Exam 2 Answers

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Stock & Bonds Quiz Questions 1. Today, a bond has a coupon rate of 9.64%, par value of $1000, YTM of 9.40%, and semi- annual coupons with the next coupon due in 6 months. One year ago, the bond’s price was $983.42, and the bond had 15 years until maturity. What is the current yield of the bond today? Current yield today = annual coupons / bond value today Approach: 1) Find the annual coupons 2) Find the value of the bond today 3) Find the current yield today 1) Find the annual coupons Annual coupons = par × coupon rate = 1000 × 9.64% = $96.40 2) Find bond value today If the bond had 15 years until maturity from 1 year ago, then today it has 14 years until maturity, so N = 14 years × 2 coupons per year = 28 I% = YTM ÷ # coupons per year = 9.40 ÷ 2 = 4.70 FV = par = 1,000 PMT = par × coupon rate ÷ # coupons per year = 1000 × 9.64% ÷ 2 = 48.20 END mode Enter 28 4.70 48.20 1000 N I% PV PMT FV Solve for -1,018.48 Today, the price of the bond is $1,018.48 3) Find current yield today Current yield today = annual coupons / bond value today = 96.40 / 1,018.48 = .0947 = 9.47%

2. Bond A has a coupon rate of 17.80 percent, a yield-to-maturity of 15.60 percent, and a face value of $1,000; matures in 12 years; and pays coupons annually with the next coupon expected in 1 year. What is (X + Y + Z) if X is the present value of any coupon payments expected to be made in 5 years from today, Y is the present value of any coupon payments expected to be made in 10 years from today, and Z is the present value of any coupon payments expected to be made in 15 years from today? Approach: 1) Determine the coupon payments expected in 5, 10, and 15 years 2) Determine the appropriate period length and discount rate 3) Find the present values of any coupon payments expected in 5, 10, and 15 years 4) Add up the present values of any coupon payments expected in 5, 10, and 15 years 1) Determine the coupon payments expected in 5, 10, and 15 years The expected annual coupon for bond A = par × coupon rate ÷ # coupons per year = $1,000 × 17.80% ÷ 1 = $178.00 Since the bond matures in 12 years, a coupon of $178.00 is expected in 5 years and in 10 years, but not in 15 years. 2) Determine the appropriate period length and discount rate Since coupons are paid annually, the relevant period is a year Therefore: - The coupon of $178.00 expected in 5 years, which is in 5 periods - The coupon of $178.00 expected in 10 years, which is in 10 periods - There is no coupon expected in 15 years, which is in 15 periods The relevant discount rate per period for bond A = YTM ÷ # coupons per year = 15.60 percent ÷ 1 = 15.60 percent = .1560 per year 3) Find the present values of any coupon payments expected in 5, 10, and 15 years PV 0 = C t / (1+r) t X = the present value of the coupon of $178.00 expected in 5 years = $178.00 / 1.1560 5 = $86.22 Y = the present value of the coupon of $178.00 expected in 10 years = $178.00 / 1.1560 10 = $41.77 Z = $0, because no coupon is expected in 15 years 4) Add up the present values of any coupon payments expected in 5, 10, and 15 years X + Y +Z = $86.22 + $41.77 + $0.00 = $127.99

3. Dewey has one share of stock and one bond. The total value of the two securities is $1,050. The bond has a YTM of 18.60 percent, a coupon rate of 12.40 percent, and a face value of $1,000; pays semi-annual coupons with the next one expected in 6 months; and matures in 6 years. The stock pays annual dividends that are expected to grow by 1.73 percent per year forever. The next dividend is expected to be $18.10 and paid in one year. What is the expected return for the stock? Since the stock’s dividends are expected to grow at a constant rate forever, R = (D 1 /P 0 ) + g We know that g = .0173 and D 1 = $18.10 We don’t know what P 0 and R are, but we know that bond value + stock value (P 0 ) = $1,050 If we find the bond value, we can find the stock value, and we can find R from R = (D 1 /P 0 ) + g Finding the bond value N = 6 years × 2 coupons per year = 12 I% = YTM ÷ # coupons per year = 18.60 ÷ 2 = 9.3 FV = 1,000 = par PMT = par × coupon rate ÷ # coupons per year = 1000 × 12.40% ÷ 2 = 62 END mode Enter 12 9.3 62 1000 N I% PV PMT FV Solve for -781.33 Finding the stock value Since bond value + stock value = $1,050, stock value = $1,050 – $781.33 = $268.67 Finding the expected return Since P 0 = D 1 /(R – g), then R = (D 1 /P 0 ) + g = (18.10 / 268.67) + .0173 = .0847 = 8.47 percent

