SUSSY
Galvatron Metals has a bond outstanding with a coupon rate of 5.6 percent and semiannual payments. The bond currently sells for $940 and matures in 18 years. The par value is $1,000 and the company's tax rate is 35 percent. What is the company's aftertax cost of debt?
$940 = $28.00{1 − [1/(1 + R)36]}/R + $1,000/R36 R = .0308, or 3.08% YTM = 3.080% × 2 YTM = 6.16% RD = 6.16%(1 − .35) RD = 4.00%
Three months ago, you purchased a stock for $66.23. The stock is currently priced at $71.53. What is the EAR on your investment?
3-month return = ($71.53 − 66.23)/$66.23 3-month return = .0800, or 8.00% EAR = (1 + .0800)4 - 1 EAR = .3606, or 36.06%
Over the past five years, a stock returned 8.4 percent, −8.7 percent, −3.2 percent, 1.5 percent, and 11.5 percent, respectively. What is the variance of these returns?
Average return = (.084 − .087 − .032 + .015 + .115)2 / 5 = .019 σ2 = [(.084 − .019)2 + (−.087 − .019)2 + (−.032 − .019)2 + (.015 − .019)2 + (.115 − .019)2] / (5 − 1) =.006824
A stock had returns of 18.13 percent, −5.31 percent, and 20.54 percent for the past three years. What is the variance of the returns?
Average return = (.1813 − .0531 + .2054)/3 Average return = .1112, or 11.12% Variance = 1/2[(.1813 − .1112)2 + (−.0531 − .1112)2 + (.2054 − .1112)2] Variance = .02039
A bond had a price of $1,946.61 at the beginning of the year and a price of $1,982.79 at the end of the year. The bond's par value is $2,000 and its coupon rate is 6 percent. What was the percentage return on the bond for the year?
Bond return = ($1,982.79 - 1,946.61 + 120) / $1,946.61 Bond return = .0802, or 8.02%
Brummitt Corp., is evaluating a new 4-year project. The equipment necessary for the project will cost $2,300,000 and can be sold for $293,000 at the end of the project. The asset is in the 5-year MACRS class. The depreciation percentage each year is 20.00 percent, 32.00 percent, 19.20 percent, 11.52 percent, and 11.52 percent, respectively. The company's tax rate is 34 percent. What is the aftertax salvage value of the equipment?
Book value = $2,300,000(.1152 + .0576) Book value = $397,440 Tax refund (due) = ($397,440 − 293,000)(.34) Tax refund (due) = $35,510 Aftertax salvage value = $293,000 + 35,510 Aftertax salvage value = $328,510
A company purchased an asset for $3,200,000 that will be used in a 3-year project. The asset is in the 3-year MACRS class. The depreciation percentage each year is 33.33 percent, 44.45 percent, and 14.81 percent, respectively. What is the book value of the equipment at the end of the project?
Book value = $3,200,000 − 3,200,000(.3333 + .4445 + .1481) Book value = $237,120
A project has an annual operating cash flow of $52,620. Initially, this four-year project required $5,160 in net working capital, which is recoverable when the project ends. The firm also spent $39,700 on equipment to start the project. This equipment will have a book value of $17,014 at the end of Year 4. What is the cash flow for Year 4 of the project if the equipment can be sold for $15,900 and the tax rate is 35 percent?
CF4 = $52,620 + 5,160 + 15,900 − [($15,900 − 17,014) × .35] = $74,069.90
One year ago, you bought a stock for $37.25 per share. You received a dividend of $1.27 per share last month and sold the stock today for $39.75 per share. What is the capital gains yield on this investment?
Capital gains yield = ($39.75 − 37.25) / $37.25 = .0671, or 6.71 percent
A 4-year project has an annual operating cash flow of $55,000. At the beginning of the project, $4,600 in net working capital was required, which will be recovered at the end of the project. The firm also spent $23,100 on equipment to start the project. This equipment will have a book value of $4,940 at the end of the project, but can be sold for $5,880. The tax rate is 35 percent. What is the Year 4 cash flow?
Cash flow = $55,000 + 4,600 + 5,880 + .35($4,940 − 5,880) Cash flow = $65,151
Further From Center has 11,800 shares of common stock outstanding at a price of $52 per share. It also has 295 shares of preferred stock outstanding at a price of $94 per share. There are 340 bonds outstanding that have a coupon rate of 7.1 percent paid semiannually. The bonds mature in 33 years, have a face value of $2,000, and sell at 110 percent of par. What is the capital structure weight of the preferred stock?
