826 0.751 0.683 0.621 PV (Rs) -15,000 3,436 3,285 2,742 2,937 1,056 NPV (Rs) -1,544 PI 0.90 IRR 5.59% Cumulative cash flows -15000 -11220 -7245 -3595 705 2405 Payback (years) 4 Both projects have negative NPV and IRR less than the cost of capital. They should be rejected. Problem 3 Required rate of return (RRR) 10% Tax rate 35% Outlay M: 100,000 Life (years) 5 S L depreciation: 100,000/5 20,000 Salvage value (SV) 0 Outlay N: 140,000 Life (years) 5 SV 20,000 S L depreciation: 140,000/5 28,000 PROJECT M Year 0 1 2 3 4 5 Book value (BV) 100,000 80,000 60,000 40,000 20,000 0 SL depreciation 20,000 20,000 20,000 20,000 20,000 Earnings before depreciation & tax 25,000 25,000 25,000 25,000 25,000 Less: dep. 20,000 20,000 20,000 20,000 20,000 Earnings before tax 5,000 5,000 5,000 5,000 5,000 Tax at 35% 1750 1750 1750 1750 1750 Earnings after tax (EAT) 3,250 3,250 3,250 3,250 3,250 Plus: dep. 20,000 20,000 20,000 20,000 20,000 Plus: SV 0 NCF -100,000 23,250 23,250 23,250 23,250 23,250 PVF 1.000 0.909 0.826 0.751 0.683 0.621 PV (Rs) -100,000 21,136 19,215 17,468 15,880 14,436 NPV (Rs) -11,864 IRR 5.24%  Ch. 10: Determining Cash Flows for Investment Analysis 3 Cumulative NCF -100,000 -76,750 -53,500 -30,250 -7,000 16,250 Payback (years) 4 1/2 Project N Year 0 1 2 3 4 5 Book value 140,000 112,000 84,000 56,000 28,000 0 S L depreciation 28,000 28,000 28,000 28,000 28,000 Earnings before depreciation & taxes 40,000 40,000 40,000 40,000 40,000 Less: dep. 28,000 28,000 28,000 28,000 28,000 Earnings before taxes 12,000 12,000 12,000 12,000 12,000 Tax 4,200 4,200 4,200 4,200 4,200 Earnings after tax 7,800 7,800 7,800 7,800 7,800 Plus: dep. 28,000 28,000 28,000 28,000 28,000 After-tax salvage 13,000 NCF -140,000 35,800 35,800 35,800 35,800 48,800 PVF 1.000 0.909 0.826 0.751 0.683 0.621 PV (Rs) -140,000 32,545 29,587 26,897 24,452 30,301 NPV (Rs) 3,782 IRR 11.0% Cum. NCF -140,000 -104,200 -68,400 -32,600 3,200 52,000 Payback 4 * After-tax salvage: 20,000 - .35(20,000 – 0) = Rs 13,000. Problem 4 Year 0 1 2 3 IRR NPV, 12% O -50,000 25,270 25,270 25,270 0.24 10,694.3 P -25,000 5,000 5,000 25,570 0.15 1,650.5 Q -28,000 12,670 12,670 12,670 0.17 2,431.2 (P - Q) 3,000 -7,670 -7,670 12,900 (780.7) Project O has the highest NPV; hence it should be preferred over other projects. Between projects P and Q, Q is better with higher NPV. The incremental cash flow analysis also shows that P losses NPV when compared with Q. Problem 5 Year 0 1 2 3 NPV, 10% IRR A -6,000 8,000 2,000 2,000 4,428.2 65.6% B -8,000 12,000 4,000 5,649.9 78.1% (A - B) -6,000 16,000 -10,000 -2,000 (1,221.6) Both absolute and incremental analyses reveal that B is a better project than A. Problem 6 Year 0 1 2 3 4 NPV, 10% IRR Cash flow 7,000 7,000 7,000 7,000 -25,000 7,332.6 -4.5% Problem 7 RRR 10% Tax rate 40% Purchase price 40,000 Installation 8,000 Total cost 48,000  I. M. Pandey, Financial Management, 9 th  Edition, New Delhi: Vikas. 4 Plus: WC 10,000 Less: SV, old 20,000 no tax assumed Initial outlay 38,000 SV, new (4 yrs) 14,000 SV, old (4 yrs) 4,000 Differential SV after 4 years 10,000 no tax assumed BV, old 16,000 Life (years), new 4 Life (years), old 4 SL dep., new 12,000 SL dep., old 4,000 Differential dep. 8,000 Diff. DTS (depreciation tax shield): 8,000 × 0.40 3,200 Year 0 1 2 3 4 Initial outlay -38,000 BT cash flows 16,000 16,000 16,000 16,000 AT cash flows: 16,000 × (1-.4) 9,600 9,600 9,600 9,600 DTS 3,200 3,200 3,200 3,200 Differential SV 10,000 NCF -38,000 12,800 12,800 12,800 22,800 NPV 9,404.4 IRR 20% Problem 8 Investment 300,000 Required rate 15% Tax rate 30% Investment period 13 Building 140,000 Merchandise 100,000 Working capital 60,000 Total investment 300,000 Annual receipts 390,000 Less: Costs 300,000 Less: SL dep. on build. (140,000/13) 10,769 Pre-tax savings 79,231 Tax @ 30% 23,769 Post-tax savings 55,462 Add: Dep. 10,769 Less: Loss of salary (no tax on salary assumed) 36,000 NCF (annuity) 30,231 Post-tax SV: 50,000 × (1 – 0.3) 35,000 Release of WC and merchandise 160,000
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