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4. Two years ago, the price of a bond was $955.72, and one year ago, the price of the bond was $942.21. Over the past year, the bond paid a total of $88.43 in coupon payments, which were just paid. If the bond is currently priced at $991.52 then what was the rate of return for the bond over the past year (from 1 year ago to today)? The par value of the bond is $1,000. Percentage return = (cash flows from investment + ending value – initial value) / initial value Percentage return over the past year (from 1 year ago to today) = (cash flows from investment over past year + bond price today – bond price 1 year ago) / bond price 1 year ago Cash flows from investment over past year The bond (just) made a total of $88.43 in coupon payments over the past year Initial value = bond price 1 year ago One year ago, the bond had a price of $942.21 Ending value = bond price today The bond is currently priced at $991.52 Percentage return over past year = (cash flows from investment + ending value – initial value) / initial value = (cash flows from investment over past year + bond price today – bond price 1 year ago) / bond price 1 year ago = (88.43 + 991.52 – 942.21) / 942.21 = (88.43 + 49.31) / 942.21 = 137.74 / 942.21 = .1462 = 14.62% 5. Labrador has issued bonds, common stock, and preferred stock. The YTM for the bonds is 14% and the expected annual return for the preferred stock is 19%. Which of the following assertions about the expected annual return for the common stock issued by Labrador is most likely to be true? A. The expected annual return for the common stock is 9% B. The expected annual return for the common stock is 14% C. The expected annual return for the common stock is 16% D. The expected annual return for the common stock is 19% E. The expected annual return for the common stock is 21%

Answer: E. The expected annual return for the common stock is 21% Labrador common stock is most likely to be the riskiest, Labrador bonds are most likely to be the least risky, and Labrador preferred stock is most likely to be in the middle. Therefore, Labrador common stock should have the highest expected return, Labrador bonds should have the lowest expected return as measured by YTM, and Labrador preferred stock should have an expected return between the expected return of common stock and the YTM of bonds. Since Labrador’s preferred stock has an expected return of 19%, its common stock should have a return greater than 19%, and 21% is the only alternative that is greater than 19%. 6. Branford has one share of stock and one bond. The total value of the two securities is $1,200. The bond has a YTM of 10.2 percent, a coupon rate of 9.2 percent, and a face value of $1,000; pays semi-annual coupons with the next one expected in 6 months; and matures in 8 years. The stock pays annual dividends and the next dividend is expected to be $24.87 and paid in one year. The expected return for the stock is 15.2 percent. What is the price of the stock expected to be in 1 year? P 0 = (D 1 + P 1 ) / (1 + R) Since we know that D 1 = $24.87 and R = 15.2 percent, we can find P 1 if we know P 0 If we find the bond value, we can find the stock value (P 0 ), and we can find P 1 Finding the bond value N = 8 years × 2 coupons per year = 16 I% = YTM ÷ # coupons per year = 10.2 ÷ 2 = 5.1 FV = 1,000 = par

