Pract-Final

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Apr 3, 2024

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Page 1 of 56 PRACTICE QUESTIONS FOR THE FINAL Important comment: The sample questions below focus on the second half of the course. The final exam is however comprehensive . For sample questions regarding the midterm material please refer to the posted practice midterm questions. Question 1 Evaluate the following statements: I. The IRR is insensitive to the scale of the project. (TRUE) II. The profitability index is insensitive to the scale of the project. (TRUE) III. The IRR and the profitability index methods are both insensitive to the scale of the project, therefore, for the case of independent projects the two methods are equivalent. (FALSE) Question 2 Dot.com must install a machine that costs $700,000. The machine will require $50,000 of maintenance each year and it must be replaced every 25 years. The appropriate discount rate is 10%. Calculate the equivalent annual annuity, i.e. , EAA, of the machine. ( Notice that some of the magnitudes below, that is, options b to e below, are negative.) a. $ 27,118 b. $ -246,148 c. $ -27,118 d. $ -1,153,852 e. $ -127,118 $1,153,852 ) 1 . 0 1 ( 1 1 1 . 0 1 50,000 700,000 PV 25 − =         + − − − = $127,118 ) 1 . 0 1 ( 1 1 1 . 0 1 1,153,852 - 25 − =         + − = EAA

Page 2 of 56 Question 3 Punto.com must decide whether to install machine A or machine B . Both machines cost $100,000. Machine A generates $50,000 each year and it must be replaced every 17 years. Machine B generates $45,000 each year and it must be replaced every 27 years. The appropriate discount rate is 10%. Which machine should Punto.com install? a. Machine B because it has an NPV of $315,675 b. Machine A because it has an NPV of $301,077 c. Machine B because it has an EAA of $34,174 d. Machine A because it has an EAA of $37,534 e. Machine B because it has an EAA of $38,255 $301,078 ) 1 . 0 1 ( 1 1 1 . 0 1 50,000 100,000 NPV 17 A =         + − + − = $37,534 ) 1 . 0 1 ( 1 1 1 . 0 1 301,077 17 =       + − = A EAA $315,675 ) 1 . 0 1 ( 1 1 1 . 0 1 5,000 4 100,000 NPV 27 B =         + − + − = $34,174 ) 1 . 0 1 ( 1 1 1 . 0 1 315,675 27 =         + − = B EAA

Page 3 of 56 Question 4 Dot.com is considering investing in a project with the following expected free cash flows: Year 1 Year 2 Year 3 37,500 -86,250 49,500 Which of the following statements is correct? a. The IRR of the project is 2% and if the cost of capital is 3% the project should be undertaken because it creates value. b. The IRR of the project is 20% and if the cost of capital is 19% the project should be undertaken because it creates value. c. The IRR of the project is 6% and if the cost of capital is 5% the project should be undertaken because it creates value. d. The IRR of the project is 10% and if the cost of capital is 11% the project should be undertaken because it creates value. e. The IRR of the project is 10% and if the cost of capital is 9% the project should be undertaken because it creates value. • There are two IRR (10% and 20%) but if the cost of capital is 19% or 11% the project destroys value (NPV < 0) while if the cost of capital is 9% the project creates value (NPV > 0).

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Page 4 of 56 Question 5 BestBuy must decide whether to install vending machine A or vending machine B . Machine A costs $200,000, generates a revenue of $28,000 per year, and it must be replaced every 20 years. Machine B costs $100,000, generates a revenue of $14,000 per year and it must be replaced every 10 years. The appropriate discount rate is 12%. Which machine should BestBuy install? a. Machine A because it has an EAA of $9,144.42 b. Machine A because it has an EAA of $1,224.24 c. Machine B because it has an EAA of $3,698.42 d. Machine B because it has an EAA of $1,320.33 e. BestBuy is indifferent between installing machine A or B. ` $9,144.42 ) 12 . 0 1 ( 1 1 12 . 0 1 ,000 8 2 200,000 PV 20 A =         + − + − = $1,224.24 ) 12 . 0 1 ( 1 1 12 . 0 1 9,144.42 20 =         + − = A EAA 0 $20,896.88 ) 12 . 0 1 ( 1 1 12 . 0 1 ,000 14 100,000 PV 10 B  − =         + − + − = 0 $3,698.42 ) 12 . 0 1 ( 1 1 12 . 0 1 20,896.88 - 10  − =         + − = B EAA [ Note: Installing machine B is negative NPV. ]

Page 5 of 56 Question 6 Dixon Inc. is considering investing in a project with the following expected free cash flows: Year 0 Year 1 Year 2 10,000 -22,000 12,084 Which of the following statements is correct? a. The IRR of the project is 17% and if the cost of capital is 14% the project should be undertaken because it creates value. b. The IRR of the project is 14% and if the cost of capital is 11% the project should be undertaken because it creates value. c. The IRR of the project is 11% and if the cost of capital is 6% the project should be undertaken because it creates value. d. The IRR of the project is 6% and if the cost of capital is 3% the project should be undertaken because it creates value. e. The IRR of the project is 3% and if the cost of capital is 0% the project should be undertaken because it creates value. Comment There are two IRR (6% and 14%) but if the cost of capital is 11% the project destroys value (NPV < 0) while if the cost of capital is 3% the project creates value (NPV > 0).