Common stock:11,800 × $52=$613,600 Preferred stock:295 × $94= 27,730 Debt:340 × $2,000 × 1.10= 748,000 Total value: $1,389,330 XP = $27,730/$1,389,330 XP = .0200
Here I Sit Sofas has 7,800 shares of common stock outstanding at a price of $101 per share. There are 880 bonds that mature in 37 years with a coupon rate of 7.5 percent paid semiannually. The bonds have a par value of $2,000 each and sell at 112 percent of par. The company also has 6,700 shares of preferred stock outstanding at a price of $54 per share. What is the capital structure weight of the debt?
Common stock:7,800 × $101=$787,800 Preferred stock:6,700 × $54= 361,800 Debt:880 × $2,000 × 1.12= 1,971,200 Total value: $3,120,800 XD = $1,971,200/$3,120,800 XD = .6316
You recently purchased a stock that is expected to earn 22 percent in a booming economy, 11 percent in a normal economy, and lose 4 percent in a recessionary economy. There is 24 percent probability of a boom, 67 percent chance of a normal economy, and 9 percent chance of a recession. What is your expected rate of return on this stock?
E(R) = .24(.22) + .67(.11) + .09(-.04) E(R) = .1229, or 12.29%
he common stock of Flavorful Teas has an expected return of 26.87 percent. The return on the market is 17 percent and the risk-free rate of return is 2.9 percent. What is the beta of this stock?
E(R) = .2687 = .029 + β(.170 − .029) .2397 = .141β β = 1.70
Your firm is contemplating the purchase of a new $485,000 computer-based order entry system. The system will be depreciated straight-line to zero over its 6-year life. It will be worth $63,000 at the end of that time. You will save $169,000 before taxes per year in order processing costs, and you will be able to reduce working capital by $46,000 at the beginning of the project. Working capital will revert back to normal at the end of the project. The tax rate is 21 percent. What is the aftertax salvage value of the equipment? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) What is the annual operating cash flow? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) What is the IRR for this project? (Do not round intermediate calculations and round your answer as a percent rounded to 2 decimal places, e.g., 32.16.);
First, we will calculate the annual depreciation of the new equipment. It will be: Annual depreciation charge = $485,000/6 Annual depreciation charge = $80,833 The aftertax salvage value of the equipment is: Aftertax salvage value = $63,000(1 - .21) Aftertax salvage value = $49,770 Using the tax shield approach, the OCF is: OCF = $169,000(1 - .21) + .21($80,833) OCF = $150,485 Now we can find the project IRR. There is an unusual feature that is a part of this project. Accepting this project means that we will reduce NWC. This reduction in NWC is a cash inflow at Year 0. This reduction in NWC implies that when the project ends, we will have to increase NWC. So, at the end of the project, we will have a cash outflow to restore the NWC to its level before the project. We must also include the aftertax salvage value at the end of the project. The IRR of the project is: NPV = 0 = -$485,000 + $46,000 + $150,485(PVIFAIRR%,6) + [($49,770 - $46,000)/(1 + IRR)6]IRR = 25.61%
Fama's Llamas has a weighted average cost of capital of 8.9 percent. The company's cost of equity is 13 percent, and its pretax cost of debt is 6.2 percent. The tax rate is 23 percent. What is the company's target debt-equity ratio? (Do not round intermediate calculations and round your answer to 4 decimal places, e.g., 32.1616.)
