Sirmans FINC 3610 Final Exam
$-1,021.52 The NPV of a project is the PV of the outflows minus the PV of the inflows. The equation for the NPV of the project at a 38 percent required return is: NPV = - $31,000 + $24,000/1.38 + $16,000/1.382 + $11,000/1.383 = $-1,021.52 At a 38 percent required return, the NPV is negative, so we would reject the project.
A firm evaluates all of its projects by using the NPV decision rule. Year Cash Flow 0 -$31,000 1 24,000 2 16,000 3 11,000 At a required return of 38 percent, what is the NPV for this project?
Answer 1: $9,834.05 Answer 2: 21.55%
Mahjong, Inc., has identified the following two mutually exclusive projects. If the required return is 8 percent, Project A has an NPV of $9,834.05 and an IRR of 21.55% . Year Cash Flow (A) Cash Flow (B) 0 -$36,000 -$36,000 1 18,900 6,100 2 14,400 12,600 3 11,900 19,100 4 8,900 23,100
1.37 NWC = CA - CL CA = CL + NWC = $4,450 + $1,640 = $6,090 So, the current ratio is: Current ratio = CA / CL = $6,090/$4,450 = 1.37 times
SDJ, Inc., has net working capital of $1,640, current liabilities of $4,450, and inventory of $1,895. What is the current ratio? Hint: Current ratio is CR = CA / CL.
4.42 The weighted average flotation cost is the weighted average of the flotation costs for debt and equity, so: fT = .02(.65/1.65) + .06(1/1.65) fT = .0442, or 4.42%
Suppose your company needs $43 million to build a new assembly line. Your target debt-equity ratio is .65. The flotation cost for new equity is 6 percent and the flotation cost for debt is 2 percent. Your boss has decided to fund the project by borrowing money because the flotation costs are lower and the needed funds are relatively small. What is your company's weighted average flotation cost, assuming all equity is raised externally? Round to the nearest XX.XX%.
4,755.34 To find the price of this bond, we need to find the present value of the bond's cash flows. So, the price of the bond is: P = $72.50(PVIFA1.70%,24) + $5,000(PVIF1.70%,24) P = $4,755.34
Union Local School District has bonds outstanding with a coupon rate of 2.9 percent paid semiannually and 12 years to maturity. The yield to maturity on these bonds is 3.4 percent and the bonds have a par value of $5,000. What is the dollar price of each bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
sole proprietorships
Which of the following legal forms of organization has the ease of dissolution?
Corporations
Which of the following legal forms of organization is most expensive to organize?
0.8996 (with margin: 0.01) First set up the WACC equation: WACC = 0.115 = 0.17(E/V) + 0.07(D/V)(1 - 0.31) where V = E+D. Then rearrange and try substituting V/E = 1 + D/E. Ultimately, you want to solve for D/E.
Fama's Llamas calculated the weighted average cost of capital (WACC) using its target debt-equity ratio and found it to be 11.5 percent. The company's cost of equity is 17.5 percent, and its pretax cost of debt is 7 percent. The aftertax cost of debt is used in the WACC calculation with a tax rate of 31 percent. What is the company's target debt-equity ratio (D/E)? Round to the nearest X.XXX.
22.31 Taxes = .10($9,525) + .12($38,700 − 9,525) + .22($82,500 − 38,700) + .24($157,500 − 82,500)+ .32($189,000 − 157,500) Taxes = $42,169.50 The average tax rate is the total tax paid divided by taxable income, so: Average tax rate = $42,169.50/$189,000 Average tax rate = .2231, or 22.31%
Terri Simmons is single and had $189,000 in taxable income. What is the average tax rate?
10.91 CAPM states the relationship between the risk of an asset and its expected return. CAPM is: E(Ri) = Rf + [E(RM) − Rf] × βi Substituting the values we are given, we find: E(Ri) = .035 + (.10 − .035)(1.14) E(Ri) = .1091, or 10.91%
A stock has a beta of 1.14, the expected return on the market is 10 percent, and the risk-free rate is 3.5 percent. What must the expected return on this stock be? Round to the nearest XX.XX%
5.67 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) = .110 = Rf + (.090 − Rf)(1.60) .110 = Rf + .14400 − 1.60Rf Rf = .0567, or 5.67%
A stock has an expected return of 11 percent, its beta is 1.60, and the expected return on the market is 9 percent. What must the risk-free rate be? Round to the nearest XX.XX%
15.4 Using the DuPont identity, the ROE is: ROE = (PM)(TAT)(EM) ROE = (.061)(1.87)(1.35) ROE = .1540, or 15.40%
If Muenster, Inc., has an equity multiplier of 1.35, total asset turnover of 1.87, and a profit margin of 6.1 percent, what is its ROE? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Hint: Use the DuPont Identity.
2.57 (with margin: 0.03)
Suppose a stock had an initial price of $76 per share, paid a dividend of $1.95 per share during the year, and had an ending share price of $84. What was the dividend yield? Round to the nearest XX.XX%.
11.48 The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. The return of this stock is: R = ($96 - 88 + 2.10) / $88 R = .1148, or 11.48%
Suppose a stock had an initial price of $88 per share, paid a dividend of $2.10 per share during the year, and had an ending share price of $96. Compute the percentage total return. Round to the nearest XX.XX%.