Page 6 of 56 Question 7 Apple must decide whether to install vending machine A or vending machine B in the Airport. Machine A costs $300,000, generates a revenue of $45,000 per year, and it must be replaced every 15 years. Machine B costs $100,000, generates a revenue of $24,000 per year, and it must be replaced every 10 years. The appropriate discount rate is 10%. Which machine should Apple install and what is the EAA of installing this machine? a. Apple is indifferent between installing machine A or B. b. Should install Machine A, which generates an EAA of $9,244.42 c. Should install Machine A, which generates an EAA of $5,557.87 d. Should install Machine B, which generates an EAA of $3,223.32 e. Should install Machine B, which generates an EAA of $7,725.46 Solution ` $42,273.58 ) 1 . 0 1 ( 1 1 1 . 0 000 , 45 300,000 NPV 15 A =         + − + − = $5,557.87 ) 1 . 0 1 ( 1 1 1 . 0 1 42,273.58 15 =         + − = A EAA 61 . 469 , 47 $ ) 1 . 0 1 ( 1 1 1 . 0 ,000 24 100,000 NPV 10 B =         + − + − = $7,725.46 ) 1 . 0 1 ( 1 1 1 . 0 1 47,469.61 10 =         + − = B EAA

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Page 7 of 56 Question 8 Becks Inc. is considering investing in a project with the following expected free cash flows: Year 0 Year 1 Year 2 10,000 -39,000 30,629 Which of the following statements is correct? a. The IRR of the project is 5% and if the cost of capital is 12% the project should be undertaken because it has a positive NPV. b. The IRR of the project is 12% and if the cost of capital is 10% the project should be undertaken because it has a positive NPV. c. The IRR of the project is 5% and if the cost of capital is 9% the project should be undertaken because it has a positive NPV. d. The IRR of the project is 9% and if the cost of capital is 3% the project should be undertaken because it has a positive NPV. e. The IRR of the project is 4% and if the cost of capital is 6% the project should be undertaken because it has a positive NPV. Solution The Project has an IRR of 9% and if the cost of capital is 3% it is NPV positive. (Note: 4%, 5%, and 12% are not IRR).

Page 8 of 56 Question 9 Laval Construction must choose between two pieces of equipment. Tamper A costs $600,000 and it needs to be replaced every five years. This tamper will require $110,000 of maintenance each year. Tamper B costs $750,000, but it will last seven years. Maintenance costs for Tamper B are $90,000 per year. Laval incurs all maintenance costs at the end of the year. The appropriate discount rate for Laval Construction is 12 percent. Which machine should Laval purchase? Solution Tamper A : 8 $996,525.3 ) 12 . 0 1 ( 1 1 12 . 0 1 110,000 600,000 PV 5 − =         + − − − = 4 $276,445.8 ) 12 . 0 1 ( 1 1 12 . 0 1 996,525.38 - 5 − =         + − = EAA Tamper B: .09 $1,160,738 ) 12 . 0 1 ( 1 1 12 . 0 1 90,000 750,000 PV 7 =         + − − − = 0 $254,338.3 ) 12 . 0 1 ( 1 1 12 . 0 1 09 1,160,738. 7 − =         + − − = EAA Choose Tamper B (Note: The problem assumes that the company needs one machine, Tamper A or B, in order to implement “ some other positive NPV project ”.)

Page 9 of 56 Question 10 Assume you are considering taking one of two mutually exclusive projects: Project A: Year 0 1 2 3 FCF -100 100 10 10 Project B: Year 0 1 2 3 FCF -100 10 10 120 a) Calculate the IRR for these projects. b) For which discount rates is the NPV of project A greater than the NPV of project B: Solution a) Calculate the IRR for these projects. ( ) ( ) % 04 . 16 0 1 10 1 10 1 100 100 3 2 =  = + + + + + + − A A A A IRR IRR IRR IRR ( ) ( ) % 94 . 12 0 1 120 1 10 1 10 100 3 2 =  = + + + + + + − B B B B IRR IRR IRR IRR b) For which discount rates is the NPV of project A greater than the NPV of project B: ( ) ( ) 3 2 1 10 1 10 1 100 100 r r r NPV A + + + + + + − = ( ) ( ) 3 2 1 120 1 10 1 10 100 r r r NPV B + + + + + + − = Hence: ( ) ( )         + − + = + − + + − = − 2 3 1 110 90 1 1 1 120 10 1 10 100 r r r r NPV NPV B A Therefore:

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Page 10 of 56 ( ) % 55 . 10 0 1 110 90 0 2    + −   − r r NPV NPV B A NPV PROJECT B PROJECT A 10.55 12.94 16.04 Rate (%)