PMT = par × coupon rate ÷ # coupons per year = 1000 × 9.2% ÷ 2 = 46 END mode Enter 16 5.1 46 1000 N I% PV PMT FV Solve for -946.19 Finding the current stock price Since bond value + stock value = $1,200, stock value = $1,200 – $946.19 = $253.81 Finding the expected price in one year P 0 = (D 1 + P 1 ) / (1 + R) 253.81 = (24.87 + P 1 ) / 1.152  P 1 = (253.81 × 1.152) – 24.87 = $267.52 7. If 1) the expected return for Mindy’s Mending stock is 14.30 percent; 2) the dividend is expected to be $0 in one year, $4.53 in two years, $0 in three years, $5.68 in four years, and $6.44 in five years; and 3) after the dividend is paid in five years, the dividend is expected to grow by 2.40 percent per year forever, then what is the current price of the stock? Time 0 1 2 3 4 5 6 7 … Exp Div 0 0 4.53 0 5.68 6.44 6.44 × (1.0240) 6.44 × (1.0240) 2 … Mindy’s Mending dividends are expected to grow at a variable rate before growing at constant rate after 5 years from today The stock of a company that pays a dividend that does not grow at its long-term constant rate during the next N+1 years, before growing forever at that constant rate after N+1 years can be valued as

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P 0 = D 1 /(1+R) + D 2 /(1+R) 2 + ... + D N /(1+R) N + P N /(1+R) N where P N = D N+1 /(R − g) After the dividend in 5 years, Mindy’s Mending dividends will begin growing at a constant rate of 2.4 percent, so N + 1 = 5 and N = 4 P 0 = D 1 /(1+R) + D 2 /(1+R) 2 + D 3 /(1+R) 3 + D 4 /(1+R) 4 + P 4 /(1+R) 4 Where P 4 = D 5 /(R − g) P 4 = D 5 /(R − g) = 6.44/ (.1430 – .0240) = 6.44 / .1190 = 54.12 P 0 = 0/(1.1430) + 4.53/(1.1430) 2 + 0/(1.1430) 3 + 5.68/(1.1430) 4 + 54.12/(1.1430) 4 = $38.50 8. Electric Pink stock is expected to pay a dividend of $1.36 in 1 year. The stock is currently priced at $22.50, is expected to be priced at $25.26 in 1 year, and is expected to be priced at $27.84 in 2 years. What is the dividend in 2 years expected to be for Electric Pink stock? The stock’s dividend is paid annually and the next dividend is expected in 1 year. We want to determine the value of D 2 and we know that P 1 = (D 2 + P 2 ) / (1 + R) We are given P 1 and P 2 , but do not know R However, we can get R from P 0 = (D 1 + P 1 ) / (1 + R), because we are given P 0 , P 1 , and D 1 Approach: 1) Find R 2) Find D 2 1) Find R P 0 = (D 1 + P 1 ) / (1 + R) P 0 = 22.50

P 1 = 25.26 D 1 = 1.36 22.50 = (1.36 + 25.26) / (1 + R) = (26.62) / (1 + R) So 22.50 × (1 + R) = 26.62 So 1 + R = 26.62 / 22.50 = 1.1831 So R = 1.1831 – 1 = 0.1831 = 18.31% 2) Find D 2 P 1 = (D 2 + P 2 ) / (1 + R) P 1 = 25.26 P 2 = 27.84 R = 0.1831 25.26 = (D 2 + 27.84) / 1.1831  25.26 × 1.1831 = (D 2 + 27.84)  D 2 = (25.26 × 1.1831) – 27.84 = $2.05 Answers may differ slightly due to rounding 9. Today, a bond has a coupon rate of 9.64%, par value of $1000, YTM of 9.40%, and semi- annual coupons with the next coupon due in 6 months. One year ago, the bond’s price was $983.42, and the bond had 15 years until maturity. What is the current yield of the bond today? Current yield today = annual coupons / bond value today Approach: 1) Find the annual coupons 2) Find the value of the bond today 3) Find the current yield today 1) Find the annual coupons Annual coupons = par × coupon rate = 1000 × 9.64% = $96.40

