Chapter 02 - Financial Statements, Taxes, and Cash Flow 2. The income statement starts with revenues and subtracts costs to arrive at EBIT. We then subtract out interest to get taxable income, and then subtract taxes to arrive at net income. Doing so, we get: Income Statement Sales $585,000 Costs 273,000 Depreciation 71,000 EBIT $241,000 Interest 38,000 Taxable income $203,000 Taxes 71,050 Net income $131,950 16. We can fill in the balance sheet with the numbers we are given. The balance sheet will be: Balance Sheet Cash $193,000 Accounts payable $296,000 Accounts receivable 253,000 Notes payable 189,000 Inventory 538,000 Current liabilities $485,000 Current assets $984,000 Long-term debt 1,250,000 Total liabilities $1,735,000 Tangible net fixed assets $5,100,000 Intangible net fixed assets 847,000 Common stock ?? Accumulated retained earnings 4,586,000 Total assets $6,931,000 Total liabilities & owners’ equity $6,931,000 Owners’ equity has to be total liabilities & equity minus accumulated retained earnings and total liabilities, so: Owner’s equity = Total liabilities & equity – Accumulated retained earnings – Total liabilities Owners’ equity = $6,931,000 – 4,586,000 – 1,735,000 Owners’ equity = $610,000 21. a. To calculate the OCF, we first need to construct an income statement. The income statement starts with revenues and subtracts costs to arrive at EBIT. We then subtract out interest to get taxable income, and then subtract taxes to arrive at net income. Doing so, we get: Income Statement Sales $19,780 Cost of goods sold 13,980 Depreciation 2,370 EBIT $ 3,430 Interest 345 Taxable income $ 3,085 Taxes (35%) 1,080 Net income $ 2,005 b. OCF = EBIT + Depreciation – Taxes OCF = $3,430 + 2,370 – 1,080 = $4,720 34. Short-term solvency ratios: Current ratio = Current assets / Current liabilities Current ratio2010 = $23,150 / $4,739 Current ratio2010 = 4.88 times Quick ratio = (Current assets – Inventory) / Current liabilities Quick ratio2010 = ($23,150 – 13,822) / $4,739 Quick ratio2010 = 1.97 times Cash ratio = Cash / Current liabilities Cash ratio2010 = $3,507 / $4,739 Cash ratio2010 = 0.74 times Asset utilization ratios: Total asset turnover = Sales / Total assets Total asset turnover = $186,570 / $96,119 Total asset turnover = 1.94 times Inventory turnover = COGS / Inventory Inventory turnover = $125,803 / $13,822 Inventory turnover = 9.10 times Receivables turnover = Sales / Receivables Receivables turnover = $186,570 / $5,821 Receivables turnover = 32.05 times Long-term solvency ratios: Total debt ratio = (Current liabilities + Long-term debt) / Total assets Total debt ratio2010 = ($4,739 + 16,560) / $96,119 Total debt ratio2010 = 0.22 Debt-equity ratio = (Current liabilities + Long-term debt) / Total equity Debt-equity ratio2010 = ($4,739 + 16,560) / $74,820 Debt-equity ratio2010 = 0.28 Equity multiplier = 1 + D/E ratio Equity multiplier2010 = 1 + 0.28 Equity multiplier2010 = 1.28 Times interest earned = EBIT / Interest Times interest earned = $55,394 / $1,470 Times interest earned = 37.68 times Cash coverage ratio = (EBIT + Depreciation) / Interest Cash coverage ratio = ($55,394 + 5,373) / $1,470 Cash coverage ratio = 41.34 times Profitability ratios: Profit margin = Net income / Sales Profit margin = $35,051 / $186,570 Profit margin = 0.1879 or 18.79% Return on assets = Net income / Total assets Return on assets = $35,051 / $96,119 Return on assets = 0.3647 or 36.47% Return on equity = Net income / Total equity Return on equity = $35,051 / $74,820 Return on equity = 0.4685 or 46.85% 36. To find the price-earnings ratio we first need the earnings per share. The earnings per share are: EPS = Net income / Shares outstanding EPS = $35,051 / 10,000 EPS = $3.51 P/E ratio = Share