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Q.4. An investment pays you $ 30,000 at the end of this year, and $ 15,000 at the end of each of the four following years. What is the present value (PV) of this investment, given that the interest rate is 3 % per year? Q.6. Total Future Value =[ 1000(1.09)^4]+[2000(1.09)^3]+[3000(1.09)^2]+[4000(1.09)] Q.8. A perpetuity will pay 800 per year, starting five years after the perpetuity is purchased. What is the present value (PV) of this perpetuity on the date that it is purchased, given that the interest rate is 9%? A. (800/.09)*1/(1+.09)^4 Q.!. PV(D.Annuity)=C/r*[1- 1/(1+r)^t]*1/(1+r)^t Q.13. A rich donor gives a hospital $1,040,000 one year from today. Each year after that, the hospital will receive a payment 6% large r than the previous payment, with the last payment occurring in ten yearsʹ time. What is the present value (PV) of this donation, given that the interest r ate is 11% g? A. PV = {$1,040,000 ÷ (0.11 - 0.06)} × {1 - [(1+0.6)÷(1+0.11)]^10] = {$1,040,000 ÷ (0.05)} × {1 - [(1.06)÷(1.11)]^10] = {$1,040,000 ÷ (0.05)} × {1 - [(1.06)÷(1.11)]^10] = $20,800,000 × (1 - 0.630708763) = $20,800,000 × 0.369291237 = $7,681,257.74 Q.14. make deposits on each of their daughter's birthdays, starting with her first birthday ; educational savings account will return a constant 9%. The parents deposit $2000 on their daughter's first birthday , increase the size of their deposits by 5% each year ; the parents have already made the deposit for their daughter's 18th birthday, then the amount available for the daughter's college expenses on her 18th birthday is closest to? A. FV=2000*[(1.09)^18-(1.05)^18]/(.09-.05)= 115,525 Q.15. 30 years old today ; you are planning on retirement at age 65. Your current salary is 40,000 and you expect your salary to increase at a rate of 4% per year ; you plan on making annual contributions to a retirement account ; y our first contribution will be made on your 31st birthday and will be 8% of this year's salary ; de p osit 8% of your salary each year until you reach age 65 ; rate of interest is 10%. The present value (PV) (at age 30) of your retirement savings is closest to : A. C=.08*40000=3200 PV=[3200/(.10-.04)][1-((1.04/1.10)^35)]=45844 FV=45844(1.10)^35 Ch. 12&13 Q.1 . the S&P 500 was down 1.8% today relative to the risk-free rate (the market's excess return was -1.8). a. If Zynga's beta is 1.3, what is your best guess as to Zynga's excess return today? A. =-1.8%*1.3=2.3% Q.2. The risk-free rate is 2% and you believe that the S&P 500's excess return will be 7% over the next year. If you invest in a stock with a beta of 1.6 (and a standard deviation of 30%), what is your best guess as to its expected excess return over the next year? A. =1.6*7%=11.20% Q.4. Suppose Intel stock has a beta of 1.74, whereas Boeing stock has a beta of 0.85. If the risk-free interest rate is 4.8% and the expected return of the market portfolio is 12.7%, according to the CAPM, a. What is the expected return of Intel stock? - =4.8%+1.74*(12.7%-4.8%)=18.5% b. What is the expected return of Boeing stock? - =4.8%+0.85*(12.7%-4.8%)=11.5% c. What is the beta of a portfolio that consists of 65% Intel stock and 35%Boeing stock? - =1.74*65%+0.85*35%=1.43 d. What is the expected return of a portfolio that consists of 65% Intel stock and 35% Boeing stock? =4.8%+1.43*(12.7%- 4.8%)=16.10% Q.5. At the beginning of 2007 (the year the iPhone was introduced), Apple's beta was 1.3 and the risk-free rate was about 3.7%. Apple's price was $82.35. Apple's price at the end of 2007 was $196.15. If you estimate the market risk premium to have been 6.7%, did Apple's managers exceed their investors' required return as given by the CAPM? A. Expected Return=3.7%+1.3*6.7%=12.41% Realized Return= (196.15-82.35)/82.35=138.19% Q.6. MV Corporation has debt with market value of 96 million, common equity with a book value of 104 million, and preferred stock worth 22 million outstanding. Its common equity trades at 53 per share, and the firm has 5.8 million shares outstanding. What weights should MV Corporation use in its WACC? A. Market Value of Common Equity=53*5.8=307 Total Market Value of Firm = 96+22+307=425 Weight of Debt WACC=96/425=22.59% Weight of Preferred Stock WACC=22/425=5.18% Weight of Equity for WACC=307/425=72.24% Q.7. Andyco , Inc., has the following balance sheet and an equity market-to-book ratio of 1.6. Assuming the market value of debt equals its book value, what weights should it use for its WACC calculation? Assets:1050|Liabilities & Equities: Debt-450 Equity- 600 A. Market Value of Equity=600*1.6=960 Total Market Value of Firm=450+960=1410 D%=450/1410=31.91% E%=960/1410=68.09% Q.8. Laurel, Inc., has debt outstanding with a coupon rate of 6.1% and a yield to maturity of 6.8%. Its tax rate is 38%. What is Laurel's effective(after-tax) cost of debt? Note: Assume that the debt has annual coupons. A. After Tax Cost of Debt=0.068*(1-0.38)=0.04216 Q.9. CoffeeCarts has a cost of equity of 15.8%, has an effective cost of debt of 4.3%, and is financed 66% with equity and 34% with debt. What