2) Find bond value today If the bond had 15 years until maturity from 1 year ago, then today it has 14 years until maturity, so N = 14 years × 2 coupons per year = 28 I% = YTM ÷ # coupons per year = 9.40 ÷ 2 = 4.70 FV = par = 1,000 PMT = par × coupon rate ÷ # coupons per year = 1000 × 9.64% ÷ 2 = 48.20 END mode Enter 28 4.70 48.20 1000 N I% PV PMT FV Solve for -1,018.48 Today, the price of the bond is $1,018.48. 3) Find current yield today Current yield today = annual coupons / bond value today = 96.40 / 1,018.48 = .0947 = 9.47% 10. Two years ago, the price of a bond was $955.72, and one year ago, the price of the bond was $942.21. Over the past year, the bond paid a total of $88.43 in coupon payments, which were just paid. If the bond is currently priced at $991.52 then what was the rate of return for the bond over the past year (from 1 year ago to today)? Percentage return = (cash flows from investment + ending value – initial value) / initial value Percentage return over the past year (from 1 year ago to today) = (cash flows from investment over past year + bond price today – bond price 1 year ago) / bond price 1 year ago Cash flows from investment over past year The bond (just) made a total of $88.43 in coupon payments over the past year Initial value = bond price 1 year ago One year ago, the bond had a price of $942.21

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Ending value = bond price today The bond is currently priced at $991.52 Percentage return over past year = (cash flows from investment + ending value – initial value) / initial value = (cash flows from investment over past year + bond price today – bond price 1 year ago) / bond price 1 year ago = (88.43 + 991.52 – 942.21) / 942.21 = (88.43 + 49.31) / 942.21 = 137.74 / 942.21 = .1462 = 14.62% 2. Retriever has issued bonds, common stock, and preferred stock. The YTM for the bonds is 12% and the expected annual return for the common stock is 17%. Which of the following assertions about the expected annual return for the preferred stock issued by Retriever is most likely to be true? A. The expected annual return for the preferred stock is 4% B. The expected annual return for the preferred stock is 12% C. The expected annual return for the preferred stock is 14% D. The expected annual return for the preferred stock is 17% E. The expected annual return for the preferred stock is 21% (Spring 2015, test 2, question 6) (Fall 2015, final, question 7) Answer: C. The expected annual return for the preferred stock is 14% Retriever common stock is most likely to be the riskiest, Retriever bonds are most likely to be the least risky, and Retriever preferred stock is most likely to be in the middle. Therefore, Retriever common stock should have the highest expected return, Retriever bonds should have the lowest expected return as measured by YTM, and Retriever preferred stock should have an expected return between the expected return of common stock and the YTM of bonds.

Since Retriever’s bonds have YTM of 12% and its common stock has an expected return of 17%, its preferred stock should have a return between 12% and 17%, and 14% is the only alternative that is between 12% and 17%. 1. Wooden Forests is evaluating a project that would require an initial investment of $54,300 today. The project is expected to produce annual cash flows of $6,200 each year forever with the first annual cash flow expected in 1 year. The NPV of the project is $3,700. What is the IRR of the project? Can not use the irr function with financial calculator – there are an infinite number of cash flows By definition of IRR: 0 = C 0 + [C 1 / (1+IRR)] + [C 2 / (1+IRR) 2 ] + ... In this case, C 0 = -54,300 C 1 = C 2 = C 3 = … = 6,200 C 1 , C 2 , C 3 , … represent a fixed perpetuity with annual cash flows of $6,200 So [C 1 / (1+IRR)] + [C 2 / (1+IRR) 2 ] + ... = (C / IRR) = ($6,200 / IRR) So 0 = -54,300 + (6,200 / IRR) So 54,300 = 6,200 / IRR So IRR = 6,200 / 54,300 = 0.1142 = 11.42% Note that the NPV is not relevant to finding IRR, since IRR is the discount rate at which the present value of the expected cash flows is 0.

