Final Exam Fall 2011 Solutions

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University of North Carolina, Chapel Hill *

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408

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Finance

Date

May 6, 2024

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docx

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Uploaded by CommodoreCrane4137 on coursehero.com

A project is expected to create operating cash flows of $22,500 a year for three years. The initial cost of the fixed assets is $50,000. These assets will be worthless at the end of the project. An additional $3,000 of net working capital will be required throughout the life of the project. What is the project's net present value if the required rate of return is 10%? $5,208.11 CF0 -53,000 ; C01 22,500 ; F01 2 C02 25,500 ; F02 1 ; I=10% ; NPV CPT Winston Enterprises has a 15-year bond issue outstanding that pays a 9% coupon. The bond is currently priced at $894.60 and has a par value of $1,000. Interest is paid semiannually. What is the yield to maturity? 10.40% Angelina's made two announcements concerning its common stock today. First, the company announced that its next annual dividend has been set at $2.16 a share. Secondly, the company announced that all future dividends will increase by 4% annually. What is the max amount you should pay to purchase a share of Angelina's stock if your goal is to earn a 10% rate of return? How much are you willing to pay for one share of stock if the company just paid an $.80 annual dividend, the dividends increase by 4% annually and you require an 8% rate of return? Majestic Homes' stock traditionally provides an 8% rate of return. The company just paid a $2 a year dividend which is expected to increase by 5% per year. If you are planning on buying 1,000 shares of this stock next year, how much should you expect to pay per share if the market rate of return for this type of security is 9% at the time of your purchase? The Reading Co. has adopted a policy of increasing the annual dividend on its common stock at a constant rate of 3% annually. The last dividend it paid was $0.90 a share. What will the company's dividend be in six years? The Merriweather Co. just announced that it will pay a dividend next year of $1.60 and is establishing a policy whereby the dividend will increase by 3.5% annually thereafter. How much will one share be worth five years from now if the required rate of return is 12%? Company A last paid a $1.50 per share annual dividend. The company is planning on paying $3.00, $5.00, $7.50, and $10.00 a share over the next four years, respectively. After that the dividend will be a constant $2.50 per share per year. What is the market price of this stock if the market rate of return is 15%? NU YU announced today that it will begin paying annual dividends. The first dividend will be paid next year in the amount of $.25 a share. The following dividends will be $.40, $.60, and $.75 a share annually for the following three years, respectively. After that, dividends are projected to increase by 3.5% per year. How much are you willing to pay to buy one share of this stock if your desired rate of return is 12%? The Red Bud Co. just paid a dividend of $1.20 a share. The company announced today that it will continue to pay this constant dividend for the next 3 years after which time it will discontinue paying dividends permanently. What is one share of this stock worth today if the required rate of return is 7%? Which of the following amounts is closest to what should be paid for Overland common stock? Overland has just