28.56 The constant dividend growth model is: Pt = Dt × (1 + g) / (R - g) So the price of the stock today is: P0 = D0 (1 + g) / (R - g) = $1.36 (1.05) / (.10 - .05) = $28.56
The Jackson-Timberlake Wardrobe Co. just paid a dividend of $1.36 per share on its stock. The dividends are expected to grow at a constant rate of 5 percent per year indefinitely. If investors require a 10 percent return on The Jackson-Timberlake Wardrobe Co. stock, what is the current price?
9.64 With the information given, we can find the cost of equity using the CAPM. The cost of equity is: RS = .027 + .95(.10 − .027) RS = .0964, or 9.64%
The Nixon Corporation's common stock has a beta of .95. If the risk-free rate is 2.7 percent and the expected return on the market is 10 percent, what is the company's cost of equity capital? Round to the nearest XX.XX%. Hint: Use the CAPM formula.
Corporations
Under which of the following legal forms of organization is ownership readily transferable?
-3.32 The average return for large-company stocks over this period was: Large company stocks average return = 19.41%/6 = 3.24% And the average return for T-bills over this period was: T-bills average return = 39.31%/6 = 6.55% The difference is 3.24 - 6.55 = -3.31.
Year l-Company Stocks US Treasury Bills 1 -14.69 7.29 2 -26.47 7.99 3 37.23 5.87 4 23.93 5.07 5 -7.16 5.45 6 6.57 7.64 On average, how much more did large-company stocks generate in return over US Treasury bills? Compute the average return of large-company stocks, then for US Treasury bills, and then compute the difference (large stocks minus US T-bills). Round your answer to the nearest XX.XX%.
$52,366.85 Future Value=FV(rate,nper,pmt,pv)= $52,366.85 rate=8.00% nper=6 pmt=0 pv=$(33,000.00)
You are scheduled to receive $33,000 in two years. When you receive it, you will invest it for 6 more years at 8.0 percent per year. How much will you have in 8 years?
14.88 E(RP) = .32(.10) + .20(.20) + .48(.16) E(RP) = .1488, or 14.88%
You own a portfolio that is 32 percent invested in Stock X, 20 percent in Stock Y, and 48 percent in Stock Z. The expected returns on these three stocks are 10 percent, 20 percent, and 16 percent, respectively. What is the expected return on the portfolio? Round to the nearest XX.XX%
Taxable as personal income when received by shareholders even though that income was taxed at the corporate level.
1. Corporate dividends are:
sole proprietorships
1. Which of the following forms of organizations is the easiest to form?
limited liability
1. Which of the following is a strength of a corporation?
Increasing current profits when doing so lowers the value of the firm's equity
1. Which one of the following actions by a financial manager is most apt to create an agency problem?
Maximize the current value per share
1. Which one of the following best states the primary goal of financial management?
10.1 The required return of a stock is made up of two parts: The dividend yield and the capital gains yield. So, the required return of this stock is: R = Dividend yield + Capital gains yield R = .049 + .052 R = .1010, or 10.10%
Change, Inc., is expected to maintain a constant 4.9 percent growth rate in its dividends, indefinitely. The company has a dividend yield of 5.2 percent. What is the required return on the company's stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
53,562 Income Statement Sales $865,000 Cost of goods sold 455,000 Selling costs 210,000 Depreciation 105,000 EBIT$95,000 Interest 27,200 Taxable income$67,800 Taxes (21%) 14,238 Net income$53,562
During the year, the Senbet Discount Tire Company had gross sales of $865,000. The firm's cost of goods sold and selling expenses were $455,000 and $210,000, respectively. The company also had notes payable of $680,000. These notes carried an interest rate of 4 percent. Depreciation was $105,000. The tax rate was 21 percent. What was the company's net income? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars, rounded to the nearest whole dollar amount, e.g., 1,234,567.) Hint: Build the income statement. The interest expense for the company is the amount of debt times the interest rate on the debt.
EBIT = Sales - costs - other expenses - depreciation expense = $214000 - $91000 - $6100 - $9100 = $107800 Operating cash flow = EBIT + Depreciation expense - Taxes = $107800 + $9100 - $37800 = $79,100
Jetson Spacecraft Corp. shows the following information on its 2019 income statement: sales = $214,000; costs = $91,000; other expenses = $6,100; depreciation expense = $9,100; interest expense = $13,300; taxes = $37,800; dividends = $10,100. In addition, you're told that the firm issued $7,900 in new equity during 2009 and redeemed $9,500 in outstanding long-term debt. What is the 2019 operating cash flow? Hint: OCF = EBIT + Depreciation - Taxes.
$78,826 NI = (ROE)(TE) NI = (0.1564)($504,000) = $78,826
Organic Chicken Company has a debt-equity ratio of 0.70. Return on assets is 9.20 percent, and total equity is $504,000. What is the net income? Hint: You'll need the ROE...
$500
Penguin Pucks, Inc., has current assets of $3,400, net fixed assets of $18,500, current liabilities of $2,900, and long-term debt of $7,700. How much is net working capital? Hint: NWC = CA − CL.
$11,300 OE = $21,900 − 7,700 − 2,900 = $11,300
Penguin Pucks, Inc., has current assets of $3,400, net fixed assets of $18,500, current liabilities of $2,900, and long-term debt of $7,700. What is the value of the shareholders' equity account for this firm? Hint: Construct a simple balance sheet and remember the two sides must balance.
