Answers-to-Assignments-3

11-7 a. Project A: CF0 = -6000; CF1-5 = 2000; I/YR = 14. Solve for NPVA = $866.16. IRRA = 19.86%. MIRR calculation: 0 | 14% -6,000 1 | 2 | 3 | 4 | 2,000 2,000 2,000 2,000  1.14  (1.14)2 3  (1.14)  (1.14)4 5 | 2,000 2,280.00 2,599.20 2,963.09 3,377.92 13,220.21 Using a financial calculator, enter N = 5; PV = -6000; PMT = 0; FV = 13220.21; and solve for MIRRA = I/YR = 17.12%. Payback calculation: 0 | -6,000 Cumulative CF: -6,000 1 | 2,000 -4,000 2 | 2,000 -2,000 3 | 2,000 0 4 | 2,000 2,000 5 | 2,000 4,000 Regular PaybackA = 3 years. Discounted payback calculation: 0 14% 1 2 3 4 5 | | | | | | -6,000 2,000 2,000 2,000 2,000 2,000 Discounted CF: -6,000 1,754.39 1,538.94 1,349.94 1,184.16 1,038.74 Cumulative CF: -6,000 -4,245.61 -2,706.67 -1,356.73 -172.57 866.17 Discounted PaybackA = 4 + $172.57/$1,038.74 = 4.17 years. Project B: CF0 = -18000; CF1-5 = 5600; I/YR = 14. Solve for NPVB = $1,225.25. IRRB = 16.80%. MIRR calculation: 0 14% 1 | | -18,000 5,600 2 | 5,600 3 | 5,600 4 | 5,600  1.14  (1.14)2  (1.14)3 4  (1.14) 5 | 5,600 6,384.00 7,277.76 8,296.65 9,458.18 37,016.59 Using a financial calculator, enter N = 5; PV = -18000; PMT = 0; FV = 37016.59; and solve for MIRRB = I/YR = 15.51%. Payback calculation: 0 1 | | -18,000 5,600 Cumulative CF: -18,000 -12,400 2 | 5,600 -6,800 3 | 5,600 -1,200 4 | 5,600 4,400 5 | 5,600 10,000 Regular PaybackB = 3 + $1,200/$5,600 = 3.21 years. Discounted payback calculation: 0 14% 1 2 3 4 5 | | | | | | -18,000 5,600 5,600 5,600 5,600 5,600 Discounted CF: -18,000 4,912.28 4,309.02 3,779.84 3,315.65 2,908.46 Cumulative CF: -18,000 -13,087.72 -8,778.70 -4,998.86 -1,683.21 1,225.25 Discounted PaybackB = 4 + $1,683.21/$2,908.46 = 4.58 years. Summary of capital budgeting rules results: NPV IRR MIRR Payback Discounted payback Project A $866.16 19.86% 17.12% 3.0 years 4.17 years Project B $1,225.25 16.80% 15.51% 3.21 years 4.58 years b. If the projects are independent, both projects would be accepted since both of their NPVs are positive. c. If the projects are mutually exclusive then only one project can be accepted, so the project with the highest positive NPV is chosen. Accept Project B. d. The conflict between NPV and IRR occurs due to the difference in the size of the projects. Project B is 3 times larger than Project A. 11-12 Input the appropriate cash flows into the cash flow register, and then calculate NPV at 10% and the IRR of each of the projects: Project S: CF0 = -1000; CF1 = 900; CF2 = 250; CF3-4 = 10; I/YR = 10. Solve for NPVS = $39.14; IRRS = 13.49%. Project L: CF0 = -1000; CF1 = 0; CF2 = 250; CF3 = 400; CF4 = 800; I/YR = 10. Solve for NPVL = $53.55; IRRL = 11.74%. Since Project L has the higher NPV, it is the better project, even though its IRR is less than Project S’s IRR. The IRR of the better project is IRRL = 11.74%. 12-2 a. Project cash flows: t = 1 Sales revenues Operating costs Depreciation EBIT Taxes (40%) EBIT(1 – T) Add back depreciation Project cash flow = EBIT(1 – T) + DEP $10,000,000 7,000,000 2,000,000 $ 1,000,000 400,000 $ 600,000 2,000,000 $ 2,600,000 b. The cannibalization of existing sales needs to be considered in this analysis on an after-tax basis, because the cannibalized sales represent sales revenue the firm would realize without the new project but would lose if the new project is accepted. Thus, the after-tax effect would reduce the project’s cash flow by $1,000,000(1 – T) = $1,000,000(0.6) = $600,000. Thus, the project’s cash flow would now be $2,000,000 rather than $2,600,000. c. If the tax rate fell to 30%, the project’s cash flow would change to: EBIT Taxes (30%) EBIT(1 – T) Add back depreciation Project cash flow = EBIT(1 – T) + DEP $1,000,000 300,000 $ 700,000 2,000,000 $2,700,000 Thus, the project’s cash flow would increase by $100,000. 