paid a dividend of $2.25. These dividends are expected to grow at a rate of 5% in the foreseeable future. The required rate of return is 11%. V of S= D0(1 + g)/(r - g) = $2.25(1 + 0.05)/(0.11 - 0.05) = $39.375 The Felix Corp. projects to pay a dividend of $.75 next year and then have it grow at 12% for the following 3 years before growing at 8% indefinitely thereafter. The equity has a required return of 10% in the market. The price of the stock should be? Value of stock = [($.75/1.1) + ($.84/(1.1)2) + ($.94/(1.1)3) + ($1.05/(1.1)4) + (($1.13/.02)/(1.1)4) = $41.67 A stock you are interested in paid a dividend of $1 last week. The anticipated growth rate in dividends and earnings is 20% for the next year and 10% the year after that before settling down to a constant 5% growth rate. The discount rate is 12%. Calculate the expected price of the stock. Price = $1.00(1.20)/1.12 + $1.20(1.100)/1.2544 + [$1.32(1.05)/(.12 - .05)]/1.2544 = $17.90 A stock had returns of 8%, -2%, 4%, and 16% over the past 4 years. What is the st. dev. of this stock for the past four years? Avg return = (.08 - .02 + .04 + .16)/4 = .065; Total squared dev = (.08 - .065)^2 + (-.02 - .065)^2 + (.04 - .065)^2 + (.16 - .065)^2 = .000225 + .007225 + .000625 + .009025 = .0171; St dev = sq rt(.0171 /(4 - 1) = sq rt .0057 = .075498 = 7.5% What are the arithmetic and geometric average returns for a stock with annual returns of 4%, 9%, -6%, and 18%? Arithmetic average = (.04 + .09 - .06 + .18) / 4 = 6.25%; Geometric return = (1.04 x 1.09 x .94 x 1.18)^.25 - 1 = 5.89% The returns on your portfolio over the last 5 years were -5%, 20%, 0%, 10% and 5%. What is the st dev of your return? St Dev = sq rt [(-.05 - .06)^2 + (.20 - .06)^2 + (0 - .06)^2 + (.10 - .06)^2 + (.05 - .06)^2]/4 = sq rt.0370/4 = sq rt.00925 = .09617 = 9.62% Zelo, Inc. stock has a beta of 1.23. The risk-free rate of return is 4.5% and the market rate of return is 10%. What is the amount of the risk premium on Zelo stock? Risk premium = 1.23 x (.10 - .045) = .06765 = 6.77% If the economy booms, RTF, Inc. stock is expected to return 10%. If the economy goes into a recessionary period, then RTF is expected to only return 4%. The probability of a boom is 60% while the probability of a recession is 40%. What is the variance of the returns on RTF, Inc. stock? E(r) = (.60 x .10) + (.40 x.04) = .06 + .016 = .076 ; Var = .60 x (.10 - .076)^2 + .40 x (.04 - .076)^2 = .0003456 + .0005184 = .000864 Red Hat’s stock is quite cyclical. In a boom economy, the stock is expected to return 30% in comparison to 12% in a normal economy and a negative 20% in a recessionary period. The prob. of a recession is 15%. There is a 30% chance of a boom economy. The remainder of the time, the economy will be at normal levels. What is the st dev of the returns on this stock? E(r) = (.30 x .30) + (.55 x .12) + (.15 x -.20) = .09 + .066 - .03 = .126 ; Var = .30 x (.30 - .126)^2 + .55 x (.12 - .126)^2 + .15 x (-.20 - .126)^2 = .0090828 + .0000198 + .0159414 = .025044 ; Std dev = sq rt .025044 = .15825 = 15.83% What is the expected return on a portfolio which is invested 20% in stock A, 50% in stock B, and 30% in stock C? E(r)Boom=(.20x 18)+(.50x.09)+(.30x.06) = .036 + .045 + .018 = .099 E(r)Normal = (.20 x .11) + (.50 x .07) + (.30 x .09) = .022 + .035 + .027 = .084 E(r)Bust = (.20 x -.10) + (.50 x .04) + (.30 x .13) = -.020 + .020 + .039 = .039 E(r)Portfolio = (.20 x .099) + (.70 x .084) + (.10 x .039) = .02376 + .0588 + .0039 = .0825 = 8.25% What is the portfolio variance if 30% is invested in stock S and 70% is invested in stock T? E(r)Boom = (.30 x .12) + (.70 x .20) = .036 + .14 = .176 