Page 11 of 56 Question 11 Dot.com is considering investing in a project with the following expected free cash flows: Year 1 Year 2 Year 3 -15,000 34,500 -19,800 Which of the following statements is correct? a. The IRR of the project is 2% and if the cost of capital is 3% the project should be undertaken because it creates value. b. The IRR of the project is 5% and if the cost of capital is 7% the project should be undertaken because it creates value. c. The IRR of the project is 20% and if the cost of capital is 21% the project should be undertaken because it creates value. d. The IRR of the project is 30% and if the cost of capital is 41% the project should be undertaken because it creates value. e. The IRR of the project is 10% and if the cost of capital is 11% the project should be undertaken because it creates value. Comments • There are two IRR (10% and 20%) but if the cost of capital is 21% the project destroys value (NPV < 0) while if the cost of capital is 11% the project creates value (NPV > 0): Two IRR (i.e., 10% and 20%): 0 1 . 1 800 , 19 1 . 1 500 , 34 1 . 1 000 , 15 3 2 = − + + − 0 2 . 1 800 , 19 2 . 1 500 , 34 2 . 1 000 , 15 3 2 = − + + − NPV with cost of capital 21% < 0: 0 21 . 1 800 , 19 21 . 1 500 , 34 21 . 1 000 , 15 %) 21 ( 3 2  − + + − = NPV NPV with cost of capital 11% > 0: 0 11 . 1 800 , 19 11 . 1 500 , 34 11 . 1 000 , 15 %) 11 ( 3 2  − + + − = NPV

Page 12 of 56 Question 12 Dot.com is a private company founded more than ten years ago that has a marginal tax rate of 40%, a firm cost of capital of 7% and the following information: Year 0 Year 1 Year 2 Operating Revenues 90,000 110,000 Operating Costs 42,000 42,000 Depreciation 3,000 3,500 Interest Payments 2,000 6,000 CAPX 10,000 20,000 Inventory 1,000 1200 3000 Account Receivables 850 325 400 Account Payable 100 120 140 After year 2, the firm’s free cash -flows are expected to grow at 2% per year indefinitely. I. Estimate the value of Dot.com II. If comparable firms have forward P/E ratios of 9, estimate the current value of Dot.com’s debt Solution I. Estimate the value of Dot.com NWC (0) = 1,000 + 850 – 100 = 1,750 NWC (1) = 1,200 + 325 – 120 = 1,405 NWC (2) = 3,000 + 400 – 140 = 3,260 FCF (1) = (1- 0.4) (90,000 – 42,000) + 0.4 x 3,000 – 10,000 – (1,405 – 1,750) = 20,345 FCF (2) = (1- 0.4) (110,000 – 42,000) + 0.4 x 3,500 – 20,000 – (3,260 – 1,405) = 20,345 038 , 415 02 . 0 07 . 0 ) 02 . 0 1 ( 345 , 20 ) 2 ( TV = − +  =

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Page 13 of 56 294 . 399 $ ) 07 . 1 ( 038 , 415 345 , 20 07 . 1 345 , 20 ) (V Value Firm 2 0 = + + = II. Estimate the current va lue of Dot.com’s debt Net Income (1) = (1- 0.4) (90,000 – 42,000 – 3,000 – 2,000) = 25,800 Since the (P/E) ratio is equal to the value of equity divided by the net income then: Equity (0) = 9 x 25,800 = 232,200 Debt (0) = Firm Value – Equity (0) = 399,294 – 232,200 = $167,094 Comments • The firm is more than 10 years old hence the net working capital (NWC) already in place in year zero, i.e., $1,750, reflects the investment in NWC since the firm was founded. Dot.com’s firm value is the present value of all future cash-flows • The (P/E) ratio is the price per share divided by the earnings per share or equivalently the value of equity divided by the net income.

Page 14 of 56 Question 13 Taco-Taco has an equity beta of 1.5 and a target debt to value ratio of 30%, and its debt is virtually risk-free. Taco-Taco is considering investing in a new line of Mexican pre- cooked food. Launching this new line would require today (i.e., year 2014) an investment of $5 million in CAPX, and of $1 million in inventory. In the table below you will find the investment’s projections f or the next 3 years (i.e., 2015-2017). After the year 2017, the firm’s cash -flows will continue growing at 3% indefinitely. Year ( in housands of $ ) 2014 2015 2016 2017 Sales $10,000 $12,000 $14,000 Manufacturing Costs $3,000 $4,000 $5,000 Marketing Costs $2,000 $0 $0 Depreciation $400 $400 $400 Inventory $1,000 $1,200 $1,400 $1,600 Accounts Receivables $1,000 $1,200 $800 CAPX $5,000 $1,000 $1,000 $1,000 All data is in thousands of dollars Currently, the government interest rate is 5% and the marginal tax rate is 40%. Below you will find historical information on annual holding-period securities returns for selected securities and market indexes: Years S&P 500 Index Government Bonds 2000-2014 8% 4% 1929-2014 13% 6% Calculate the NPV of the project.