2. Project A would cost $76,000 today and have the following other expected cash flows: $38,000 in 1 year, $29,000 in 2 years, $7,000 in 3 years, and $11,000 in 4 years. The cost of capital for project A is 8.21 percent. Project B would cost $88,000 today and have the following other expected cash flows: $43,000 in 1 year, $31,000 in 2 years, $12,000 in 3 years, and $13,000 in 4 years. The cost of capital for project B is 7.91 percent. Statement 1: Project A would be accepted based on the project’s net present value (NPV) and the NPV rule Statement 2: Project B would be accepted based on the project’s payback period and the payback rule if the payback threshold is 3.18 years A. Statement 1 is true and statement 2 is true B. Statement 1 is true and statement 2 is false C. Statement 1 is false and statement 2 is true D. Statement 1 is false and statement 2 is false Answer: C. statement 1 is false and statement 2 is true NPV - Statement 1 is false NPV = [-76,000] + [38,000 / 1.0821] + [29,000 / 1.0821 2 ] + [7,000 / 1.0821 3 ] + [11,000 / 1.0821 4 ] = -$2,569 npv(8.21,-76000,{38000,29000,7000,11000})  -$2,569 Reject project A, because NPV < 0 Payback - Statement 2 is true Assume expected cash flows occur uniformly throughout the year Year Expected CF Expected CF needed after year-end 0 -88,000 88,000 1 43,000 88,000 – 43,000 = 45,000 2 31,000 45,000 – 31,000 = 14,000 3 12,000 14,000 – 12,000 = 2,000 4 13,000 2,000 – 13,000 = -11,000 Payback occurs between 3 and 4 years After 3 years, 2,000 in expected cash flows are needed In year 4, the expected cash flow is $13,000 Therefore, it would take ($2,000 / $13,000) = 0.15 of year 4 to reach payback So payback = 3 + 0.15 = 3.15 years Accept project B, because its payback period is 3.15 years, which is less than the threshold of 3.18 years

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3. Karim’s Kabobs is evaluating a project that would last for 3 years. The project’s cost of capital is 9.7 percent; its NPV is $6,700; and the expected cash flows are -$65,000 at time 0, $52,000 in 1 year, -$12,000 dollars in 2 years, and X in 3 years. What is X? A. An amount equal to or greater than $28,000 but less than $36,000 B. An amount equal to or greater than $36,000 but less than $44,000 C. An amount equal to or greater than $44,000 but less than $52,000 D. An amount less than $36,000 or an amount equal to or greater than $52,000 E. The amount can not be determined or does not exist because the cash flows are not conventional NPV = [C 0 ] + [C 1 / (1 + r)] + [C 2 / (1 + r) 2 ] + [C 3 / (1 + r) 3 ] NPV = 6,700 C 0 = -65,000 C 1 = 52,000 C 2 = - 12,000 C 3 = X r = .097 6,700 = [-65,000] + [52,000 / 1.097] + [ - 12,000 / 1.097 2 ] + [X / 1.097 3 ]  6,700 = [-65,000] + [47,402] + [-9,972] + [X / 1.097 3 ]  6,700 = -27,570 + [X / 1.097 3 ]  6,700 + 27,570 = [X / 1.097 3 ]  34,270 = [X / 1.097 3 ]  X = C 3 = 34,270 × 1.097 3 = 45,241 Answers may differ slightly due to rounding

4. Striped Potato is evaluating a project that would require the purchase of a piece of equipment for $365,000 today. During year 1, the project is expected to have relevant revenue of $216,000, relevant costs of $57,000, and relevant depreciation of $84,000. Striped Potato would need to borrow $365,000 today to pay for the equipment and would need to make an interest payment of $14,000 to the bank in 1 year. Relevant net income for the project in year 1 is expected to be $44,000. What is the tax rate expected to be in year 1? The $14,000 interest payment is not included in the analysis. Projects should be evaluated solely on cash flows expected to be produced by assets. It does not matter if funds are borrowed to pay for the project or whether new stock is issued or whether the firm uses cash it already has. Ignore any and all cash flows associated with debt and equity including debt-issuance proceeds, debt payments, equity-issuance proceeds, dividends, and stock buybacks. To solve: 1) Find expected taxable income 2) Find expected taxes paid 3) Find the expected tax rate 1) Find expected taxable income Taxable income = EBIT = revenues – costs – depreciation 216,000 – 57,000 – 84,000 = 75,000 2) Find expected taxes paid Net income = taxable income – taxes paid 44,000 = 75,000 – taxes paid So taxes paid = 75,000 – 44,000 = 31,000 Tables are useful for steps 1 and 2 Given Step 1 Step 2 Year 1 Year 1 Year 1 Revenue 216,000 216,000 216,000 – Costs 57,000 57,000 57,000 – Annual depreciation 84,000 84,000 84,000 = EBIT = taxable income 75,000 75,000 – Taxes 31,000 = Net income 44,000 44,000 44,000 3) Find the expected tax rate The tax rate = taxes paid / taxable income = 31,000 / 75,000 = 0.4133 = 41.33%