E(r)Normal = (.30 x .06) + (.70 x .04) = .018 + .028 = .046 E(r)Portfolio = (.40 x .176) + (.60 x .046) = .0704 + .0276 = .098 VarPortfolio = [.40 x (.176 - .098)^2] + [.60 x (.046 - .098)^2] = .0024336 + .0016224 = .004056 Your portfolio has a beta of 1.18. The portfolio consists of 15% U.S. Treasury bills, 30% in stock A, and 55% in stock B. Stock A has a risk-level equivalent to that of the overall market. What is the beta of stock B? BetaPortfolio = 1.18 = (.15 x 0) + (.30 x 1.0) + (.55 x betaB) = 0 + .3 + .55 betaB; .88 = .55 betaB; betaB = 1.6 The beta of a risk-free asset is zero. The beta of the market is 1. The common stock of Flavorful Teas has an expected return of 14.4%. The return on the market is 10% and the risk-free rate of return is 3.5%. What is the beta of this stock? E(r) = .144 = .035 + beta x (.10 - .035); .109 = .065beta; beta = 1.68 GenLabs has been a hot stock the last few years, but is risky. The expected returns for GenLabs are highly dependent on the state of the economy as follows: what is std dev? .05(-.50 - .125)^2 + .1(-.15 - .125)^2 + .2(.05 - .125)^2 + .3(.15 - .125)^2 + .2(.25 - .125)^2 + .15(.40 - .125)^2 = .0428 Square root of (.0428) = .2069 Peter's Audio has a cost of debt of 7%, a cost of eq. of 11%, and a cost of pref. stock of 8%. The firm has 104,000 shares of common stock outstanding at a mkt price of $20 a share. There are 40,000 shares of preferred stock outstanding at a market price of $34 a share. The bond issue has a total face value of $500,000 and sells at 102% of face value. The tax rate is 34%. What is the weighted average cost of capital for Peter's Audio? Debt: $500,000 x 1.02 = $.51m Preferred: 40,000 x $34 = $1.36m Common: 104,000 x $20 = $2.08m Total = $.51m + $1.36m + $2.08m = $3.95m Slippery Slope Roof Contracting has an equity beta of 1.2, capital structure with 2/3 debt, and a zero tax rate. What is it’s as beta? BA = (E/(D + E.) BE = (1/3)(1.2) = .40 The Template Corporation has an equity beta of 1.2 and a debt beta of .8. The firm's market value debt to equity ratio is .6. Template has a zero tax rate. What is the asset beta? .8(.6/1.6) + 1.2(1/1.6) = 1.05 Thompson is an all equity firm that has 500,000 shares of stock outstanding. The firm is in the process of borrowing $8 million at 9% interest to repurchase 200,000 shares of the outstanding stock. What is the value of this firm if you ignore taxes? Price per share = $8m  200k = $40; [(500,000 - 200,000) x $40] + $8m = 500,000 x $40 = $20m Zelo has a cost of equity of 13.56% and a pre-tax cost of debt of 7%. The required return on the assets is 11%. What is the firm's debt-equity ratio based on MM Proposition II with no taxes? . 1356 = .11 + (.11 - .07) x D/E; D/E = .64 Comp. A has an unlevered cost of capital of 10%, a tax rate of 34%, and expected EBIT of $1,600. The company has $3,000 in bonds outstanding that have an 8% coupon and pay interest annually. The bonds are selling at par value. Cost of equity? VU = [EBIT x (1 - Tc)] / RU = [$1,600 x (1- .34)] / .10 = $10,560 VL = VU + (Tc x D) = $10,560 + (.34 x $3,000) = $11,580 VL - VD = VE = $11,580 - $3,000 = $8,580 RE = RU + (RU - RD) x D/E x (1 - TC) = .10 + [(.10 - .08) x ($3,000 / $8,580) x (1 - .34)] = .10 + .00462 = .10462 = 10.46% Company A has a cost of equity of 13.84% and an unlevered cost of capital of 12%. The company has $5,000 in debt that is selling at par value. The levered value of the firm is $12,000 and the tax rate is 34%. What is the pre-tax cost of debt? VE = $12,000 - $5,000 = $7,000; .1384 = .12 + (.12 - RD) x ($5,000/ $7,000) x (1 - .34); .0184 = .056571 - .471429RD; RD = .08097 = 8.10% A firm has