Here we have the WACC and need to find the debt-equity ratio of the company. Setting up the WACC equation, we find: WACC = .0890 = .13(E/V) + .062(D/V)(1 - .23) Rearranging the equation, we find: .0890(V/E) = .13 + .062(.77)(D/E) Now we must realize that the V/E is just the equity multiplier, which is equal to: V/E = 1 + D/E .0890(D/E + 1) = .13 + .04774(D/E) Now we can solve for D/E as: .04126(D/E) = .041 D/E = .9937
You have $269,000 to invest in a stock portfolio. Your choices are Stock H, with an expected return of 14.4 percent, and Stock L, with an expected return of 12 percent. If your goal is to create a portfolio with an expected return of 12.95 percent, how much money will you invest in Stock H and in Stock L? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
Here, we are given the expected return of the portfolio and the expected return of the assets in the portfolio and are asked to calculate the dollar amount of each asset in the portfolio. So, we need to find the weight of each asset in the portfolio. Since we know the total weight of the assets in the portfolio must equal 1 (or 100%), we can find the weight of each asset as: E(Rp) = .1295 = .144 xH + .120(1 - xH) xH = .3958 xL = 1 - xH xL = 1 - .3958 xL = .6042 So, the dollar investment in each asset is the weight of the asset times the value of the portfolio, so the dollar investment in each asset must be: Investment in H = .3958($269,000) Investment in H = $106,479.17 Investment in L = .6042($269,000) Investment in L = $162,520.83
A stock has an expected return of 12.2 percent and a beta of 1.18, and the expected return on the market is 11.2 percent. What must the risk-free rate be? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Here, we need to find the risk-free rate, using the CAPM. Substituting the values given, and solving for the risk-free rate, we find: E(Ri) = Rf + [E(RM) - Rf] × βi .122 = Rf + (.112 - Rf)(1.18) .122 = Rf + .13216 - 1.18Rf Rf = .0564, or 5.64%
Bruno's Lunch Counter is expanding and expects operating cash flows of $31,700 a year for 6 years as a result. This expansion requires $110,300 in new fixed assets. These assets will be worthless at the end of the project. In addition, the project requires $7,800 of net working capital throughout the life of the project. What is the net present value of this expansion project at a required rate of return of 11 percent?
NPV = 0 = −$110,300 − 7,800 + 31,700(PVIFA11%,6) + 7,800/1.116NPV = $20,178
Sarah earned a 3.3 percent real rate of return on her investments for the past year. During that time, the risk-free rate was 3.6 percent and the inflation rate was 3.1 percent. What was her nominal rate of return?
Nominal rate = (1.033 ×1.031) − 1 = .0650, or 6.50 percent
What are the portfolio weights for a portfolio that has 195 shares of Stock A that sell for $96 per share and 170 shares of Stock B that sell for $130 per share? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., .1616.)
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. The portfolio weight of an asset is the total investment in that asset divided by the total portfolio value. First, we will find the portfolio value, which is: Total value = 195($96) + 170($130) Total value = $40,820 The portfolio weight for each stock is: xA = 195($96)/$40,820 xA = .4586, or 45.86% xB = 170($130)/$40,820 xB = .5414, or 54.14%
A stock has a beta of 1.29 and an expected return of 11.57 percent. If the risk-free rate is 4.4 percent, what is the stock's reward-to-risk ratio?
Reward-to-risk ratio = (.1157 − .044)/1.29 Reward-to-risk ratio = .0556, or 5.56%
Suppose a stock had an initial price of $102 per share, paid a dividend of $3.30 per share during the year, and had an ending share price of $80.50. a.Compute the percentage total return. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b.What was the dividend yield? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) c.What was the capital gains yield? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. Using the equation for total return, we find: R = [($80.50 - 102) + 3.30]/$102R = -.1784, or -17.84% And the dividend yield and capital gains yield are: Dividend yield = $3.30/$102 Dividend yield = .0324, or 3.24% Capital gains yield = ($80.50 - 102)/$102 Capital gains yield = -.2108, or -21.08%
Smathers Corp. stock has a beta of 1.19. The market risk premium is 7.40 percent and the risk-free rate is 3.02 percent annually. What is the company's cost of equity?
RE = .0302 + 1.19(.0740) RE = .1183, or 11.83%
The stock in Bowie Enterprises has a beta of .93. The expected return on the market is 12.30 percent and the risk-free rate is 3.18 percent. What is the required return on the company's stock?
RE = .0318 + .93(.1230 − .0318) RE = .1166, or 11.66%
Bethesda Water has an issue of preferred stock outstanding with a coupon rate of 6.00 percent that sells for $96.62 per share. If the par value is $100, what is the cost of the company's preferred stock?
RP = $6.00/$96.62 RP = .0621, or 6.21%
What range of returns should you expect to see with a 99 percent probability on an asset that has an average return of 10.61 percent and a standard deviation of 24.52 percent?
Range = 10.61% +/− (24.52*3)% Range = −62.95% to 84.17%
Bermuda Cruises issues only common stock and coupon bonds. The firm has a debt-equity ratio of 1.17. The cost of equity is 12.3 percent and the pretax cost of debt is 7 percent. What is the capital structure weight of the firm's equity if the firm's tax rate is 35 percent?