5. Vermont Technology is considering a project that would last for 3 years and have a cost of capital of 21.72 percent. The relevant level of net working capital for the project is expected to be $2,000 immediately (at year 0); $5,000 in 1 year; $15,000 in 2 years; and $0 in 3 years. Relevant expected revenue, costs, depreciation, and cash flows from capital spending in years 0, 1, 2, and 3 are presented in the following table. The tax rate is 50 percent. What is the net present value of this project? Year 0 Year 1 Year 2 Year 3 Revenue $0 $12,000 $12,000 $12,000 Costs $0 $4,000 $4,000 $4,000 Depreciation $0 $2,000 $2,000 $2,000 Cash flows from capital spending -$7,000 $0 $0 $4,000 Relevant cash flows in a given year = OCF + CF effects from ΔNWC + CF from capital spending + terminal value In this problem, terminal value = 0 Therefore, relevant cash flows in a given year = OCF + CF effects from ΔNWC + CF from capital spending. We are given CF from capital spending. We can compute OCF from revenue, costs, depreciation, and the tax rate. We are given NWC for each point in time (years 0, 1, 2, and 3) and must compute ΔNWC as NWC at the end of a period minus NWC at the start of the period and the cash flow effects from ΔNWC as – ΔNWC. Year 0 1 2 3 Revenue 12,000 12,000 12,000 Costs 4,000 4,000 4,000 Depreciation 2,000 2,000 2,000 EBIT = revenues – costs – depreciation 6,000 6,000 6,000 tax rate 0.50 0.50 0.50 Taxes = tax rate × EBIT 3,000 3,000 3,000 net inc 3,000 3,000 3,000 OCF = net income + depreciation 0 5,000 5,000 5,000 NWC 2,000 5,000 15,000 0 ΔNWC = NWC at end of period minus NWC at start of period (except ΔNWC 0 = NWC 0 ) 2,000 5k – 2k = 3,000 15k – 5k = 10,000 0 – 15k = -15,000 Cash flow effects from ΔNWC = -ΔNWC -2,000 -3,000 -10,000 15,000 Cash flows from capital spending -7,000 0 0 4,000 Rel CF (OCF + CF ΔNWC + CF cap spend) -9,000 2,000 -5,000 24,000 npv(21.72,-9000,{2000,-5000,24000})  2,577

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7. Monroe Printing is evaluating the pamphlet project. The project would require an initial investment of $73,000 that would be depreciated to $13,000 over 4 years using straight-line depreciation. The first annual operating cash flow of $17,000 is expected in 1 year, and annual operating cash flows of $17,000 are expected each year forever. Monroe Printing expects the project to have an after-tax terminal value of $108,000 in 3 years. The tax rate is 30%. What is (X+Y)/Z if X is the project’s relevant expected cash flow for NPV analysis in year 3, Y is the project’s relevant expected cash flow for NPV analysis in year 4, and Z is the project’s relevant expected cash flow for NPV analysis in year 2? Recall that in a given year: Relevant CF for a project = OCF + CF effects from ΔNWC + CF from capital spending + terminal value For year 3: X = relevant CF for the pamphlet project = $17,000 + $0 + $0 + $108,000 = $125,000 Since we have a terminal value for year 3, in years 4 and later: Relevant CF for the pamphlet project (for Monroe Printing analysis) = $0 For year 4: Y = relevant CF for the pamphlet project = $0 + $0 + $0 + $0 = $0 For year 2: Z = relevant CF for the pamphlet project = $17,000 + $0 + $0 + $0 = $17,000 So (X + Y) / Z = ($125,000 + $0) / $17,000 = $125,000 / $17,000 = 7.35 Note that the depreciation information is not relevant. It is used to compute OCF, but OCF is provided. The tax rate information is not relevant either, as all necessary figures are given as after-tax cash flows.