debt of $5,000, equity of $16,000, a leveraged value of $8,900, a cost of debt of 8%, a cost of equity of 12%, and a tax rate of 34%. What is the firm's weighted average cost of capital? WACC = [($16k /$21k) x .12] + [($5k / $21k) x .08 x (1 - .34) = .091429 + .012571 = .1040 = 10.40% A firm has a d/e ratio of 1. Its cost of equity is 16%, and its cost of debt is 8%. If there are no taxes or other imperfections, what would be its cost of equity if the debt-to-equity ratio were 0? Rs = 16 = r0 + 1(r0 -.08) .16 = 2r0 - .08 .24 = 2r0 r0 = .12 = 12% WACC = rd wd + rd we = .08(.5) + .16(.5) = .12 = 12% A firm has a debt-to-equity ratio of .5. Its cost of equity is 22%, and its cost of debt is 16%. If the corporate tax rate is .40, what would its cost of equity be if the debt-to-equity ratio were 0? Rs = Ro + (B/S)(1 - Tc)( Ro - rB ) .22 = ro + (.5) (1 - .40) (Ro - .16) .22 = ro + .3ro - .048 .268 = 1.3Ro Ro = 20.61% A firm has debt of $7,000, equity of $12,000, a leveraged value of $8,900, a cost of debt of 7%, a cost of equity of 14%, and a tax rate of 30%. What is the firm's weighted average cost of capital? WACC = [($12k / $19k) x .14] + [($7k / $19k) x .07 x (1 - .30) = .088421 + .018053 = .1065 = 10.65%

- Tar Heel Recreation, Inc. has been a mildly profitable enterprise since starting 3 years ago. As a result, they have built up book value of equity to $13,000. They have lawn equipment purchased at inception of the business for $30,000, and they have been depreciating on a straight-line basis over 5 years. This equipment is worth about $10,000 today. To run the day-to-day business they have $8,000 in net working capital. How much long-term debt are they carrying? -assets(current+fixed)=liabilities(current+long term)+shareholders equity -nwc=current assets-current liabilities -nwc(cur. Ass. - cur. Liab.) + fixed assets = long term liab. +shareholders equity -depreciation: 30,000/5 years= 6000 per year; 3 years currently, so 18,000 dep. -8000 + 30,000-18,000 = x + 13,000 ; x=7000 -Your first trip to Vegas and BING, you hit the jackpot on the $1 slots. You are the $1,000,000 winner. In the glow of the neon lights and flash photography, the casino management details how you can collect your winnings (excluding taxes): either, $1M in cash 20 years from now, 20 payments of $50,000 (starting 1 year from today), or $400,000 today. If your personal rate of return is 7%, which would you choose? - FV= 1,000,000 N=20 I=7 PV= ?  PV=$258,419.00 - PMT= 50,000 I=7 N=20 PV=?  PV= $529,000.71 ***winner - 400,000 - You just made the last monthly payment on a 30 year mortgage -- the house is yours! In your joyous moment, you calculate how much you made in payments over those 30 years, and it is $647,514! If your interest rate was an APR of 6%, and you made equal monthly payments, how much did you originally borrow for this house? - 360 payments made (30*12) -$647,514/360= 1,798.65 =PMT -PMT: 1,798.65 N=360 I=6/12 PV=299,999.99 ** - You decide to give back to UNC because of the great experience you had while attending, and want to be remembered here in perpetuity. Because of your success and wealth, you have the ability to establish a fund that will be able to grant a single scholarship to a worthy student each year. You want this to continue forever. If the annual cost of college today is $25,000, and is expected to grow at 5% a year, and the UNC-KFBS investment advisors have an annual return of about 8%, approximately how much money will you need to give to establish your scholarship? - [(25,00*1.05)/(.08-.05)]= $875,000 -current ratio=current assets/current liabilities -LT Debt Equity Ratio=LT Debt/equity(common stock+RE) -inventory turnover=COGS/inventory -Net Capital Spending=Net Fixed Assets+Deprec. (negative so sub.) -Dupont model: (1) asset turnover= sales/ total assets (2)equity multiplier= total assets/equity (3) PM=net income/sales - You want to have a nest egg (investment account) of $5,000,000 when you retire, 40 years from now. Approximately how much would you need to save annually, assuming you could earn 8.5% per year. You won’t be able to make your first payment until 1 year from today. - FV=5,000,000 N=39 I=8.5 PMT=?  