$110 NWC = Current assets - Current liabilities NWC at the end of year 2018 (at the beginning of year 2019) = 1490 -980 = 510 NWC at the end of year 2019 = 1700- 1080 = 620 Changes in NWC for the year 2019 = 620- 510= 110
The 2018 balance sheet of Saddle Creek, Inc., showed current assets of $1,490 and current liabilities of $980. The 2019 balance sheet showed current assets of $1,700 and current liabilities of $1,080. What was the company's 2019 change in net working capital, or NWC? Hint: Change in NWC = NWCend - NWCbeg
10.46 R = (D1/P0) + g R = ($2.95/$53.10) + .048 R = .1036, or 10.36%
The next dividend payment by Skippy, Inc., will be $2.95 per share. The dividends are anticipated to maintain a growth rate of 4.8 percent, forever. The stock currently sells for $53.10 per share. What is the required return (in percentage terms, round your answer to 2 decimal places)? Hint: Use the formula R = (D1/P0) + g
24.26% 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 = -$9,444 + $5,700/(1+IRR) + $4,200/(1+IRR)^2 + $4,100/(1+IRR)^3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 24.26%
What is the IRR of the following set of cash flows? Year Cash Flow 0 -$9,444 1 5,700 2 4,200 3 4,100
$226,800 Income Statement Sales$704,000 Costs -255,000 Depreciation - 39,000 EBIT= $410,000 Interest - 32,000 EBT= $378,000 Taxes (40%) = - 151,200 Net income = $226,800
XXL Roach Exterminators, Inc., has sales of $704,000, costs of $255,000, depreciation expense of $39,000, interest expense of $32,000, and a tax rate of 40 percent. What is the net income for firm? Hint: Construct a simple income statement using the information given.
0.37 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: Portfolio value = 145($47) + 130($86) Portfolio value = $17,995 The portfolio weight for each stock is the dollar value of the investment in that stock divided by the portfolio value, or: WeightA = 145($47)/$17,995 WeightA = .3787 WeightB = 130($86)/$17,995 WeightB = .6213
Your portfolio has 145 shares of Stock A that sell for $47 per share and 130 shares of Stock B that sell for $86 per share. What is the portfolio weight for Stock A? Your answer should be between 0 and 1 with two decimal places. Hint: The portfolio weight of an asset is the total investment in that asset divided by the total portfolio value. Remember that total investment (in dollars) is equal to the stock price multiplied by the number of shares.
$2,302.38 The NPV of a project is the PV of the outflows minus by the PV of the inflows. Since the cash inflows are an annuity, the equation for the NPV of this project at an 9 percent required return is: NPV = -$13,100 + $2,400(PVIFA0.09%, 10) = $2,302.38 At an 9 percent required return, the NPV is positive, so we would accept the project.
A project that provides annual cash flows of $2,400 for 10 years costs $13,100 today. If the required return is 9 percent, what is the NPV for this project?
12.1 Using the CAPM, the cost of equity is: RS = .037 + 1.15(.11 − .037) RS = .1210, or 12.10%
Floyd Industries stock has a beta of 1.15. The company just paid a dividend of $.75 and the dividends are expected to grow at 4.5 percent per year. The expected return on the market is 11 percent and Treasury bills are yielding 3.7 percent. The most recent stock price for the company is $84. Calculate the cost of equity using the Capital Asset Pricing Model. Round to the nearest XX.XX%.
15.64% The equity multiplier is: EM = 1 + D/E EM = 1 + 0.70 = 1.70 Then use: ROE = (ROA)(EM) = 0.092(1.70) = 0.1564 or 15.64% You can also use ROE = NI / TE.
Organic Chicken Company has a debt-equity ratio of 0.70. Return on assets is 9.20 percent, and total equity is $504,000. What is the return on equity (ROE)? Hint: First find the equity multiplier, EM = 1 + D/E. Then use the EM to convert ROA to ROE.
7.6 We have a special case where the portfolio is equally weighted, so we can sum the returns of each asset and divide by the number of assets. The expected return of the portfolio is: E(RP) = (.116 + .036)/2 E(RP) = .0760, or 7.60%
A stock has a beta of 1.08 and an expected return of 11.6 percent. A risk-free asset currently earns 3.6 percent. What is the expected return on a portfolio that is equally invested in the two assets?
5.43 (with margin: 0.05)
Floyd Industries stock has a beta of 1.15. The company just paid a dividend of $.75 and the dividends are expected to grow at 4.5 percent per year. The expected return on the market is 11 percent and Treasury bills are yielding 3.7 percent. The most recent stock price for the company is $84. Calculate the cost of equity using the dividend growth method. Round to the nearest XX.XX%.
$1,400 To find owners' equity, we must construct a balance sheet as follows: Balance Sheet CA$4,300 CL$2,900 NFA 24,000 LTD 10,700 OE ?? TA$28,300 TL & OE$28,300 We know that total liabilities and owners' equity (TL & OE) must equal total assets of $28,300. We also know that TL & OE is equal to current liabilities plus long-term debt plus owners' equity, so owners' equity is: NWC = Current assets − Current liabilities NWC = $4,300 − 2,900 NWC = $1,400
Alesha, Inc., has current assets of $4,300, net fixed assets of $24,000, current liabilities of $2,900, and long-term debt of $10,700.(Do not round intermediate calculations.) How much is net working capital? Hint: Total assets = Current assets + Net fixed assets = Current liabilities + Long-term debt + Owners' equity Net working capital = Current assets − Current liabilities
$-589.11 The NPV at a 22 percent required return is: NPV = -$9,900 + $4,900/1.22 + $3,700/1.22^2 + $5,100/1.22^3 = $-589.11
For the following set of cash flows, what is the NPV at a discount rate of 22 percent? Year Cash Flow 0 -$9,900 1 4,900 2 3,700 3 5,100
$815 New investment in fixed assets is found by: Net investment in FA = (NFAend - NFAbeg) + Depreciation Net investment in FA = $675 + 140 = $815 The company bought $815 in new fixed assets; this is a use of cash.