8. Scarlet operates coffee shops in Ohio. The firm is evaluating the Cleveland project, which would involve opening a new coffee shop in Cleveland. During year 1, Scarlet would have total revenue of $335,000 and total costs of $171,000 if it pursues the Cleveland project, and the firm would have total revenue of $288,000 and total costs of $163,000 if it does not pursue the Cleveland project. Depreciation taken by the firm would be $203,000 if the firm pursues the project and $181,000 if the firm does not pursue the project. The tax rate is 25%. What is the relevant operating cash flow (OCF) for year 1 of the Cleveland project that Scarlet should use in its NPV analysis of the Cleveland project? In evaluating the Cleveland project, Scarlet should use incremental revenue, incremental costs, and incremental depreciation, which is what those values would be with the project minus what they would be without the project. The incremental effects reflect the effect of the project, which is what is of interest. Incremental revenue = revenue with project – revenue without project = $335,000 – $288,000 = $47,000 Incremental costs = costs with project – costs without project = $171,000 – $163,000 = $8,000 Incremental depreciation = depreciation with project – depreciation without project = $203,000 – $181,000 = $22,000 Year 1 Revenue 47,000 – Costs 8,000 – Annual depreciation 22,000 = EBIT 17,000 × Tax rate 0.25 = Taxes paid 4,250 Net income = EBIT – taxes 12,750 + Annual depreciation 22,000 = OCF 34,750 Alternatively With in year 1 Without in year 1 Incremental in year 1 Revenue 335,000 288,000 47,000 – Costs 171,000 163,000 8,000 – Annual depreciation 203,000 181,000 22,000 = EBIT -39,000 -56,000 17,000 × Tax rate 0.25 0.25 0.25 = Taxes paid -9,750 -14,000 4,250 Net income = EBIT – taxes -29,250 -42,000 12,750 + Annual depreciation 203,000 181,000 22,000 OCF = net income + dep 173,750 139,000 34,750

9. Washington Football owns a football team in Washington, DC. The objective of its managers is to maximize shareholder value. The firm is evaluating the stadium project, which involves building a new stadium in Fairfax County. Which assertion is true, based on the information given in the question and the following table on the project? Base-case NPV (based on final estimates and expectations) -$130,000 Value created if the team wins 11 games a season (based on scenario analysis) $2,700,000 Value created if worst-case taxes occur (based on sensitivity analysis) -$650,000 Value created if best-case taxes occur (based on sensitivity analysis) $2,900,000 Probability that project will create more than $0 of value (based on simulation analysis) 82.7% A. Washington Football should be indifferent between accepting and rejecting the stadium project B. Washington Football should accept the stadium project C. Washington Football should reject the stadium project D. It is not clear whether Washington Football should accept or reject the stadium project, because the information provided is contradictory with respect to answering the question E. It is not clear whether Washington Football should accept or reject the stadium project, because the cost of capital for the project is not given Answer: C. Washington Football should reject the stadium project Recall that you should compute a base-case NPV based on final estimates, pursue the project when that base-case NPV is positive, and reject the project when that base- case NPV is negative. In this case, the base-case NPV based on final estimates and expectations is negative, so Washington Football should reject the project. If a what-if analysis indicates that the amount of value created would be negative, but the base-case NPV based on expectations is positive, then pursue the project. If a what-if analysis indicates that the amount of value created would be positive, but the base-case NPV based on expectations is negative, then do not pursue the project.