XE = 1/(1 + 1.17) XE = .4608
Kenny, Inc., is looking at setting up a new manufacturing plant in South Park. The company bought some land six years ago for $7.1 million in anticipation of using it as a warehouse and distribution site, but the company has since decided to rent facilities elsewhere. The land would net $9.9 million if it were sold today. The company now wants to build its new manufacturing plant on this land; the plant will cost $21.1 million to build, and the site requires $860,000 worth of grading before it is suitable for construction. What is the proper cash flow amount to use as the initial investment in fixed assets when evaluating this project? (Do not round intermediate calculations and enter your answer in dollars, not millions, rounded to the nearest whole number, e.g., 1,234,567.)
The $7.1 million acquisition cost of the land six years ago is a sunk cost. The $9.9 million current aftertax value of the land is an opportunity cost if the land is used rather than sold off. The $21.1 million cash outlay and $860,000 grading expenses are the initial fixed asset investments needed to get the project going. Therefore, the proper Year 0 cash flow to use in evaluating this project is: Cash flow = $9,900,000 + 21,100,000 + 860,000Cash flow = $31,860,000
A stock has a beta of 1.24, the expected return on the market is 11.8 percent, and the risk-free rate is 4.55 percent. What must the expected return on this stock be? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
The CAPM states the relationship between the risk of an asset and its expected return. The CAPM is: E(Ri) = Rf + [E(RM) - Rf] × βi Substituting the values we are given, we find: E(Ri) = .0455 + (.1180 - .0455)(1.24) E(Ri) = .1354, or 13.54%
Consider an asset that costs $715,000 and is depreciated straight-line to zero over its 10-year tax life. The asset is to be used in a 7-year project; at the end of the project, the asset can be sold for $201,000. What is the book value of the equipment at the end of the 7 years? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) If the relevant tax rate is 21 percent, what is the aftertax cash flow from the sale of this asset? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)
The asset has a useful life of 10 years and we want to find the book value of the asset after 7 years. With straight-line depreciation, the depreciation each year will be: Annual depreciation = $715,000/10Annual depreciation = $71,500 So, after 7 years, the accumulated depreciation will be: Accumulated depreciation = 7($71,500)Accumulated depreciation = $500,500 The book value at the end of Year 7 is thus: BV7 = $715,000 - 500,500BV7 = $214,500 The asset is sold at a loss to book value, so the depreciation tax shield of the loss is recaptured. Aftertax salvage value = $201,000 + ($214,500 - 201,000)(.21) Aftertax salvage value = $203,835 To find the taxes on salvage value, remember to use the equation: Taxes on salvage value = (BV - MV)TC This equation will always give the correct sign for a tax inflow (refund) or outflow (payment).
You own a stock portfolio invested 30 percent in Stock Q, 14 percent in Stock R, 40 percent in Stock S, and 16 percent in Stock T. The betas for these four stocks are .99, 1.05, 1.45, and 1.90, respectively. What is the portfolio beta? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. So, the beta of the portfolio is: βp = .30(.99) + .14(1.05) + .40(1.45) + .16(1.90) βp = 1.33
Sixth Fourth Bank has an issue of preferred stock with a $6.30 stated dividend that just sold for $125 per share. What is the bank's cost of preferred stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
The cost of preferred stock is the dividend payment divided by the price, so: RP = $6.30/$125 RP = .0504, or 5.04%
You own a portfolio that has $2,500 invested in Stock A and $3,600 invested in Stock B. Assume the expected returns on these stocks are 10 percent and 16 percent, respectively. What is the expected return on the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. The total value of the portfolio is: Total value = $2,500 + 3,600 Total value = $6,100 So, the expected return of this portfolio is: E(Rp) = ($2,500/$6,100)(.10) + ($3,600/$6,100)(.16) E(Rp) = .1354, or 13.54%
Consider the following information: State ofEconomyProbability of Stateof EconomyRate of Returnif State Occurs Recession.25 -.09 Normal.45 .11 Boom.30 .30 Calculate the expected return. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
The expected return of an asset is the sum of the probability of each state occurring times the rate of return if that state occurs. So, the expected return is: E(R) = .25(-.09) + .45(.11) + .30(.30) E(R) = .1170, or 11.70%
You purchased 250 shares of a particular stock at the beginning of the year at a price of $76.13. The stock paid a dividend of $1.35 per share, and the stock price at the end of the year was $82.64. What was your dollar return on this investment? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
To calculate the dollar return, we multiply the number of shares owned by the change in price per share and the dividend per share received. The total dollar return is: Dollar return = 250($82.64 - 76.13 + 1.35) Dollar return = $1,965.00
McCanless Co. recently purchased an asset for $2,750,000 that will be used in a 3-year project. The asset is in the 3-year MACRS class. The depreciation percentage each year is 33.33 percent, 44.45 percent, 14.81 percent, and 7.41 percent, respectively. What is the amount of depreciation in Year 2?