For the year just ended, Ypsilanti Yak Yogurt shows an increase in its net fixed assets account of $675. The company took $140 in depreciation expense for the year. How much did the company spend on new fixed assets?
6.8 Using the equation to calculate WACC, we find: RWACC = .101 = (1/1.38)(.12) + (.38/1.38)(1 − .25)RB RB = .0680, or 6.80%
Kose, Inc., has a target debt-equity ratio of .38. Its WACC is 10.1 percent and the tax rate is 25 percent. If the company's cost of equity is 12 percent, what is its pretax cost of debt? Round to the nearest XX.XX%. Hint: Set up the WACC equation, leaving pretax cost of debt unknown, and solve for it.
Answer 1: $12,592 NPV of Project B is: NPVB = -$36,000 + $6,100/1.08 + $12,600/1.08^2 + $19,100/1.08^3 + $23,100/1.08^4 NPVB = $12,592 Answer 2: 20.03% The equation for the IRR of Project B is: 0 = -$36,000 + $6,100/(1+IRR) + $12,600/(1+IRR)^2 + $19,100/(1+IRR)^3 + $23,100/(1+IRR)^4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 20.03%
Mahjong, Inc., has identified the following two mutually exclusive projects. If the required return is 8 percent, Project B has an NPV of $12,592 and an IRR of 20.03% . Year Cash Flow (A) Cash Flow (B) 0 -$36,000 -$36,000 1 18,900 6,100 2 14,400 12,600 3 11,900 19,100 4 8,900 23,100
10.60% Here we are finding the YTM of a semiannual coupon bond. The bond price equation is: P = 1,000 = $53(PVIFAr%,32) + $1,000(PVIFr%,32) Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find: R = 5.3000% Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR of the bond, so: YTM = 2 × 5.3000% = 10.60%
Ngata Corp. issued 18-year bonds 2 years ago at a coupon rate of 10.6 percent. The bonds make semiannual payments. If these bonds currently sell for 100 percent of par value, what is the YTM?
10.51% The effective annual yield is the same as the EAR, so using the EAR equation: Effective annual yield = (1 + 0.05125)2 - 1 = 0.1051 or 10.51%
One More Time Software has 8.8 percent coupon bonds on the market with 15 years to maturity. The bonds make semiannual payments and currently sell for 89.0 percent of par. What is the effective yield? To answer this, remember the difference between the stated rate and effective rate. In this case, use the YTM you found in the previous problem as the stated rate.
10.25% The bond price equation for this bond is: P0 = $890 = $44(PVIFA r%,30) + $1,000(PVIF r%,30) Using a spreadsheet, financial calculator, or trial and error we find: R = 5.125% This is the semiannual interest rate, so the YTM is: YTM = 2 × 5.125% = 10.25%
One More Time Software has 8.8 percent coupon bonds on the market with 15 years to maturity. The bonds make semiannual payments and currently sell for 89.0 percent of par. What is the yield to maturity (YTM)?
12.79 Given V = $511,000,000 + 132,350,000 = $643,350,000 And the market value weights of equity and debt are: E/V = $511,000,000/$643,350,000 = 0.7943 D/V = 1 - E/V = 0.2057 Using the costs we found previously and relative weights of debt and equity, the WACC is: WACC = 0.7943(0.1466) + 0.2057(0.0558) = 0.1279 or 12.79%
Filer Manufacturing has 7 million shares of common stock outstanding. The current share price is $73, and the book value per share is $8. The most recent dividend was $4.5 and the dividend growth rate is 8 percent. Filer Manufacturing also has two bond issues outstanding. The first bond issue has a face value of $75 million, has a 8 percent coupon, and sells for 98 percent of par. The second issue has a face value of $55 million, has a 9 percent coupon, and sells for 107 percent of par. The first issue matures in 23 years, the second in 7 years. Assume that the overall cost of debt is the weighted average (using market values) of that implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 30 percent. What is the weighted average cost of capital (WACC)? It should include the aftertax cost of debt. Round to the nearest XX.XX%.
1,907.45 To find the price of this bond, we need to find the present value of the bond's cash flows. So, the price of the bond is: P = $49(PVIFA2.70%, 26) + $2,000(PVIF2.70%, 26) P = $1,907.45
Yan Yan Corp. has a $2,000 par value bond outstanding with a coupon rate of 4.9 percent paid semiannually and 13 years to maturity. The yield to maturity of the bond is 5.4 percent. What is the dollar price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
20.33 σ = [SUM((x -mean(x))^2)/(N-1)]^1/2 σ = .04133^1/2 σ = .2033, or 20.33%
Year Returns 1 12 2 24 3 -27 4 14 5 19 Using the returns shown above, calculate the standard deviation. (Do not round intermediate calculations. Enter your standard deviation as a percent rounded to 2 decimal places, e.g., 32.16.)
capital expenditures manager
1. A ______ is responsible for evaluating and recommending proposed long-term investments.
10.67 (with margin: 0.05)
A stock has had returns of 23 percent, 11 percent, 37 percent, −3 percent, 22 percent, and −17 percent over the last six years. What is the geometric average return for the stock? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Hint: Use the formula Geometric average return = [(1 + R1) × (1 + R2) × ... × (1 + RT)]1/T − 1
7.12% Here we need to find the YTM of a bond. The equation for the bond price is: P = $907.03 = $60(PVIFAR%,13) + $1,000(PVIFR%,13) Notice the equation cannot be solved directly for R. Using a spreadsheet, a financial calculator, or trial and error, we find: R = YTM = 7.12%
Ackerman Co. has 6 percent coupon bonds on the market with thirteen years left to maturity. The bonds make annual payments. If the bond currently sells for $907.03, what is its YTM? Assume a par value of $1,000.