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10. Washington Football owns a football team in Washington, DC. The objective of its managers is to maximize shareholder value. The firm is evaluating the stadium project, which involves building a new stadium in Fairfax County. Which assertion is true, based on the information given in the question and the following table on the project? Base-case NPV (based on final estimates and expectations) $215,000 Value created if the team loses 11 games a season (based on scenario analysis) -$3,400,000 Value created if worst-case taxes occur (based on sensitivity analysis) -$1,700,000 Value created if best-case taxes occur (based on sensitivity analysis) $450,000 Probability that project will create more than $0 of value (based on simulation analysis) 16.1% A. Washington Football should be indifferent between accepting and rejecting the stadium project B. Washington Football should accept the stadium project C. Washington Football should reject the stadium project D. It is not clear whether Washington Football should accept or reject the stadium project, because the information provided is contradictory with respect to answering the question E. It is not clear whether Washington Football should accept or reject the stadium project, because the cost of capital for the project is not given Answer: B. Washington Football should accept the stadium project Recall that you should compute a base-case NPV based on final estimates, pursue the project when that base-case NPV is positive, and reject the project when that base- case NPV is negative. In this case, the base-case NPV based on final estimates and expectations is positive, so Washington Football should accept the project. If a what-if analysis indicates that the amount of value created would be negative, but the base-case NPV based on expectations is positive, then pursue the project. If a what-if analysis indicates that the amount of value created would be positive, but the base-case NPV based on expectations is negative, then do not pursue the project.

11. Riverton Silver is considering buying a new extraction system. The new extraction system would be purchased today for $56,000. It would be depreciated straight-line to $0 over 2 years. In 2 years, the extraction system would be sold for an after-tax cash flow of $3,000. Without the extraction system, costs are expected to be $97,000 in 1 year and $123,000 in 2 years. With the extraction system, costs are expected to be $75,000 in 1 year and $37,000 in 2 years. If the tax rate is 40% and the cost of capital is 18.29%, what is the net present value of the new extraction system project? The initial investment is $56,000 The investment is depreciated to $0 over 2 years Annual depreciation in years 1 and 2 is ($56,000 – $0) / 2 = $28,000 Relevant costs = costs with the project – costs without project In year 1, relevant costs = $75,000 – $97,000 = -$22,000 In year 1, costs are expected to be $22,000 lower with the extraction system In year 2, relevant costs = $37,000 – $123,000 = -$86,000 In year 2, costs are expected to be $86,000 lower with the extraction system Year 0 1 2 Revenues 0 0 0 - Costs 0 -22,000 -86,000 - Annual depreciation 0 28,000 28,000 = EBIT (revs - costs - depreciation) 0 -6,000 58,000 × Tax rate 0.40 0.40 0.40 = Taxes paid 0 -2,400 23,200 Net income = EBIT – taxes paid 0 -3,600 34,800 OCF = net income + depreciation 0 24,400 62,800 OCF 0 24,400 62,800 + CF effects from ΔNWC 0 0 0 + CF from capital spending -56,000 0 3,000 + Terminal value 0 0 0 = Relevant CF -56,000 24,400 65,800 NPV = -56,000 + [24,400/(1.1829) 1 ] + [65,800/(1.1829) 2 ] = 11,652 npv(18.29,-56000,{24400,65800})  11,652

12. What is the expected after-tax cash flow from selling a piece of equipment if TwoPlus purchases the equipment today for $160,000, the tax rate is 30 percent, the equipment is sold in 3 years for $37,500, and MACRS depreciation is used where the depreciation rates in years 1, 2, 3, 4, and 5 are 42%, 31%, 15%, 8%, and 4%, respectively? CF from asset sale = sales price of asset – taxes paid on sale of asset Taxes paid = (sales price of asset – book value of asset) × tax rate = taxable gain × tax rate Book value = initial price of asset – accumulated depreciation Accumulated depreciation equals depreciation in year 1 + depreciation in year 2 + depreciation in year 3 Depreciation in year 1 = 42% × 160,000 = 67,200 Depreciation in year 2 = 31% × 160,000 = 49,600 Depreciation in year 3 = 15% × 160,000 = 24,000 Accumulated depreciation = 67,200 + 49,600 + 24,000 = 140,800 Book value = 160,000 – 140,800 = 19,200 Taxes paid on sale of asset = (37,500 – 19,200) × 0.30 = 18,300 × 0.30 = 5,490 After-tax CF from asset sale = 37,500 – 5,490 = 32,010

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