18,410*** - Assume you want $5,000,000 at retirement in 40 years. However, you have some free cash today that you’d like to invest, and let it grow to at least partially fund that $5,000,000. If your money can earn 8.5% annually, and you have $125,000 to invest, how much are you short today in allowing you to reach your goal? - PV= 125,000 I=8.5 N=40 FV=?  3,266,626.95  need 1,733,373.05 -FV=1,733,373.05 I=8.5 N=40 PV=66,329** - Earls Enterprises has a 12-year, 8% annual coupon bond with a $1,000 par value, and has a yield to maturity of 6%. Which of the following statements are correct if the market yield increases to 7%? -Present: FV=1000 N=12 PMT=80 I=6 PV=1,167.68 -Future: FV=1000 N=12 PMT=80 I=7 PV= 1,079.43 - [(1079.43-1167.68)/1167.68]= -.07558 = -7.56% - Wine and Roses, Inc. offers a 7% coupon bond with semiannual payments and a yield to maturity of 7.73%. The bonds mature in 9 years. What is the market price of a $1,000 face value bond? - N=9.2 I=7.73/2 PMT=35 FV=1000 PV=?  953.282 -The bonds issued by Jensen & Son bear a 6% coupon, payable semiannually. The bond matures in 8 years and has a $1,000 face value. Currently, the bond sells at par. What is the yield to maturity? -PV= 1000 FV= 1000 PMT= 30 N= 16 I=?  3.00*2= 6  6% - A corporate bond with a face value of $1,000 matures in 4 years and has an 8% coupon paid at the end of each year. The current price of the bond is $932. What is the yield to maturity for this bond? -FV= 1000 N = 4 PMT= 80 PV= 932 I =10.15 - B&K Enterprises will pay an annual dividend of $2.08 a share on its common stock next year. Last week, the company paid a dividend of $2.00 a share. The company adheres to a constant rate of growth dividend policy. What will one share of B&K common stock be worth ten years from now if the applicable discount rate is 8%? - g=[(2.08-2.00)/2.00]= 0.04  g= 0.04 -D= {[(2.08 * (1+.04)^10] / [(.08 - .04)]} = $76.97 - Can't Hold Me Back, Inc. is preparing to pay its first dividends. It is going to pay $1.00, $2.50, and $5.00 a share over the next three years, respectively. After that, the company has stated that the annual dividend will be $1.25 per share indefinitely. What is this stock worth to you per share if you demand a 7% rate of return? - First, we can get the value of the stock, when it is acting like a perpetuity (D 4 and beyond) 1.25 / .07 = 17.8571 -This is a year 3 value, as the first payment is in year 4 -Discount back the three specified dividends and the year 3 value of the perpetuity (1 / 1.07) + (2.50 / 1.07 2 ) + (5 / 1.07 3 ) + (17.8571 / 1.07 3 )= $21.78 -Kurt's Adventures, Inc. stock is quite cyclical. In a boom economy, the stock is expected to return 30% in comparison to 12% in a normal economy and a negative 20% in a recessionary period. The probability of a recession is 15%. There is a 30% chance of a boom economy. The remainder of the time, the economy will be at normal levels. What is the standard deviation of the returns on Kurt's Adventures, Inc. stock? -E(r )= (.30*.30) + (.55 * .12) + (.15 * -.20) = .09 + .066 - .03 = 0.126 -Var= [.30* (.30-.126)^2] + [.55(.12 -.126)^2] + [.15* ( -.2 - .126)^2] = .0090828 + .0000198 + .0159414= .025044 -Std. Dev= Sqrt.