-13.17% we will construct the equation for future value at the annual rate of return at which a principal of 1,680,000 return 1,100,000 in three years: Principal 1,680,000 time 3 years Amount 1,100,000 rate r 1,680,00(1+r)^3 = 1,100,000 r= 3| -------------------- \ | 1,100,00 / 1,680,000 - 1 r = -0.131650681 = -13.17% As expected, because the amount after three years is lower than the principal the rate of return is negative
Although appealing to more refined tastes, art as a collectible has not always performed profitably. During 2010, Deutscher-Menzies sold Arkie under the Shower, a painting by renowned Australian painter Brett Whiteley, at auction for a price of $1,100,000. Unfortunately for the previous owner, he had purchased it three years earlier at a price of $1,680,000. What was his annual rate of return on this painting? (A negative value 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.)
-4.46% FV = PV(1 + r)^t Solving for r, we get: r = (FV / PV)^(1 / t) - 1 r = ($10,309,500 / $12,374,500)^(1/4) - 1 = -4.46% Notice that the interest rate is negative. This occurs when the FV is less than the PV.
Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, a sculpture was sold at auction for a price of $10,309,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,374,500. What was his annual rate of return on this sculpture?
1.82 years When we use discounted payback, we need to find the value of all cash flows today. The value today of the project cash flows for the first four years is: Value today of Year 1 cash flow = $5,200/1.19 = $4,369.75 Value today of Year 2 cash flow = $6,300/1.192 = $4,448.84 Value today of Year 3 cash flow = $7,100/1.193 = $4,213.25 Value today of Year 4 cash flow = $8,400/1.194 = $4,188.82 To find the discounted payback, we use these values to find the payback period. The discounted first year cash flow is 4,369.75, so the discounted payback for an $8,000 initial cost is: Discounted payback = 1 + ($8,000 − 4,369.75)/$4,448.84 = 1.82 years
An investment project has annual cash inflows of $5,200, $6,300, $7,100, and $8,400, and a discount rate of 19 percent. What is the discounted payback period for these cash flows if the initial cost is $8,000?
5.6 years For an initial cost of $3,640, the payback period is: Payback = $3,640 / $650 = 5.6 years
An investment project provides cash inflows of $650 per year for 9 years. What is the project payback period if the initial cost is 3,640?
2,419.35 A consol is a perpetuity. To find the PV of a perpetuity, we use the equation: PV = C/r PV = $75/.031 PV = $2,419.35
An investor purchasing a British consol is entitled to receive annual payments from the British government forever. What is the price of a consol that pays $75 annually if the next payment occurs one year from today? The market rate is 3.1 percent. (Round your answer to 2 decimal places, e.g., 32.16.)
206.08 The price of any financial instrument is the PV of the future cash flows. The future dividends of this stock are an annuity for 10 years, so the price of the stock is the PVA, which will be: P0 = $28(PVIFA 6%,10) = $206.08
Apocalyptica Corp. pays a constant $28 dividend on its stock. The company will maintain this dividend for the next 10 years and will then cease paying dividends forever. If the required return on this stock is 6 percent, what is the current share price?
9.40% Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P = $1,286.50 = C(PVIFA3.2%,30) + $1,000(PVIF3.2%,30) Solving for the coupon payment, we get: C = $47.00 Since this is the semiannual payment, the annual coupon payment is: 2 × $47.00 = $93.99
Ashes Divide Corporation has bonds on the market with 15 years to maturity, a YTM of 6.4 percent, and a current price of $1,286.50. The bonds make semiannual payments. What must the coupon rate be on these bonds?
0.26 This question gives all of the necessary ratios for the DuPont Identity except the equity multiplier, so, using the DuPont Identity: ROE = (PM)(TAT)(EM) ROE = 0.1871 = (0.107)(1.39)(EM) EM = 0.1871 / (0.107)(1.39) = 1.26 D/E = EM - 1 = 1.26 - 1 = 0.26
Braam Fire Prevention Corp. has a profit margin of 10.70 percent, total asset turnover of 1.39, and ROE of 18.71 percent. What is its firm's debt-equity ratio? Hint: Refer to the Du Pont Identity.