12-7 a. CF0 = -$178,000: Initial investment outlay at t = 0: Price Modification CAPEX NOWC Initial investment outlay ($140,000) (30,000) ($170,000) (8,000) ($178,000) b. Project’s operating cash flows: Savings Depreciation EBIT Taxes (40%) EBIT(1 – T) Add Depreciation EBIT(1 –T) + DEP Year 1 $50,000 56,100 ($ 6,100) (2,440) ($ 3,660) 56,100 $52,440 Year 2 $50,000 76,500 ($26,500) (10,600) ($15,900) 76,500 $60,600 Terminal cash flows at t = 3: Salvage value Tax on salvage value AT salvage value NOWC = Recovery of NOWC Project FCFs = EBIT(1 – T) + DEP – CAPEX – NOWC Year 3 $50,000 25,500 $24,500 9,800 $14,700 25,500 $40,200 $60,000 19,240 $40,760 8,000 $52,440 $60,600 $88,960 Notes: 1. The depreciation expense in each year is the depreciable basis, $170,000, times the MACRS allowance percentages of 0.33, 0.45, and 0.15 for Years 1, 2, and 3, respectively. Depreciation expense in Years 1, 2, and 3 is $56,100, $76,500, and $25,500. 2. Remaining BV in Year 4 = $170,000(0.07) = $11,900. Tax on SV = ($60,000 – $11,900)(0.4) = $19,240. c. The project has an NPV of ($19,549). Thus, it should not be accepted. Year 0 1 2 3 Cash Flows ($178,000) 52,440 60,600 88,960 PV @ 12% ($178,000) 46,821 48,310 63,320 NPV = ($ 19,549) Alternatively, place the free cash flows on a time line: Initial investment outlay EBIT(1 – T) + DEP Terminal cash flows Project FCFs 0 | -178,000 -178,000 12% 1 | 2 | 3 | 52,440 60,600 52,440 60,600 40,200 48,760 88,960 With a financial calculator, input the cash flows into the cash flow register, I/YR = 12, and then solve for NPV = -$19,548.65  -$19,549. 12-9 First determine the net cash flow at t = 0: Purchase price Sale of old machine Tax on sale of old machine Change in net operating working capital Total investment ($8,000) 2,500 (160)a (1,500)b ($7,160) a The market value is $2,500 – $2,100 = $400 above the book value. Thus, there is a $400 recapture of depreciation, and Dauten would have to pay 0.40($400) = $160 in taxes. b The change in net operating working capital is a $2,000 increase in current assets minus a $500 increase in accounts payable, which totals to $1,500. Now, examine the annual cash inflows: Sales increase Cost decrease Increase in pre-tax revenues After-tax revenue increase: $2,500(1 – T) = $2,500(0.60) = $1,500. $1,000 1,500 $2,500 Depreciation: Year Newa Old Change 1 $1,600 350 $1,250 2 $2,560 350 $2,210 3 $1,520 350 $1,170 4 $960 350 $610 5 $880 350 $530 6 $480 350 $130 Depreciation tax savingsb $ 500 $ 884 $ 468 $244 $212 $ 52 a Depreciable basis = $8,000. Depreciation expense in each year equals depreciable basis times the MACRS percentage allowances of 0.20, 0.32, 0.19, 0.12, 0.11, and 0.06 in Years 1-6, respectively. b Depreciation tax savings = T(Depreciation) = 0.4(Depreciation). Now recognize that at the end of Year 6 Dauten would recover its net operating working capital investment of $1,500, and it would also receive $800 from the sale of the replacement machine. However, since the machine would be fully depreciated, the firm must pay 0.40($800) = $320 in taxes on the sale. Also, by undertaking the replacement now, the firm forgoes the right to sell the old machine for $500 in Year 6; thus, this $500 in Year 6 must be considered an opportunity cost in that year. Taxes of $500(0.4) = $200 would be due because the old machine would be fully depreciated in Year 6, so the opportunity cost of the old machine would be $500 – $200 = $300. Finally, place all the cash flows on a time line: Net investment After-tax revenue increase Depreciation