Page 15 of 56 Solution - First we calculate the FCF associated to the new line of pre-cooked food : Year ( in housands of $ ) 2014 2015 2016 2017 Sales $10,000 $12,000 $14,000 Manufacturing Costs $3,000 $4,000 $5,000 Marketing Costs $2,000 $0 $0 EBITD $5,000 $8,000 $9,000 EBITD (1-T) $3,000 $4,800 $5,400 Depreciation $400 $400 $400 Depreciation x T $160 $160 $160 Inventory $1,000 $1,200 $1,400 $1,600 Accounts Receivables $1,000 $1,200 $800 NWC $1,000 $2,200 $2,600 $2,400 Change in NWC $1,000 $1,200 $400 -$200 CAPX $5,000 $1,000 $1,000 $1,000 FCF -$6,000 $960 $3,560 $4,760 - Second we calculate Taco-Taco ’s cost of capital: % 5 . 15 ) 06 . 0 13 . 0 ( 5 . 1 0.05 = −  + = − + = ) r (r β r r f M E f E % 75 . 11 3 . 0 ) 4 . 0 1 ( 05 . 0 7 . 0 155 . 0 1 =  −  +  =  − +  = V D ) T ( r V E r r C D E WACC - Third we calculate the TV in 2012: K 032 , 56 $ 03 . 0 1175 . 0 ) 03 . 0 1 ( 760 , 4 ) 1 ( 2017 2017 = − +  = − + = K g r g FCF TV WACC - Finally we calculate NPV of the project: K K K K K K 271 , 41 $ 1175 . 1 032 , 56 1175 . 1 760 , 4 1175 . 1 560 , 3 1175 . 1 960 000 , 6 NPV 3 3 2 = + + + + − = Therefore, Taco-Taco should launch the new line of pre-cooked food.

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Page 16 of 56 Question 14 In one year Dot.com firm value will be either $1,090 with probability 0.5 or $3,270 with probability 0.5. Dot.com has outstanding debt with a face value of $1,500 due in one year. Punto.com , a company in a similar business as Dot.com , has a current value of $1,100 and generates an annual free cash flow of $99 in perpetuity. The risk-free rate is 5%. Calculate the current value of Dot.com ’s debt. Solution - First we need to find the discount rate using the comparable firm ( i.e. , Punto.com ): % 9 100 , 1 99 99 100 , 1 = =  = WACC WACC r r - Second we need to find the current value of the firm ( i.e. , the underlying asset): 000 , 2 $ 0.09 1 5 . 0 3,270 0.5 1,090 V Dot.com 0 = +  +  = - Third we calculate the value of equity taking into account that equity is a call option on the value of the firm (i.e., underlying asset) with strike price equal to the FVD: S o = 2,000 S U = 3,270 S D = 1,090 C o =? C U = max {3,270-1500, 0) = 1,770 C D = max {1,090-1500, 0) = 0 Using the binomial formula: 781 $ 1090) - (3270 0.05) (1 270 , 3 0 1090 1770 2000 1090 - 3270 0 1770 ) S (S ) r (1 S C S C S S S C C C D U T f U D D U 0 D U D U 0 =  +  −  −  − = = −  + − −  − − = - Fourth we calculate the value of the debt at t = 0: Debt = Firm Value – Equity Value = 2,000 - 781 = $1,219

Page 17 of 56 Question 15 Punto.com currently has FCF of $40,000. This state of affairs is expected to continue for seven years. After seven years FCF will start to decrease at a rate of 3% per year. If Punto.com cost of capital is 10%, the value of its debt is $150,000, and there are 2,000 shares outstanding, calculate Punto.com ’s current share price. a. $ 86 b. $ 99 c. $ 106 d. $ 123 e. $ 174 Solution 895 , 347 ) 03 . 0 ( 1 . 0 ) 03 . 0 1 ( 40 1 . 1 1 1 . 1 1 1 1 . 0 40 Value Firm 7 7 = − − −  +       − = K K Equity Value = 347,895 – 150,000 = 197,895 99 $ 000 , 2 895 , 197 Price Share = =

Page 18 of 56 Question 16 A stock's beta measures: a. the systematic risk of the stock. ( TRUE) b. the difference between the return of the stock and the return of the market portfolio. ( FALSE) c. the risk premium of the stock. ( FALSE) d. the systematic risk of the market portfolio. ( FALSE) Question 17 Your portfolio is worth $1 million and has a beta of 1.8. Stock A contributes 10 percent of the dollar value of your portfolio and has a beta of 2. If you sell all your holdings in Stock A and replace it with a $50,000 investment in Stock W with a beta of 0.5 and another $50,000 investment in Stock Z with a beta of 1.5, what is the beta of the new portfolio? a. 1.00 b. 1.64 c. 1.70 d. 1.75 e. 1.82 Solution Before: 7778 . 1 9 . 0 2 1 . 0 8 . 1 9 . 0 2 1 . 0 8 . 1 Remain Remain =  − =  +  =   After selling A and including W and Z: 70 . 1 7778 . 1 9 . 0 5 . 1 05 . 0 5 . 0 05 . 0 9 . 0 5 . 1 05 . 0 5 . 0 05 . 0 Remain =  +  +  =  +  +  =   New Portfolio