40.67 This stock has a constant growth rate of dividends, but the required return changes twice. To find the value of the stock today, we will begin by finding the price of the stock at Year 6, when both the dividend growth rate and the required return are stable forever. The price of the stock in Year 6 will be the dividend in Year 7, divided by the required return minus the growth rate in dividends. So: P6 = D6(1 + g)/(R − g) P6 = D0(1 + g)^7/(R - g) P6 = $3.15(1.04)^7/(.11 − .04) P6 = $59.22 Now we can find the price of the stock in Year 3. We need to find the price here since the required return changes at that time. The price of the stock in Year 3 is the PV of the dividends in Years 4, 5, and 6, plus the PV of the stock price in Year 6. The price of the stock in Year 3 is: P3 = $3.15(1.04)^4/1.13 + $3.15(1.04)^5/1.132 + $3.15(1.04)^6/1.133 + $59.22/1.13^3 P3 = $50.07 Finally, we can find the price of the stock today. The price today will be the PV of the dividends in Years 1, 2, and 3, plus the PV of the stock in Year 3. The price of the stock today is: P0 = $3.15(1.04)/1.15 + $3.15(1.04)^2/(1.15)^2 + $3.15(1.04)^3/(1.15)^3 + $50.07/(1.15)^3 P0 = $40.67
Bretton, Inc., just paid a dividend of $3.15 on its stock. The growth rate in dividends is expected to be a constant 4 percent per year, indefinitely. Investors require a 15 percent return on the stock for the first three years, a 13 percent return for the next three years, and then an 11 percent return thereafter. What is the current share price for the stock? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
9,213.51 PV = FV/(1 + r)^t PV = $13,827/(1.07)^6 = $9,213.51
Compute the present value given the following information. Present Value ??? Years . 6 Interest Rate 7% Future value $13,827
9,425.69 To find the PV of a lump sum, we use: PV = FV/(1 + r)^t PV = $43,852/(1.15)^11 = $9,425.69
Compute the present value given the following information. Present Value ??? Years 11 Interest Rate 15% Future value 43,852
185,762 OCF = EBIT + Depreciation − Taxes OCF = $95,000 + 105,000 − 14,238 OCF = $185,762
During the year, the Senbet Discount Tire Company had gross sales of $865,000. The firm's cost of goods sold and selling expenses were $455,000 and $210,000, respectively. The company also had notes payable of $680,000. These notes carried an interest rate of 4 percent. Depreciation was $105,000. The tax rate was 21 percent. What was the company's operating cash flow? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars, rounded to the nearest whole dollar amount, e.g., 1,234,567.) Hint: OCF = EBIT + Depreciation − Taxes
43.46 With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the PV of the future stock price, plus the PV of all dividends during the supernormal growth period. The stock begins constant growth in Year 4, so we can find the price of the stock in Year 4, at the beginning of the constant dividend growth, as: P4 = D4 (1 + g) / (R - g) = $3(1.07) / (.15 - .07) = $40.13 The price of the stock today is the PV of the first four dividends, plus the PV of the Year 4 stock price. So, the price of the stock today will be: P0 = $11 / 1.15 + $7 / 1.15^2 + $6 / 1.15^3 + $3 / 1.15^4 + $40.13 / 1.15^4 = $43.46
Far Side Corporation is expected to pay the following dividends over the next four years: $11, $7, $6, and $3. Afterward, the company pledges to maintain a constant 7 percent growth rate in dividends forever. If the required return on the stock is 15%, what is the current share price?
9.01% Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P = $930 = C(PVIFA10.0%,13) + $1,000(PVIF10.0%,13) Solving for the coupon payment, we get: C = $90.15 The coupon payment is the coupon rate times par value. Using this relationship, we get:Coupon rate = $90.15 / $1,000 = 0.0901 or 9.01%
Kiss the Sky Enterprises has bonds on the market making annual payments, with 13 years to maturity, and selling for $930. At this price, the bonds yield 10.0 percent. What must the coupon rate be on the bonds?
Project B because the NPV is greater. The NPV indicates how much value is created for the firm, and the NPV of project B is higher than that of project A.
Mahjong, Inc., has identified the following two mutually exclusive projects. If the required return is 8%, which project creates more value for the firm? Year Cash Flow (A) Cash Flow (B) 0 -$36,000 -$36,000 1 18,900 6,100 2 14,400 12,600 3 11,900 19,100 4 8,900 23,100
47.02 Here we have a stock that pays no dividends for 9 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. It is important to remember the general constant dividend growth formula is: Pt = [Dt × (1 + g)] / (R - g) This means that since we will use the dividend in Year 9, we will be finding the stock price in Year 8. The dividend growth model is similar to the PVA and the PV of a perpetuity: The equation gives you the PV one period before the first payment. So, the price of the stock in Year 8 will be: P8 = D9 / (R - g) = $10 / (.13 - .05) = $125.00 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: P0 = $125.00 / 1.13^8 = $47.02
Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next 8 years because the firm needs to plow back its earnings to fuel growth. The company will pay a $10 per share dividend in 9 years and will increase the dividend by 5 percent per year thereafter. If the required return on this stock is 13 percent, what is the current share price?
100.00 Using the constant growth model, we find the price of the stock today is: P0 = D1 / (R- g) = $4.60/(.092 - .046) = $100.00
Metroplex Corporation will pay a $4.60 per share dividend next year. The company pledges to increase its dividend by 4.60 percent per year indefinitely. If you require an 9.20 percent return on your investment, how much will you pay for the company's stock today?
8.95 Using the equation to calculate the WACC, we find: RWACC = .70(.109) + .30(.057)(1 − .23) RWACC = .0895, or 8.95%
Mullineaux Corporation has a target capital structure of 70 percent common stock and 30 percent debt. Its cost of equity is 10.9 percent and the cost of debt is 5.7 percent. The relevant tax rate is 23 percent.What is the company's WACC? Round to the nearest XX.XX%.