tax savings NOWC recovery Salvage value of new machine Tax on salvage value of new machine Opportunity cost of old machine Project cash flows 0 15% | (7,160) 1 | 1,500 500 2 | 1,500 884 3 | 1,500 468 4 | 1,500 244 5 | 1,500 212 6 | 1,500 52 1,500 800 (320) (7,160) 2,000 2,384 1,968 1,744 1,712 (300) 3,232 The net present value of this incremental cash flow stream, when discounted at 15%, is $921.36. Thus, the replacement should be made. 13-2 The optimal capital structure is that capital structure where WACC is minimized and stock price is maximized. Because Jackson’s stock price is maximized at a 30% debt-to-capital ratio, the firm’s optimal capital structure is 30% debt and 70% equity. This is also the debt level where the firm’s WACC is minimized. 13-4 From the Hamada equation, b = bU[1 + (1 – T)(D/E)], we can calculate bU as bU = b/[1 + (1 – T)(D/E)]. bU = 1.2/[1 + (1 – 0.4)($2,000,000/$8,000,000)] bU = 1.2/[1 + 0.15] bU = 1.0435. 13-6 a. 8,000 units $200,000 140,000 120,000 $260,000 ($ 60,000) Sales Fixed costs Variable costs Total costs Gain (loss) b. QBE = 18,000 units $450,000 140,000 270,000 $410,000 $ 40,000 F $140,000 = = 14,000 units. $10 PV SBE = QBE(P) = (14,000)($25) = $350,000. Dollars 800,000 600,000 Sales Costs 400,000 200,000 Fixed Costs 0 5 10 15 20 Units of Output (Thousands) c. If the selling price rises to $31, while the variable cost per unit remains fixed, P – V rises to $16. The end result is that the break-even point is lowered. QBE = $140,000 F = = 8,750 units. $16 PV SBE = QBE(P) = (8,750)($31) = $271,250. Dollars 800,000 Sales 600,000 Costs 400,000 200,000 Fixed Costs 0 5 10 15 20 Units of Output (Thousands) The break-even point drops to 8,750 units. The contribution margin per each unit sold has been increased; thus the variability in the firm’s profit stream has been increased, but the opportunity for magnified profits has also been increased. d. If the selling price rises to $31 and the variable cost per unit rises to $23, P – V falls to $8. The end result is that the break-even point increases. QBE = F $140,000 = = 17,500 units. P-V $8 SBE = QBE(P) = (17,500)($31) = $542,500. The break-even point increases to 17,500 units because the contribution margin per each unit sold has decreased. Dollars 800,000 Sales Costs 600,000 400,000 200,000 Fixed Costs 0 13-9 a. 5 10 15 20 Units of Output (Thousands) The current dividend per share, D0, = $400,000/200,000 = $2.00. D1 = $2.00(1.05) = $2.10. Therefore, P0 = D1/(rs – g) = $2.10/(0.134 – 0.05) = $25.00. b. Step 1: Calculate EBIT before the recapitalization: EBIT = $1,000,000/(1 – T) = $1,000,000/0.6 = $1,666,667. Note: The firm is 100% equity financed, so there is no interest expense. Step 2: Calculate net income after the recapitalization: [$1,666,667 – 0.11($1,000,000)]0.6 = $934,000. Step 3: Calculate the number of shares outstanding after the recapitalization: 200,000 – ($1,000,000/$25) = 160,000 shares. Step 4: Calculate D1 after the recapitalization: D0 = 0.4($934,000/160,000) = $2.335. D1 = $2.335(1.05) = $2.45175. Step 5: Calculate P0 after the recapitalization: P0 = D1/(rs – g) = $2.45175/(0.145 – 0.05) = $25.8079  $25.81. 14-1 70% Debt; 30% Equity; Capital budget = $3,000,000; NI = $2,000,000; PO = ? Equity retained = 0.3($3,000,000) = $900,000. NI – Additions to RE Earnings remaining Payout = 14-2 $2,000,000 900,000 $1,100,000 $1,100,000 = 55%. $2,000,000 P0 = $90; Split = 3 for 2; New P0 = ? $90 = $60. 3 /2 14-3 NI = $2,000,000; Shares = 1,000,000; P0 = $32; Repurchase = 20%; New P0 = ? Repurchase = 0.2  1,000,000 = 200,000 shares. Repurchase amount = 200,000  $32 = $6,400,000. EPSOld = P/E = $2,000,000 NI = $2.00. = 1,000,000 Shares $32 = 16. $2 EPSNew = $2,000,000 $2,000,000 = = $2.50. 