is this firm's WACC? A. rwacc=0.158*0.66+0.043*0.34=0.119 Q.10. Pfd Company has debt with a yield to maturity of 7.8%, a cost of equity of 14.2%, and a cost of preferred stock of 10.3%. The market values of its debt, preferred stock, and equity are 11.7 million, 3.2 million, and 13.5 million, respectively, and its tax rate is 38%. What is this firm's after-tax WACC? A. rwacc=0.142*(13.5/28.4)+0.103*(3.2/28.4)+0.078*(1-0.38)*(11.7/28.4)= 0.099 Q.13. CoffeeStop primarily sells coffee. It recently introduced a premium coffee-flavored liquor (BF Liquors). Suppose the firm faces a tax rate of 40% and collects the following information. If it plans to finance 14% of the new liquor-focused division with debt and the rest with equity, what WACC should it use for its liquor division? Assume a cost of debt of 5.1%, a risk-free rate of 3.4%, and a market risk premium of 5.9%. A. Cost of Equity=0.034+0.23*0.059=0.04757 rwacc=0.04757*0.86+0.051*(1-0.4)*0.14=0.0452 Ch.7&10 Q.1. Suppose Acap Corporation will pay a dividend of $2.75 per share at the end of this year and $2.87 per share next year. You expect Acap's stock price to be $53.10 in two years. Assume that Acap's equity cost of capital is 8.5%. a. What price would you be willing to pay for a share of Acap stock today if you planned to hold the stock for two years? - P0=2.75/ (1+0.085)+(2.87+53.10)/((1+0.085)^2)=50.08 b. Suppose instead you plan to hold the stock for one year. For what price would you expect to be able to sell a share of Acap stock in one year? -P1=(2.87+53.10)/(1+0.085)=51.59 c. Given your answer in (b), what price would you be willing to pay for a share of Acap stock today, if you planned to hold the stock for one year? How does this compare to your answer in (a)? -P0=(2.75+51.59)/(1+0.085)=50.08 its the same price as part a Q.3.Assume Gillette Corporation will pay an annual dividend of $0.68 one year from now. Analysts expect this dividend to grow at 12.2% per year thereafter until the 4th year. Thereafter, growth will level off at 1.9% per year. According to the dividend- discount model, what is the value of a share of Gillette stock if the firm's equity cost of capital is 8.3%? A. PV1-4= 0.68/0.083-0.122 * [1-(1+0.122/1+0.083)^4]=2.65 PV4=0.68*(1+0.122)^3*(1+0.019)/0.083-0.019=15.29 PV0=15.29/ (1+0.083)^4=11.11 P0=2.65+11.11=13.76 Q.4. CX Enterprises has the following expected dividends: $1.05 in one year, $1.18 in two years, and $1.26 in three years. After that, its dividends are expected to grow at 4.1% per year forever (so that year 4's dividend will be 4.1% more than $1.26 and so on). If CX's equity cost of capital is 12.4%, what is the current price of its stock? A. PV3=1.26*(1+0.041)/0.124-0.041=15.80 P0=1.05/(1+0.124)+1.18/(1+0.124)^2+(1.26+15.80)/(1+0.124)^3=13.88 Q.5. This year, FCF Inc. has earnings before interest and taxes of $12,000,000, depreciation expenses of $1,900,000, capital expenditures of $2,100,000, and has increased its net working capital by $460,000. If its tax rate is 32%, what is its free cash flow? A. Free cash flow=12,000,000*(1-0.32)+1,900,000-2,100,000-460,000=7,500,000 |EBIT*(1-tax rate)+Depreciation-Cap exp.- Increases in net cap Q.7. The present value of JECK Co.'s expected free cash flow is 111 million. If JECK has 36 million in debt, 9 million in cash, and 5 million shares outstanding, what is its share price? A. PO=111+9-36/5 | P0=V0+Cash-Debt/shares outstanding Q.9. Heavy Metal Corporation is expected to generate the following free cash flows over the next five years: Year 1 2 3 4 5 56 71 81 79 85 After that, the free cash flows are expected to grow at the industry average of 4.7% per year. Using the discounted free cash flow model and a weighted average cost of capital of 16%: a. Estimate the enterprise value of Heavy Metal: V0= 56/(1+0.160)+71/(1+0.160)^2+81/(1+0.160)^3…+85*1.047/(1+0.160)^5*(0.160-0.047)=612 b. If Heavy Metal has no excess cash, debt of 325 million, and 50 million shares outstanding, estimate its share price.- P0=(612+0-325)/50=5.74 Q.11. CSH has EBITDA of 7 million. You feel that an appropriate EV/EBITDA ratio for CSH is 8.5. CSH has 12 million in debt, 6 million in cash, and 740,000 shares outstanding. What is your estimate of CSH's stock price? A. V0=EBITDA*EV/EBITDA RATIO| V0=7,000,000*8.5=59,500,000 P0=(59,500,000+6,000,000-12,000,000)/740,000= 72.30 Q.12. Suppose Rocky Brands has earnings per share of $2.55 and EBITDA of $31.8 million. The firm also has 6.0 million shares outstanding and debt of $145 million (net of cash). You believe Jared's Outdoor Corporation is comparable to Rocky Brands in terms of its underlying business, but Jared's has no debt. If Jared's has a P/E of 13.7 and an enterprise value to EBITDA multiple of 7.75, estimate the value of Rocky Brands stock using both multiples. Which estimate is likely to be more accurate? A. Stock Price=2.55*13.7=34.94 per share| Value=34.94*6=209.6 ←P/E Ratio| EBITDA RATIO=31.8*7.75=246.5|246.5- 145=101.5| Stock value using EBITDA RATIO is =101.5/6= 16.92 per share | use EBITDA Ratio

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