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Page 19 of 56 Question 18 Dot.com is currently worth $700, and in one year, it will be worth either $500 or $1300. The risk-free interest rate is 5%. Dot.com ’s equity is currently worth $174. 85 and its debt matures in one-year. Calculate the face value of Dot.com ’s debt. a. $ 625 b. $ 675 c. $ 725 d. $ 775 e. $ 825 Solution S o = 700 S U = 1,300 S D = 500 C o =174.85 C U = max {1300-K, 0) = 1300-K C D = max {500-K, 0) = 0 Using the binomial formula: 85 . 174 $ 500) - 1300 ( 0.05) (1 1300 0 500 ) 1300 ( 700 500 - 1300 1300 ) S (S ) r (1 S C S C S S S C C C D U T f U D D U 0 D U D U 0 =  +  −  − −  − = = −  + − −  − − = K K Solving the above equation we get K =$675

Page 20 of 56 Question 19 Below is a graph of the value of a portfolio at maturity as a function of the price of the underlying stock ( S T ). Value of Portfolio at Maturity K A K B S T To which portfolio does the above graph correspond? a. Buy a call option with strike price K A and short a put option with strike price K B . b. Buy a call option with strike price K B and short a put option with strike price K A . c. Short a call option with strike price K A and buy a put option with strike price K B . d. Short a call option with strike price K B and buy a put option with strike price K A . Solution Short a call option with strike price K B and buy a put option with strike price K A . K A 0

Page 21 of 56 Question 20 Below is a graph of the value of a portfolio at maturity as a function of the price of the underlying stock ( S T ). Value of Portfolio at Maturity K A K B S T To which portfolio does the above graph correspond? a. Buy a call option with strike price K A and buy a put option with strike price K B . b. Buy a call option with strike price K A and short a put option with strike price K B . c. Buy a call option with strike price K B and short a put option with strike price K A . d. Short a call option with strike price K A and short a put option with strike price K B . e. Short a call option with strike price K A and buy a put option with strike price K B . Solution Short a call option with strike price K A and buy a put option with strike price K B . (SEE GRAPH BELOW) K B 0

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Page 22 of 56 Value of Portfolio at Maturity Short a Call Buy a Put K A K B S T K B Portfolio T

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Page 23 of 56 Question 21 One-year European call options are available on Springtime Corporation stock with the exercise price of $100. Springtime stock is now selling at $90 per share. Assume that on exercise day Springtime shares sell at one of two possible prices: $80 or $120. If the Treasury bill rate is 4%, how much would you pay for one call option on Springtime stock? a. $6.54 b. $10.00 c. $13.08 d. $19.23 e. $23.14 S o = 90 S U = 120 S D = 80 C o =? C U = max {120-100, 0) = 20 C D = max {80-100, 0) = 0 Solution Using the binomial formula: 54 . 6 $ 80) - 120 ( 0.04) (1 120 0 80 20 90 80 - 120 0 20 ) S (S ) r (1 S C S C S S S C C C D U T f U D D U 0 D U D U 0 =  +  −  −  − = = −  + − −  − − =

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Page 24 of 56 Question 22 Dot.com stock is now selling at $110 per share. In two years Dot.com shares will sell at one of two possible prices: $90 or $180. If the Treasury bill rate is 8%. How much would you pay for a two-year European put option on Dot.com stock with an exercise price of $120? a. $ 14.77 b. $ 18.89 c. $ 17.78 d. $ 21.89 e. $ 7.63 Solution S o = 110 S U = 180 S D = 90 C o =? C U = max {180-120, 0) = 60 C D = max {90-120, 0) = 0 Using the binomial formula: 89 . 21 $ 90) - 180 ( 0.08) (1 180 0 90 60 110 90 - 180 60 ) S (S ) r (1 S C S C S S S C C C 2 D U T f U D D U 0 D U D U 0 =  +  −  −  = = −  + − −  − − = Using the put-call parity relation: 77 . 14 $ 08 . 1 120 110 89 . 21 1 2 0 0 0 = + − = + + − = T f ) r ( K S C P

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Page 25 of 56 Question 23 Evaluate the following statements: I- If a stock has a beta greater than one, its return must have a positive correlation with the return of the market portfolio. (TRUE) II- If a stock has a beta smaller than one, its return must have a negative or a zero correlation with the return of the market portfolio. (FALSE) III- With Dot.com stock and the risk-free asset an investor can form up to three different portfolios. (FALSE) Question 24 Evaluate the following statements about diversification: I- Diversifiable risk is the only risk that matters to a diversified investor. (FALSE) II- Diversification is the process of reducing the market risk associated with individual assets by spreading the investment across numerous assets. (FALSE) Question 25 The current stock price of Dot.com is $40. The price of the stock in one year from today will be either $30 or $90. The risk free interest rate is 5%. How many shares of Dot.com do you need to replicate 50 European call options with a strike price of $60? (Note: Each call option gives the right to buy one share of the stock one year from today at $60). a. 25 shares b. 0.5 shares c. 20 shares d. 1 share e. 50 shares Solution C U = 90-60 = $30 C D = $0 Number of shares needed to replicate one call 5 . 0 30 90 0 30 = − − = − − = D U D U S S C C Number of shares needed to replicate 50 calls 25 5 . 0 50 =  =