price / EPS P/E ratio = $73 / $3.51 P/E ratio = 20.83 Sales per share = Sales / Shares outstanding Sales per share = $186,570 / 10,000 Sales per share = $18.66 P/S ratio = Share price / Sales per share P/S ratio = $73 / $18.66 P/S ratio = 3.91 Dividends per share = Total dividends /Shares outstanding Dividends per share = $11,865 / 10,000 shares Dividends per share = $1.19 per share To find the market-to-book ratio, we first need the book value per share. The book value per share is: Book value per share = Total equity / Shares outstanding Book value per share = $74,820 / 10,000 shares Book value per share = $7.48 per share Market-to-book ratio = Share price / Book value per share Market-to-book ratio = $73 / $7.48 Market-to-book ratio = 9.76 times 11. To find the PV of a lump sum, we use: PV = FV / (1 + r)t PV = $2,000,000 / (1.09)80 PV = $2,027.26 18. To find the FV of a lump sum, we use: FV = PV(1 + r)t FV = $5,000(1.1050)45 FV = $446,963.97 If you wait 10 years, the value of your deposit at your retirement will be: FV = $5,000(1.1050)35 FV = $164,683.37 Better start early! 9. Here we have the PVA, the length of the annuity, and the interest rate. We want to calculate the annuity payment. Using the PVA equation: PVA = C({1 – [1/(1 + r)t]} / r ) $60,000 = C{[1 – (1/1.09)7 ] / .09} We can now solve this equation for the annuity payment. Doing so, we get: C = $60,000 / 5.03295 C = $11,921.43 50. Here, we have an annuity with two different interest rates. To answer this question, we simply need to find the present value in multiple steps. The present value of the last six years payments at a 7 percent interest rate is: PVA = C({1 – [1/(1 + r)t]} / r )) PVA = $2,500[{1 – 1 / [1 + (.07/12)]72} / (.07/12)] PVA = $146,636.11 We can now discount this value back to time zero. We must be sure to use the number of months as the periods since interest is compounded monthly. We also need to use the interest rate that applies during the first four years. Doing so, we find: PV = FV / (1 + r)t PV = $146,636.11 / (1 + .09/12)48 PV = $102,442.06 Now we can find the present value of the annuity payments for the first four years. The present value of these payments is: PVA = C({1 – [1/(1 + r)t]} / r ) PVA = $2,500[{1 – 1 / [1 + (.09/12)]48} / (.09/12)] PVA = $100,461.95 So, the total present value of the cash flows is: PV = $102,442.06 + 100,461.95 PV = $202,904.01 4. Here, we need to find the YTM of a bond. The equation for the bond price is: P = $1,145.70 = $100(PVIFAR%,9) + $1,000(PVIFR%,9) Notice the equation cannot be solved directly for R. Using a spreadsheet, a financial calculator, or trial and error, we find: R = YTM = 7.70% If you are using trial and error to find the YTM of the bond, you might be wondering how to pick an interest rate to start the process. First, we know the YTM has to be lower than the coupon rate since the bond is a premium bond. That still leaves a lot of interest rates to check. One way to get a starting point is to use the following equation, which will give you an approximation of the YTM: Approximate YTM = [Annual interest payment + (Par value – Price) / Years to maturity] / [(Price + Par value) / 2] Solving for this problem, we get: Approximate YTM = [$100 + (–$145.70 / 9)] / [($1,145.70 + 1,000) / 2] Approximate YTM = .0781 or 7.81% This is not the exact YTM, but it is close, and it will give you a place to start. 