$85,024 To find the OCF, we first calculate net income. Income Statement Sales$246,000 Costs 135,000 Other expenses 7,100 Depreciation 19,100 EBIT$84,800 Interest 10,000 Taxable income$74,800 Taxes 18,876 Net income$55,924 Dividends$9,800 Additions to RE$46,124 OCF = EBIT + Depreciation − Taxes OCF = $84,800 + 19,100 − 18,876 OCF = $85,024
Schwert Corp. shows the following information on its 2019 income statement: sales = $246,000; costs = $135,000; other expenses = $7,100; depreciation expense = $19,100; interest expense = $10,000; taxes = $18,876; dividends = $9,800. In addition, you're told that the firm issued $7,900 in new equity during 2019 and redeemed $6,800 in outstanding long-term debt. (Do not round intermediate calculations.) What is the 2019 operating cash flow? Hint: First build the income statement. OCF = EBIT + Depreciation - Taxes
12.63 Here we need to use the debt-equity ratio to calculate the WACC. Doing so, we find: WACC = 0.16(1/1.56) + 0.1(0.56/1.56)(1 - 0.34) = 0.1263 or 12.63%
Sixx AM Manufacturing has a target debt—equity ratio of 0.56. Its cost of equity is 16 percent, and its cost of debt is 10 percent. If the tax rate is 34 percent, what is the company's WACC? Round to the nearest XX.XX%.
8.5 FV = PV(1 + r)^t Solving for t, we get: t = ln(FV/PV)/ln(1 + r) FV = $1,104 = $625(1.07)^t t = ln($1,104/$625)/ln 1.07 =8.41 years
Solve for the unknown number of years in each of the following. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Present Value $625 Years ??? Interest Rate 7% Future Value $1,104
$912.89 The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond will be: P = $80({1 - [1/(1 + 0.10)]^6 } / 0.10) + $1,000[1 / (1 + 0.10)^6] = $912.89
Staind, Inc., has 8 percent coupon bonds on the market that have 6 years left to maturity. The bonds make annual payments. If the YTM on these bonds is 10 percent, what is the current bond price? Assume a par value of $1000.
1 The dividend yield is: Dividend yield = $.60 / $60 Dividend yield = .0100, or 1.00%
Suppose a stock had an initial price of $60 per share, paid a dividend of $.60 per share during the year, and had an ending share price of $53. What is the dividend yield? Round to the nearest XX.XX%.
-7.96 Using the equation for total return, we find: R = [($68 − 76) + 1.95]/$76 R = −.0796, or −7.96%
Suppose a stock had an initial price of $76 per share, paid a dividend of $1.95 per share during the year, and had an ending share price of $68. Compute the percentage total return.
13.09 The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. The return of this stock is: R = [($84 − 76) + 1.95]/$76 R = .1309, or 13.09%
Suppose a stock had an initial price of $76 per share, paid a dividend of $1.95 per share during the year, and had an ending share price of $84. Compute the percentage total return. Round to the nearest XX.XX%.
-16 The range of returns you would expect to see 95 percent of the time is the mean plus or minus 2 standard deviations: 5.2 - 2*(10.6) = -16.00%
Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 5.2 percent and the standard deviation was 10.6 percent. Using this information, you can specify the range of returns (from the lowest to the highest) that you expect this firm to have 95% of the time. What is the LOW end of this range? Round to the nearest XX.XX%.
3.49 We know the stock has a required return of 9.9 percent, and the dividend and capital gains yield are equal, so: Dividend yield = 1/2(.099) = .0495 = Capital gains yield Now we know both the dividend yield and capital gains yield. The dividend is the stock price times the dividend yield, so: D1 = .0495($74) D1 = $3.66 This is the dividend next year. The question asks for the dividend this year. Using the relationship between the dividend this year and the dividend next year: D1 = D0(1 + g) We can solve for the dividend that was just paid: $3.66 = D0(1 + .0495) D0 = $3.66/1.0495 D0 = $3.49
Suppose you know that a company's stock currently sells for $74 per share and the required return on the stock is 9.9 percent. You also know that the total return on the stock is evenly divided between a capital gains yield and a dividend yield. It's the company's policy to maintain a constant growth rate in its dividends. What is the current dividend per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Hint: First, compute the current dividend yield. Then, use that to compute the next dividend paid (in dollars per share). Then, using the constant dividend growth rate, compute the last dividend paid. The dividend is equal to the dividend yield multiplied by the stock price. Remember that the current stock price reflects future dividends, starting with D1, where D1 = D0(1 + g).
61.38 Using the equation to calculate the price of a share of stock with the PE ratio: P = Benchmark PE ratio × EPS So, with a PE ratio of 18, we find: P = 18($3.41) P = $61.38
The Rose Co. has earnings of $3.41 per share. The benchmark PE for the company is 18. What stock price would you consider appropriate? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Hint: P = Benchmark PE ratio × EPS
$3,440,000 Profit margin = Net income / Sales Net income = Sales (Profit margin) Net income = ($43,000,000)(.08) = $3,440,000 Additional practice: ROA = Net income / TA = $3,440,000 / $24,000,000 = 0.14333 or 14.33% Total Equity (TE) = $24,000,000 - 8,000,000 = $16,000,000 ROE = Net income / TE = Net income / TE = $3,440,000 / $16,000,000 = 0.215 or 21.50%
Wakers, Inc., has sales of $43 million, total assets of $24 million, and total debt of $8 million. If the profit margin is 8 percent, what is the net income? For additional practice, try calculating the ROA and ROE.
8.78 The pretax cost of debt is the YTM of the company's bonds, so: N=26, PV=-940, PMT=40, FV=1000, Calculate I/Y. I/Y =4.392%YTM = 2 × 4.392% = 8.78%
Waller, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 13 years to maturity that is quoted at 94 percent of face value. The issue makes semiannual payments and has an embedded cost of 8 percent annually. What is the company's pretax cost of debt? Round to nearest XX.XX%.