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Page 26 of 56 Question 26 Dell has an expected return of 20% and GE has an expected return of 12%. The beta of Dell is twice the beta of GE . Assuming that the CAPM holds what is the risk-free rate? a. 2% b. 4% c. 6% d. 8% e. 10% Solution If CAPM holds: GE f Dell f Dell f Mkt f Mkt Dell f Dell r r r r r r r r r     − = − = −  − + = 2 20 . 0 ) ( ) ( GE f GE f GE f Mkt f Mkt GE f GE r r r r r r r r r    − = − = −  − + = 12 . 0 ) ( ) ( Hence: % 4 2 24 . 0 20 . 0 12 . 0 2 20 . 0 =  − = −  − =  − f f f GE f GE f r r r r r   Question 27 Calculate the FCF in year 2 assuming that the firm’s corporate tax rate is 40%. Year 1 Year 2 Net Income 260,400 259,800 Depreciation 7,000 8,000 Interest Payments 9,000 9,000 CAPX 25,000 30,000 Inventory 2,500 2,500 Account Receivables 800 800 Account Payable 100 800 Solution FCF = Net Income + (1 – T C ) x Interest Paid + Depreciation – CAPX – Change in NWC Hence: FCF 2 = 259,800 + 9,000 (1 – 0.4) + 8,000 – 30,000 – [(2,500+800-800) – (2,500+800-100)] = = 259,800 + 5,400 + 8,000 – 30,000 + 700 = $243,900

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Page 27 of 56 Question 28 Dot.com is considering replacing its existing machine. You are given the following facts: • The firm has spent $5,000 studying the compatibility of the new machines and the experts have reached the conclusion that the machine is indeed compatible with the rest of the production line. • The new machine costs $300,000 and would replace the existing machine. The new machine would be depreciated in straight line at the rate of $20,000 per year and would be sold for $70,000 after 10 years. • The new machine would increase before-tax annual sales by $100,000. The new machine would also increase before-tax annual operating costs by $30,000. These changes in sales and costs would occur at year-end during the 10 years that the new machine would be operating. • The new requires $15,000 in working capital while the old machine only requires $14,000 in working capital. • The old machine was acquired 5 years ago for $90,000 and it has a current market value of $40,000. The old machine could last for another 10 years, and after 10 years would be worth $10,000. • The current book value of the old machine is $50,000 and it would be depreciated in straight line at the rate of $3,000 per year. • Dot.com’s marginal tax rate is 40%. I. Calculate the incremental FCF in year 0 of buying the new machine II. Calculate the incremental FCF in year 5 of buying the new machine III. Calculate the incremental FCF in year 10 of buying the new machine Solution I. Incremental FCF in year 0 FCF (0) = – 300,000 – 1,000 + 40,000 – 0.4 x (40,000 – 50,000) = – 257,000 II. Incremental FCF in year 5 FCF (5) = (1 – 0.4) (100,000 – 30,000) + 0.4 x (20,000 – 3,000) = 48,800 III . Incremental FCF in year 10 FCF (10) = (1 – 0.4) (100,000 – 30,000) + 0.4 x (20,000 – 3,000) + 70,000 – 0.4 x (70,000 – 100,000) – 10,000 + 0.4 x (10,000 – 20,000) + 1,000 = = 117,800

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Page 28 of 56 Question 29 Calculate the FCF in year 2 assuming that the firm’s marginal tax rate is 35%. Year 1 Year 2 Year 3 Operating Revenues 120,000 140,000 160,000 Operating Costs 50,000 50,000 50,000 Depreciation 6,000 8,000 10,000 Interest Payments 10,000 10,000 10,000 CAPX 25,000 30,000 35,000 Inventory 2,500 3,200 4,800 Account Receivables 320 500 400 Account Payable 120 800 900 a. $ 24,600 b. $ 28,400 c. $ 31,100 d. $ 31,500 e. $ 36,300 Solution Year 0 Year 1 Year 2 Year 3 Operating Revenues 120,000 140,000 160,000 Operating Costs 50,000 50,000 50,000 EBITDA 70,000 90,000 110,000 EBITDA (1-T) 45,500 58,500 71,500 Depreciation 6,000 8,000 10,000 Interest Payments 10,000 10,000 10,000 Depreciation Tax Shield 2,100 2,800 3,500 CAPX 25,000 30,000 35,000 Inventory 1,000 2,500 3,200 4,800 Account Receivables 850 320 500 400 Account Payable 100 120 800 900 NWC 1,750 2,700 2,900 4,000 Change in NWC 950 200 1,100 FCF 21,650 31,100 38,900