Year 2 depreciation = .4445($2,750,000) Year 2 depreciation = $1,222,375
Over a particular period, an asset had an average return of 11.3 percent and a standard deviation of 19.7 percent. What range of returns would you expect to see 68 percent of the time for this asset? (A negative answer should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) What about 95 percent of the time? (A negative answer should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
The mean return was 11.3 percent, with a standard deviation of 19.7 percent. The range of returns you would expect to see 68 percent of the time is the mean plus or minus 1 standard deviation(s), or: R∈ μ ± 1σ = 11.3% ± 1(19.7%) = -8.40% to 31.00% The range of returns you would expect to see 95 percent of the time is the mean plus or minus 2 standard deviations, or: R∈ μ ± 2σ = 11.3% ± 2(19.7%) = -28.10% to 50.70%
ICU Window, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 9 years to maturity that is quoted at 107 percent of face value. The issue makes semiannual payments and has an embedded cost of 6.6 percent annually. a.What is the company's pretax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)b.If the tax rate is 24 percent, what is the aftertax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
The pretax cost of debt is the YTM of the company's bonds, so: P0 = $1,070 = $33(PVIFAR%,18) + $1,000(PVIFR%,18) R = 2.800% YTM = 2 × 2.800% YTM = 5.60% And the aftertax cost of debt is: RD = .0560(1 - .24) RD = .0426, or 4.26%
Fill in the missing numbers in the following income statement: (Do not round intermediate calculations and round your answers to the nearest whole number, e.g. 32.) b.What is the OCF? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g. 32.)c.What is the depreciation tax shield? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g. 32.)
To find the OCF, we need to complete the income statement as follows: Sales$594,000 Variable costs 366,800 Depreciation 116,900 EBIT$110,300 Taxes (23%) 25,369 Net income$84,931 The OCF for the company is: OCF = EBIT + Depreciation - TaxesOCF = $110,300 + 116,900 - 25,369OCF = $201,831 The depreciation tax shield is the depreciation times the tax rate, so: Depreciation tax shield = Depreciation(TC)Depreciation tax shield = .23($116,900)Depreciation tax shield = $26,887 The depreciation tax shield shows us the increase in OCF by being able to expense depreciation.
You've observed the following returns on Yamauchi Corporation's stock over the past five years: -24.9 percent, 13.6 percent, 30.2 percent, 2.3 percent, and 21.3 percent. a.What was the arithmetic average return on the stock over this five-year period? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b.What was the variance of the returns over this period? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 32.161616.) c.What was the standard deviation of the returns over this period? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
To find the average return, we sum all the returns and divide by the number of returns, so: Arithmetic average return = (-.249 + .136 + .302 + .023 + .213)/5 Arithmetic average return = .0850, or 8.50% Using the equation to calculate variance, we find: Variance = 1/4[(-.249 - .0850)2 + (.136 - .0850)2 + (.302 - .0850)2 + (.023 - .0850)2 + (.213 - .0850)2] Variance = .045369 So, the standard deviation is: Standard deviation = .0453691/2 Standard deviation = .2130, or 21.30%
You've observed the following returns on Yamauchi Corporation's stock over the past five years: -28.5 percent, 16 percent, 35 percent, 3.5 percent, and 22.5 percent. The average inflation rate over this period was 3.35 percent and the average T-bill rate over the period was 4.3 percent. a.What was the average real return on the stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b.What was the average nominal risk premium on the stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
To find the average return, we sum all the returns and divide by the number of returns, so: Arithmetic average return = (-.285 + .160 + .350 + .035 + .225)/5 Arithmetic average return = .0970, or 9.70% a.To calculate the average real return, we can use the average return of the asset, and the average inflation rate in the Fisher equation. Doing so, we find: (1 + R) = (1 + r)(1 + h) r¯r¯ = (1.0970/1.0335) - 1r¯r¯ = .0614, or 6.14% b.The average risk premium is the average return of the asset, minus the average risk-free rate, so, the average risk premium for this asset would be: RP¯¯¯¯¯RP¯ = R¯¯¯−R¯¯¯fR¯−R¯fRP¯¯¯¯¯RP¯ = .0970 - .043RP¯¯¯¯¯RP¯ = .0540, or 5.40%
Stock J has a beta of 1.32 and an expected return of 13.76 percent, while Stock K has a beta of .87 and an expected return of 10.7 percent. You want a portfolio with the same risk as the market. a.What is the portfolio weight of each stock? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)b.What is the expected return of your portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
To find the expected return of the portfolio we first need to find the weight of each asset in the portfolio. The weights of the assets sum to 1 (or 100%), so we can solve for the weights using the betas of the each asset and the beta of the portfolio. Doing so, we find: ßp = 1 = xJ(1.32) + (1 - xJ)(.87) xJ = .2889 xK = 1 - .2889 xK = .7111 So, the expected return of the portfolio is: E(RP) = .2889(.1376) + .7111(.1070) E(RP) = .1158, or 11.58%
One year ago, Marcus purchased 400 shares of Maverick Data stock for $21,052. Today, he sold those shares for $56.00 per share. What is the total return on this investment if the dividend yield is 1.9 percent?