6. To find the price of this bond, we need to realize that the maturity of the bond is 14 years. The bond was issued one year ago, with 15 years to maturity, so there are 14 years left on the bond. Also, the coupons are semiannual, so we need to use the semiannual interest rate and the number of semiannual periods. The price of the bond is: P = $30.50(PVIFA2.65%,28) + $1,000(PVIF2.65%,28) P = $1,078.37 29. The bond price equation is: P = $35.625(PVIFA3.01%,14) + $1,000(PVIF3.01%,14) P = $1,062.37 The current yield is the annual coupon payment divided by the bond price, so: Current yield = $71.25 / $1,062.37 Current yield = .0671 or 6.71% 2. We need to find the required return of the stock. Using the constant growth model, we can solve the equation for R. Doing so, we find: R = (D1 / P0) + g R = ($2.45 / $48.50) + .055 R = .1055 or 10.55% 4. Using the constant growth model, we find the price of the stock today is: P0 = D1 / (R – g) P0 = $3.85 / (.12 – .0475) P0 = $53.10 13. Here, we have a stock that pays no dividends for nine years. Once the stock begins paying dividends, it will have a constant growth rate of dividends. We can use the constant growth model at that point. This means that since we will use the dividend in Year 10, we will be finding the stock price in Year 9. The dividend growth model is similar to the present value of an annuity and the present value of a perpetuity: The equation gives you the present value one period before the first payment. So, the price of the stock in Year 9 will be: P9 = D10 / (R – g) P9 = $12.00 / (.13 – .05) P9 = $150.00 The price of the stock today is simply the PV of the stock price in the future. We simply discount the future stock price at the required return. The price of the stock today will be: PV = ?, FV = 150, PMT = N/A, N = 9, I = 13 P0 = $49.93 3. Project A has cash flows of: Cash flows = $17,000 + 23,000 Cash flows = $40,000 during the first two years. The cash flows are still short by $5,000 of recapturing the initial investment, so the payback for Project A is: Payback = 2 + ($5,000 / $19,000) Payback = 2.26 years Project B has cash flows of: Cash flows = $19,000 + 24,000 + 35,000 Cash flows = $78,000 during the first three years. The cash flows are still short by $12,000 of recapturing the initial investment, so the payback for Project B is: Payback = 3 + ($12,000 / $250,000) Payback = 3.05 years Using the payback criterion and a cutoff of 3 years, accept project A and reject project B. 5. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is: 0 = – $145,000 + $71,000/(1+IRR) + $68,000/(1+IRR)2 + $52,000/(1+IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 16.02% Since the cash flows are conventional and the IRR is greater than the required return, we would accept the project. 6. The NPV of a project is the PV of the outflows minus by the PV of the inflows. The equation for the NPV of this project at a 10 percent required return is: NPV = – $145,000 + $71,000/1.10 + $68,000/1.102 + $52,000/1.103 NPV = $14,812.17 At a 10 percent required return, the NPV is positive, so we would accept the project. The equation for the NPV of the project at a 21 percent required return is: NPV = – $145,000 + $71,000/1.21 + $68,000/1.212 + $52,000/1.213 NPV = – $10,524.75 At a 21 percent required return, the NPV is negative, so we would reject the project. 8. We need to calculate the OCF, so we need an income statement. The lost sales of the current sound board sold by the company will be a negative since it will lose the sales. Sales of new $35,700,000 Lost sales of old –3,852,000 Variable costs 17,516,400 Fixed costs 1,250,000 Depreciation 1,350,000 EBT $11,731,600 Tax 4,458,008 Net income $ 7,273,592 The OCF for the company is: OCF = EBIT + Depreciation – Taxes OCF = $11,731,600 + 1,350,000 – 4,458,008 OCF = $8,623,592 2. Using the equation for total return, we find: R = [($71 – 83) + 1.40] / $83 R = –.1277 or –12.77% And the dividend yield and capital gains yield are: Dividend yield = $1.40 / $83 Dividend yield = .0169 or 1.69% Capital gains yield = ($71 – 83) / $83 Capital gains yield = –.1446 or –14.46% 9. a. To find the average return, we sum all the returns and divide by the number of returns, so: Arithmetic average return = (–.24 +.13 + .29 + .02 + .21)/5 Arithmetic average return = .0820 or 8.20% b. Using the equation to calculate variance, we find: Variance = 1/4[(–.24 – .082)2 + (.13 – .082)2 + (.29 – .082)2 + (.02 – .082)2 + (.21 – .082)2] Variance = 0.042370 So, the standard deviation is: Standard deviation = (0.042370)1/2 Standard deviation = 0.2058 or 20.58% 7. The expected return of an asset is the sum of the probability of each return occurring times the probability of that return occurring. So, the expected return of each stock asset is: E(RA) = .20(.01) + .55(.09) + .25(.14) E(RA) = .0865 or 8.65% E(RB) = .20(–.25) + .55(.15) + .25(.38) E(RB) = .1275 or 12.75% To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, and then sum. The result is the variance. So, the variance and standard deviation of each stock is: (A2 =.20(.01 – .0865)2 + .55(.09 – .0865)2 + .25(.14 – .0865)2 (A2 = .00189 (A = (.00189)1/2 (A = .0435 or 4.35% (B2 =.20(–.25 – .1275)2 + .55(.15 – .1275)2 + .25(.38 – .1275)2 (B2 = .04472 (B = (.04472)1/2 (B = .2115 or 21.15% 18. We will begin by finding the market value of each type of financing. We find: MVD = 9,000($1,000)(1.04) = $9,360,000 MVE = 225,000($64.50) = $14,512,500 MVP = 8,000($94) = $752,000 And the total market value of the firm is: V = $9,360,000 + 14,512,500 + 752,000 V = $24,624,500 Now, we can find the cost of equity using the CAPM. The cost of equity is: RE1 = .05 + .85(.12 – .05) RE1 = .1095 or 10.95% We can also find the cost of equity, using the dividend discount model. The cost of equity with the dividend discount model is: RE2 = ($2.70/$64.50) + .05 RE2 = .0919 or 9.19% Both estimates for the cost of equity seem reasonable, so we will use the average of the two. The cost of equity estimate is: RE = (.1095 + .0919)/2 RE = .1007 or 10.07% The cost of debt is the YTM of the bonds, so: P0 = $1,040 = $31(PVIFAR%,40) + $1,000(PVIFR%,40) R = 2.939% YTM = 2.939% × 2 YTM = 5.86% And the aftertax cost of debt is: RD = (1 – .35)(.0586) RD = .0381 or 3.81% The cost of preferred stock is: RP = $4.50/$94 RP = .0479 or 4.79% Now, we have all of the components to calculate the WACC. The WACC is: WACC = .0381($9,360,000/$24,624,500) + .0479($752,000/$24,624,500) + .1007($14,512,500/$24,624,500) 4. a. Under Plan I, the unlevered company, net income is the same as EBIT with no corporate tax. The EPS under this capitalization will be: EPS = $1,300,000/700,000 shares EPS = $1.86 Under Plan II, the levered company, net income will be reduced by the interest payment. The interest payment is the amount of debt times the interest rate, so: NI = $1,300,000 – .10($6,000,000) NI = $700,000 And the EPS will be: EPS = $700,000/450,000 shares EPS = $1.56 Plan I has the higher EPS when EBIT is $1,300,000. b. Under Plan I, the net income is $2,800,000 and the EPS is: EPS = $2,800,000/700,000 shares EPS = $4.00 Under Plan II, the net income is: NI = $2,800,000 – .10($6,000,000) NI = $2,200,000 And the EPS is: EPS = $2,200,000/450,000 shares EPS = $4.89 Plan II has the higher EPS when EBIT is $2,800,000. c. To find the breakeven EBIT for two different capital structures, we simply set the equations for EPS equal to each other and solve for EBIT. The breakeven EBIT is: EBIT/700,000 = [EBIT – .10($6,000,000)]/450,000 EBIT = $1,680,000 13. The interest tax shield is the total interest paid times the tax rate, so: Interest tax shield = Interest paid(TC) Interest tax shield = $32,000,000(.38) Interest tax shield = $12,160,000 The interest tax shield represents the tax savings in current income due to the deductibility of a firm’s qualified debt expenses.