1.06 Years To calculate the payback period, we need to find the time that the project has recovered its initial investment. After one year, the project has created: 2400 in cash flows. The project still needs to create another: $2,500 − 2,400 = $100 in cash flows. During the second year, the cash flows from the project will be $1,600. So, the payback period will be 1 year, plus what we still need to make divided by what we will make during the second year. The payback period is: Payback = 1 + ($100 / $1,600) = 1.06 years
What is the payback period for the following set of cash flows? Year Cash Flow 0 −$ 2,500 1 2,400 2 1,600 3 1,800 4 2,300
Deciding whether or not to purchase a new machine for the production line.
Which one of the following is a capital budgeting decision?
$136.44 This is a multi-step problem involving several ratios. The ratios given are all part of the DuPont Identity. The only DuPont Identity ratio not given is the profit margin. If we know the profit margin, we can find the net income since sales are given. So, we begin with the DuPont Identity: ROE = 0.11 = (PM)(TAT)(EM) = (PM)(S / TA)(1 + D/E) Solving the DuPont Identity for profit margin, we get:PM = [(ROE)(TA)] / [(1 + D/E)(S)] PM = [(0.11)($3,225)] / [(1 + 1.60)($4,600)] = 0.0297 Now that we have the profit margin, we can use this number and the given sales figure to solve for net income: PM = 0.0297 = NI / SNI = 0.0297($4,600) = $136.44
Y3K, Inc., has sales of $4,600, total assets of $3,225, and a debt−equity ratio of 1.60. If its return on equity is 11 percent, what its net income? Hint: This is a complex problem that involves the DuPont Identity. If you can figure out the profit margin, then you can find net income since sales are given.
8.4 [.12 + .24 − .27 + .14 + .19]/5 =.0840, or 8.40%
Year Returns 1 12 2 24 3 -27 4 14 5 19 Using the returns shown above, calculate the arithmetic average return. (Do not round intermediate calculations. Enter your average return as a percent rounded to 2 decimal places, e.g., 32.16.)
23.03 To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)^t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) t = ln($98,000 / $16,000) / ln(1.09) = 21.03 So, the money must be invested for 21.03 years. However, you will not receive the money for another two years. From now, you'll wait: 2 years + 21.03 years = 23.03 years
You expect to receive $16,000 at graduation in two years. You plan on investing it at 9 percent until you have $98,000. How long will you wait from now? Answer in years with two decimal points.
5,607.3 To find the price of a zero coupon bond, we need to find the value of the future cash flows. With a zero coupon bond, the only cash flow is the par value at maturity. We find the present value assuming semiannual compounding to keep the YTM of a zero coupon bond equivalent to the YTM of a coupon bond, so: Price = $10,000(PVIFA2.25%,26) Price = $5,607.30
You find a zero coupon bond with a par value of $10,000 and 13 years to maturity. If the yield to maturity on this bond is 4.5 percent, what is the dollar price of the bond? Assume semiannual compounding periods. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
32,029.74 To find the FV of a lump sum, we use: FV = PV(1 + r)^t FV = $3,000 (1.07)35 = $32,029.74
You have just made your first $3,000 contribution to your retirement account. Assuming you earn an 7 percent rate of return and make no additional contributions. What will your account be worth when you retire in 35 years?
1.39 The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. If the portfolio is as risky as the market it must have the same beta as the market. Since the beta of the market is one, we know the beta of our portfolio is one. We also need to remember that the beta of the risk-free asset is zero. It has to be zero since the asset has no risk. Setting up the equation for the beta of our portfolio, we get: βP = 1.0 = 1/3(0) + 1/3(1.61) + 1/3(βX) Solving for the beta of Stock X, we get: βX = 1.39
You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.61 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Hint: Setup the weighted average beta equation, and then solve for the unknown beta.
11.53 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: Portfolio value = $3,100 + 4,600 Portfolio value = $7,700 So, the expected return of this portfolio is: E(RP) = ($3,100/$7,700)(.098) + ($4,600/$7,700)(.127) E(RP) = .1153, or 11.53%
You own a portfolio that has $3,100 invested in Stock A and $4,600 invested in Stock B. If the expected returns on these stocks are 9.8 percent and 12.7 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.) Hint: You need to find the weighted average return.
13.69 The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. So, the expected return of the portfolio is: E(RP) = .20(.105) + .45(.161) + .35(.124) E(RP) = .1369, or 13.69%
You own a portfolio that is 20 percent invested in Stock X, 45 percent in Stock Y, and 35 percent in Stock Z. The expected returns on these three stocks are 10.5 percent, 16.1 percent, and 12.4 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.) Hint: You need to find the weighted average return.
1.33 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 = .20(.75) + .30(1.90) + .15(1.38) + .35(1.16) βP = 1.33
You own a stock portfolio invested 20 percent in Stock Q, 30 percent in Stock R, 15 percent in Stock S, and 35 percent in Stock T. The betas for these four stocks are .75, 1.90, 1.38, and 1.16, respectively. What is the portfolio beta? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
1.05 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(.76) + .25(1.14) + .35(1.15) + .10(1.32) βP = 1.05
You own a stock portfolio invested 30 percent in Stock Q, 25 percent in Stock R, 35 percent in Stock S, and 10 percent in Stock T. The betas for these four stocks are .76, 1.14, 1.15, and 1.32, respectively. What is the portfolio beta? Round to the nearest X.XX.
41.72 years To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)^t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) t = ln ($210,000 / $50,000) / ln 1.035 = 41.72 years
You're trying to save to buy a new $210,000 Ferrari. You have $50,000 today that can be invested at your bank. The bank pays 3.5 percent annual interest on its accounts. How long will it be before you have enough to buy the car?