Total return = [($56.0 − ($21,052 / 400)] / ($21,052 / 400) + .019 = .083, or 8.30 percent
H. Cochran, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $2,350,000. The fixed asset will be depreciated straight-line to zero over its three-year tax life. The project is estimated to generate $3,330,000 in annual sales, with costs of $2,330,000. The project requires an initial investment in net working capital of $180,000 and the fixed asset will have a market value of $215,000 at the end of the project. Assume that the tax rate is 23 percent and the required return on the project is 11 percent. a. What are the net cash flows of the project each year? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.) b. What is the NPV of the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Using the tax shield approach to calculating OCF (Remember the approach is irrelevant; the final answer will be the same no matter which of the four methods you use.), we get: OCF = (Sales - Costs)(1 - TC) + Depreciation(TC)OCF = ($3,330,000 - 2,330,000)(1 - .23) + .23($2,350,000/3)OCF = $950,167 The cash outflow at the beginning of the project will increase because of the spending on NWC. At the end of the project, the company will recover the NWC, so it will be a cash inflow. The sale of the equipment will result in a cash inflow, but we must also account for the taxes which will be paid on this sale. So, the cash flows for each year of the project will be: YearCash Flow 0 -$2,530,000 = -$2,350,000 - 180,000 1 950,167 2 950,167 3 1,295,717 = $950,167 + 180,000 + 215,000 + (0 - 215,000)(.23) And the NPV of the project is: NPV = -$2,530,000 + $950,167(PVIFA11%,2) + $1,295,717/1.113NPV = $44,599.45
H. Cochran, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $3,100,000. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate $3,370,000 in annual sales, with costs of $2,390,000. If the tax rate is 24 percent, what is the OCF for this project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Using the tax shield approach to calculating OCF, we get: OCF = (Sales - Costs)(1 - TC) + Depreciation(TC)OCF = ($3,370,000 - 2,390,000)(1 - .24) + .24($3,100,000/3)OCF = $992,800.00 Remember the approach is irrelevant; the final answer will be the same no matter which of the four methods you use.
Wentworth's Five and Dime Store has a cost of equity of 10.5 percent. The company has an aftertax cost of debt of 4.1 percent, and the tax rate is 35 percent. If the company's debt-equity ratio is .65, what is the weighted average cost of capital?