(.025044) = .15825 = 15.83 % - What is the standard deviation of the returns on a stock given the following information? [Chart form] (1) Boom: probability= 10% return = 16% (2) normal: probability= 60% return= 11% (3) recession: probability= 30% return= -8%. - e(r )= (.1*.16) + (.6 * .11) + (.3*-.08)=  .016+ .066 -.024=  .058 -variance= [.1 (.16-.058)^2] + [.6 *(.11-.058)^2] + [.3*(-.08-.058)^2] =  .0010404+.0016224 + .0057132= .008376 -stand. Dev.= sqrt(.008376) =  .09152=  9.15% -What is the expected return of a portfolio consisting of $3,500 in stock G and $6,500 in stock H? - Stock G: e(r )= (.15*.15)+(.85*.08) = .0225+.068= .0905 -Stock H: e(r )=(.15*.09)+ (.85*.06)= .0315+.051= .0645 -put 35% in stock G; put 65% in stock H -portfolio expected return= (.35*.0905)+(.65*.0645)= .0317+.0419= .0736= 7.36% -Jack's Construction Co. has 80,000 bonds outstanding that are selling at par value. Bonds with similar characteristics are yielding 8.5%. The company also has 4 million shares of common stock outstanding. The stock has a beta of 1.1 and sells for $40 a share. The U.S. Treasury bill is yielding 4% and the market risk premium is 8%. Jack's tax rate is 35%. What is Jack's weighted average cost of capital? -r(e )=.04+(1.1*.08)= 0.128 -debt= 80,000*1000= 80 million -common=4,000,000*$40=$160 million -total= 80 million+ 160 million= 240 million -WACC=[(160m/240m)*.128]+[(80m/240m)*.85*(1-.35)]= 0.085333+ 0.018417+0.10375= 10.38% -Jake's Sound Systems has 210,000 shares of common stock outstanding at a market price of $36 a share. Last month, Jake's paid an annual dividend in the amount of $1.593 per share. The dividend growth rate is 4%. Jake's also has 6,000 bonds outstanding with a face value of $1,000 per bond. The bonds carry a 7% coupon, pay interest annually, and mature in 4.89 years. The bonds are selling at 99% of face value. The company's tax rate is 34%. What is Jake's weighted average cost of capital? -Cost of Equity Capital = D1/Price + g = [(1.593*1.04)/(36 + .04)] = 8.60% -Cost Of Debt: FV= -1000 PV= 990 PMT= -70 N=4.89 I=?  7.25% -After Tax Cost of Debt =[ 7.25*(1-.34)] = 4.785 - Value of Equity Share Outstanding = (210000*36) = 7,560,000 - Market Value of Debt Outstanding = (6000*990) =5,940,000 -Total Market Capitalization = (7560000+5940000) = 13,500,000 - WACC =[(594/1350)*4.785] +[ (756/1350)*8.60] = 6.92% - Assuming the CAPM or one-factor model holds, what is the cost of equity for a firm if the firm's equity has a beta of 1.2, the risk-free rate of return is 2%, the expected return on the market is 9%, and the return to the company's debt is 7%? -cost of equity= risk free rate+ beta(expected return on market- risk free rate) -cost of equity= 2+1.2(9-2)= 10.4% - Hey Guys!, Inc. has debt with both a face and a market value of $3,000. This debt has a coupon rate of 7% and pays interest annually. The expected earnings before interest and taxes is $1,600, the tax rate is 34%, and the unlevered cost of capital is 10%. What is the firm’s cost of equity? -V L = V U + TS -V U = {1,600 ( 1-0.34)} / 0.10 = 10,560 -TS = 3,000 * 0.34 = 1,020 -V L = 10,560 + 1,020 = 11,580 -R E = R a + (D/E) * (1  T c )*(R a  R d ) -R E = 0.10 + (3,000/8,580) (1 – 0.34) (0.10 - 0.07) -R E = 0.10692 = 10.692% -A firm has a debt-to-equity ratio of 1. Its cost of equity is 16%, and its cost of debt is 8%. If there are no taxes or other imperfections, what would be its cost of equity if the debt-to-equity ratio were 0? - 16=r + 1(r-8) - 16=2r-8 - 24=2r - r=12%

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