800,000 1,000,000  200,000 PriceNew = EPSnew  P/E = $2.50(16) = $40. 14-4 DPS after split = $0.75. Equivalent pre-split dividend = $0.75(5) = $3.75. New equivalent dividend = Last year’s dividend(1.09) $3.75 = Last year’s dividend(1.09) Last year’s dividend = $3.75/1.09 = $3.44. 14-5 Retained earnings = Net income (1 – Payout ratio) = $5,000,000(0.55) = $2,750,000. External equity needed: Total equity required = (New investment)(1 – Debt ratio) = $10,000,000(0.60) = $6,000,000. New external equity needed = $6,000,000 – $2,750,000 = $3,250,000. 14-6 Step 1: Determine the capital budget by selecting those projects whose returns are greater than the project’s risk-adjusted cost of capital. Projects H and L should be chosen because IRR > WACC, so the firm’s capital budget = $10 million. Step 2: Determine how much of the capital budget will be financed with equity. Capital Budget  Equity % = Equity required. $10,000,000  0.5 = $5,000,000. Step 3: Determine dividends through residual model. $7,287,500 – $5,000,000 = $2,287,500. Step 4: Calculate payout ratio. $2,287,500/$7,287,500 = 0.3139 = 31.39%. 15-1 1. Sales = $15,000,000; Inventory = $2,000,000; A/R = $3,000,000; A/P = $1,000,000; COGS = 0.8(Sales); Interest on bank loan = 8%; CCC = ? CCC = Inventory conversion period + Average collection period – Payables deferral period. Inventory Cost of goods sold per day $2,000,000 = [(0.8)($15,000,000)]/365 $2,000,000 = $32,876.7123 = 60.83 days. Inventory conversion period Average collection period = Receivable s Sales/365 $3,000,000 = $15,000,000 /365 = 73 days. = Payables deferral period Payables Cost of goods sold/365 $1,000,000 = $32,876.7123 = 30.42 days. = CCC = 60.83 + 73 – 30.42 = 103.41 days. 2. Lower inventories and receivables by 10% each and increase payables by 10%. Sales and COGS remain the same. Inventory = $2,000,000  0.9 = $1,800,000. A/R = $3,000,000  0.9 = $2,700,000. A/P = $1,000,000  1.1 = $1,100,000. Calculate new CCC: Inventory conversion period Average collection period Payables deferral period $1,800,000 $32,876.7123 = 54.75 days. = $2,700,000 $15,000,000 /365 = 65.70 days. = $1,100,000 $32,876.7123 = 33.46 days. = New CCC = 54.75 + 65.70 – 33.46 = 86.99 days ≈ 87 days. 3. Cash freed up:  Inventory = (60.83 – 54.75)  $32,876.7123 = $199,890.41.  Receivables = (73 – 65.70)  $41,095.8904 = $300,000.  Payables = (30.42 – 33.46)  $32,876.7123 = -$99,945.21. Cash freed up = $199,890.41 + $300,000 – (-$99,945.21) = $599,835.62 ≈ $600,000. $600,000  0.08 = $48,000 increase in pre-tax profit. 15-3 Purchases = $8,000,000; terms = 3/5 net 60; currently pays on Day 5 and takes discounts. Forgoes discounts; additional credit = ? $8,000,000/365  55 days = $1,205,479.45. Nominal cost of trade credit = 3 365  = 3.09%  6.6364 = 20.52%. 97 55 Effective cost of trade credit = (1 + 3/97)365/55 – 1 = 1.2240 – 1 = 22.40%. Bank loan: 10%, interest paid monthly EAR = (1 + 0.10/12)12 – 1 = 1.1047 – 1 = 10.47%. Because the effective cost of the bank loan is less than half the effective cost of the trade credit, the bank loan should be used. 15-4 a. Cash conversion cycle Inventory Receivables Payables = conversion  collection  deferral period period period = 75 + 38 – 30 = 83 days. b. Average sales per day = $3,421,875/365 = $9,375. Investment in receivables = $9,375  38 = $356,250. c. Step 1: Calculate inventory balance from inventory conversion period: Inventory $3,421,875 0.75  365 Inventory 75 = $7,031.25 Inventory = $527,343.75. 75 = Step 2: Calculate inventory turnover ratio: $3,421,875 $527,343.75 = 6.49×. Inventory turnover =