WACC = (1/1.65)(10.5%) + (.65/1.65)(4.1%) WACC = 7.98%
Stock Y has a beta of 1.50 and an expected return of 13.0 percent. Stock Z has a beta of .95 and an expected return of 10.3 percent. What would the risk-free rate have to be for the two stocks to be correctly priced relative to each other? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
We need to set the reward-to-risk ratios of the two assets equal to each other, which is: (.130 - Rf)/1.50 = (.103 - Rf)/.95 We can cross multiply to get: .95(.130 - Rf) = 1.50(.103 - Rf) Solving for the risk-free rate, we find: .1235 - .95Rf = .1545 - 1.50Rf Rf = .0564, or 5.64%
Clifford, Inc., has a target debt-equity ratio of 1.15. Its WACC is 8.3 percent, and the tax rate is 22 percent. a. If the company's cost of equity is 12 percent, what is its pretax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b.If instead you know that the aftertax cost of debt is 5.9 percent, what is the cost of equity? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
a. Using the equation to calculate WACC, we find: WACC = .083 = (1/2.15)(.12) + (1.15/2.15)(1 - .22)RD RD = .0652, or 6.52% b. Using the equation to calculate WACC, we find: WACC = .083 = (1/2.15)RE + (1.15/2.15)(.059) RE = .1106, or 11.06%
Baron Corporation has a target capital structure of 75 percent common stock, 10 percent preferred stock, and 15 percent debt. Its cost of equity is 11 percent, the cost of preferred stock is 5 percent, and the pretax cost of debt is 6 percent. The relevant tax rate is 23 percent. a. What is the company's WACC? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b.What is the aftertax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
a. Using the equation to calculate the WACC, we find: WACC = .75(.11) + .10(.05) + .15(.06)(1 - .23) WACC = .0944, or 9.44% b. The aftertax cost of debt is: RD = .06(1 - .23) RD = .0462, or 4.62%
Consider the following information on large-company stocks for a period of years. Arithmetic Mean Large-company stocks12.5% Inflation3.7 a.What was the arithmetic average annual return on large-company stocks in nominal terms? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b.What was the arithmetic average annual return on large-company stocks in real terms? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
a.The nominal return is the stated return, which is 12.5 percent. b.Using the Fisher equation, the real return was: (1 + R) = (1 + r)(1 + h) r = (1.1250)/(1.037) - 1r = .0849, or 8.49%
Consider the following information: Rate of Return if State OccursState ofProbability of StateEconomyof EconomyStock AStock BStock C Boom.66 .09 .03 .34 Bust.34 .23 .29 -.14 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b.What is the variance of a portfolio invested 21 percent each in A and B and 58 percent in C? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)
a.To find the expected return of the portfolio, we need to find the return of the portfolio in each state of the economy. This portfolio is a special case since all three assets have the same weight. To find the return in an equally weighted portfolio, we can sum the returns of each asset and divide by the number of assets, so the return of the portfolio in each state of the economy is: Boom: Rp = (.09 + .03 + .34)/3 Rp = .1533, or 15.33% Bust: Rp = (.23 + .29 - .14)/3 Rp = .1267, or 12.67% This is equivalent to multiplying the weight of each asset (1/3 or .3333) times its expected return and summing the results, which gives: Boom: Rp = 1/3(.09) + 1/3(.03) + 1/3(.34) Rp = .1533, or 15.33% Bust: Rp = 1/3(.23) + 1/3(.29) + 1/3(-.14) Rp = .1267, or 12.67% To find the expected return of the portfolio, we multiply the return in each state of the economy by the probability of that state occurring, and then sum. Doing this, we find: E(Rp) = .66(.1533) + .34(.1267) E(Rp) = .1443, or 14.43% b.This portfolio does not have an equal weight in each asset. We still need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get: Boom: Rp = .21(.09) +.21(.03) + .58(.34) Rp = .2224, or 22.24% Bust: Rp = .21(.23) +.21(.29) + .58(-.14) Rp = .0280, or 2.80% And the expected return of the portfolio is: E(Rp) = .66(.2224) + .34(.0280) E(Rp) = .1563, or 15.63% 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 of the portfolio is: σp2 = .66(.2224 - .1563)2 + .34(.0280 - .1563)2 σp2 = .00848
A stock has had returns of −19.3 percent, 29.3 percent, 27.6 percent, −10.4 percent, 35.1 percent, and 27.3 percent over the last six years. What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
he arithmetic average return is the sum of the known returns divided by the number of returns, so: Arithmetic average return = (-.193 + .293 + .276 - .104 + .351 + .273)/6 Arithmetic average return = .1493, or 14.93% Using the equation for the geometric return, we find: Geometric average return = [(1 + R1) × (1 + R2) × ... × (1 + RT)]1/T - 1 Geometric average return = [(1 - .193)(1 + .293)(1 + .276)(1 - .104)(1 + .351)(1 + .273)](1/6) - 1 Geometric average return = .1272, or 12.72% Remember, the geometric average return will always be less than the arithmetic average return if the returns have any variation.
You have a portfolio that is equally invested in Stock F with a beta of 1.10, Stock G with a beta of 1.47, and the market. What is the beta of your portfolio?
βPortfolio = 1/3(1.10) + 1/3(1.47) + 1/3(1) βPortfolio = 1.19