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Page 29 of 56 The following problem applies to the next two questions. Punto.com which has a marginal tax rate of 40% is considering replacing its existing machine. You are given the following facts: • The new machine costs $1,000,000 and would replace the existing machine. The new machine would be depreciated in straight line at the rate of $75,000 per year and would be sold for $200,000 after 10 years. • The new machine would increase before-tax annual sales by $250,000. The new machine would also increase before-tax annual operating costs by $125,000. These changes in sales and costs would occur at year-end during the 10 years that the new machine would be operating. • The old machine was acquired 6 years ago for $750,000 and it has a current market value of $500,000. The old machine could last for another 10 years, and after 10 years would be worth $70,000. The current book value of the old machine is $500,000 and it would be depreciated in straight line at the rate of $50,000 per year. Question 30 Calculate the incremental FCF in year 0 of buying the new machine. a. - $ 1,000,000 b. - $ 700,000 c. - $ 500,000 d. - $ 300,000 e. - $ 200,000 Solution FCF (0) = – 1,000K + 500K – 0.4 x (500K – 500K) = – 500K Question 31 Calculate the incremental FCF in year 10 of buying the new machine. a. $ 163,000 b. $ 223,000 c. $ 263,000 d. $ 278,000 e. $ 283,000 Solution FCF (10) = (1 – 0.4) (250,000 – 125,000) + 0.4 x (75,000 – 50,000) + 200,000 – 0.4 x (200,000 – 250,000) – 70,000 + 0.4 x (70,000 – 0) = 263,000

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Page 30 of 56 Question 32 Calculate the FCF in year 2 assuming that th e firm’s co rporate tax rate is 40%. Year 1 Year 2 Net Income 260,400 259,800 Depreciation 7,000 8,000 Interest Payments 9,000 9,000 CAPX 25,000 30,000 Inventory 2,500 2,500 Account Receivables 800 800 Account Payable 100 800 Solution FCF = Net Income + (1 – T C ) x Interest Paid + Depreciation – CAPX – Change in NWC Hence: FCF 2 = 259,800 + 9,000 (1 – 0.4) + 8,000 – 30,000 – [(2,500+800-800) – (2,500+800-100)] = = 259,800 + 5,400 + 8,000 – 30,000 + 700 = $243,900

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Page 31 of 56 Question 33 Punto.com is considering the purchase of a new cutting machine for $60,000. This machine would reduce manufacturing costs by $10,000 annually and last 5 years. The new machine could be depreciated following the straight-line depreciation method to its salvage of $15,000, that is, at the rate of $9,000 per year. The firm also expects to be able to reduce net working capital by $18,000 when the machine is installed. The firm’s marginal tax rate is 40% and it has a cost of capital of 12%. What is the NPV of the new machine? Solution Incremental FCF 0 = – 60,000 + 18,000 = – $42,000 Incremental FCF 1-4 = (1-0.4) x 10,000 + 0.4 x 9,000 = $9,600 Incremental FCF 5 = (1-0.4) x 10,000 + 0.4 x 9,000 – 18,000 + 15,000 = $6,600 Note: (1) The book value of the machine in year 5 is $15,000 (= 60,000 – 9,000 x 5) hence the Punto.com does not have a capital gain (or loss) when selling the machine. (2) In year 0 and 5 we have to take into account that the 18,000 NWC, if the machine is purchased, hence we have a positive incremental cash-flow in year 0 and a negative incremental cash-flow in year 5. 0 096 , 9 $ 12 . 1 600 , 6 12 . 1 1 1 12 . 0 600 , 9 000 , 42 5 4  − = +       − + − = NPV Hence Punto.com should not purchase the new machine.

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Page 32 of 56 Question 34 Dot.com purchased a machine several years ago and wants to sell it today for its book value of $25,000. Dot.com believes that the machine has five years of useful life remaining with a salvage value of $15,000 at the end of these five years. The new machine that Dot.com considers buying costs $75,000, and could last five years with a $22,000 salvage value at the end. This new machine will increase working capital requirement by $7,500 now. Revenues for the new machine are $90,000 per year and revenues for the old machine are $58,000 also per year. The new machine and old machine operating costs are $42,000 and $30,000 per year, respectively. Both of these machines are depreciated in straight line at the rate of $3,000 per year. Assuming that the corporate tax rate is 40% and that the cost of capital is 6.50%, what is the NPV of this replacement decision? Solution Incremental FCF 0 = – 75,000 – 7,500 + 25,000 = – $57,500 Incremental FCF 1-4 = (1-0.4) x [(90,000 – 58,000) – (42,000 – 30,000)] = $12,000 Incremental FCF 5 = (1-0.4) x [(90,000 – 58,000) – (42,000 – 30,000)] + 7,500 + [22,000 – 0.4 x (22,000-60,000)] – [15,000 – 0.4 x (15,000-10,000)] = = $43,700 Note: The old machine is sold in year 0 for its book value of 25,000, and hence, there is not capital gain or loss. The book value of the new machine in year 5 is $60,000 (= 75,000 – 3,000 x 5) and the book value that the old machine would have had in year 5 is $10,000 (= 25,000 – 3,000 x 5) Hence, under the straight line depreciation method, in year 5, there is a capital loss of (22,000-60,000) in the sale of new machine and there would have been a capital gain of (15,000- 10,000) in the sale of the old machine. 0 506 , 15 $ 065 . 1 43700 065 . 1 1 1 065 . 0 12000 57500 5 4  = +       − + − = NPV Hence Dot.com should purchase the new machine. (For your information please see the next page for details on the FCF calculations.)

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Page 33 of 56 Tax Rate 40.00% Discount Rate 6.50% FCF IF THE NEW MACHINE IS PURCHASED Year 0 Year 1 Year 2 Year 4 Year 4 Year 5 Operating Revenues 90,000 90,000 90,000 90,000 90,000 Operating costs 42,000 42,000 42,000 42,000 42,000 Operating Profits 48,000 48,000 48,000 48,000 48,000 Operating Profits After Tax 28,800 28,800 28,800 28,800 28,800 Depreciation New Machine 3,000 3,000 3,000 3,000 3,000 Depreciation Tax Shield 1,200 1,200 1,200 1,200 1,200 Book Value of New Machine 75,000 72,000 69,000 66,000 63,000 60,000 Book Value of Old Machine 25,000 Salvage Value New 22,000 Taxes on Salvage Value New -15,200 Salvage Value Old 25,000 Taxes on Salvage Value Old 0 CAPX 75,000 Chage in NWC 7,500 -7,500 FCF -57,500 30,000 30,000 30,000 30,000 74,700 FCF IF THE NEW MACHINE IS NOT PURCHASED Year 0 Year 1 Year 2 Year 4 Year 4 Year 5 Operating Revenues 58,000 58,000 58,000 58,000 58,000 Operating costs 30,000 30,000 30,000 30,000 30,000 Operating Profits 28,000 28,000 28,000 28,000 28,000 Operating Profits After Tax 16,800 16,800 16,800 16,800 16,800 Depreciation Old Machine 3,000 3,000 3,000 3,000 3,000 Depreciation Tax Shield 1,200 1,200 1,200 1,200 1,200 Book Value of Old Machine 25,000 22,000 19,000 16,000 13,000 10,000 Salvage Value Old 15,000 Taxes on Salvage Value Old 2,000 CAPX Chage in NWC FCF 0 18,000 18,000 18,000 18,000 31,000 Incremental FCF -57,500 12,000 12,000 12,000 12,000 43,700 Discounted Incremental FCF -57,500 11,268 10,580 9,934 9,328 31,896 NPV $15,505

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Page 34 of 56 Question 35 Raid is considering a new household-use laser-guided cockroach search-and-destroy system that has the following characteristics: • Projected sales: $20 million per year for five years. • Projected costs: $15 million per year for five years. • The cockroach eradicator project will require $2 million NWC. • The necessary equipment to begin production will cost $10 million. Raid, a Canadian company, follo ws the Canada Revenue Agency’s CCA method and the CCA rate for this equipment is 20%. In five years, this equipment will be sold for $7 million. • The relevant tax rate is 45% and the cost of capital is 20%. Calculate the NPV of the project. Solution FCF 0 (w/o depreciation tax shied) = -10M – 2M = -12M FCF 1-4 (w/o depreciation tax shied) = (20M – 15M) (1-0.45) = 2.75M FCF 5 (w/o depreciation tax shied) = (20M – 15M) (1-0.45) + 7M + 2M = 11.75M In the previous chart we have been ignoring depreciation all along. We obtained FCFs before considering the consequences of the depreciation tax shield. Now we take care of the tax shield of depreciation: M PVTS CCA 43 . 1 $ ) 2 . 0 1 ( 1 2 . 0 2 . 0 45 . 0 2 . 0 M 7 2 . 0 1 2 2 . 0 1 2 . 0 2 . 0 45 . 0 2 . 0 M 10 5 = +  +   − + +  +   = Using all the above information we obtain that the NPV is: million 27 . 1 43 . 1 2 . 1 75 . 11 2 . 1 1 1 2 . 0 75 . 2 12 5 4 = + +       − + − = NPV

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Page 35 of 56 Question 36 Dot.com plans to purchase a new machine for $50,000, with a life span of five years. It has no salvage value at the end of its useful life. The machine generates sales of $80,000 in year 1and increase at 5% per annum. Cost of goods sold accounts for 60% of sales. The machine will be depreciated using the straight-line depreciation method at the rate of $10,000 per year. Tax rate is 40% and the cost of capital (discount rate) is 8.20%. Using NPV analysis, should Dot.com purchase the machine? Solution Since NPV is positive, we should buy the machine Year 0 1 2 3 4 5 Revenue 80000 84000 88200 92610 97241 - COGS (48000) (50400) (52920) (55566) (58344) -Depreciation (10000) (10000) (10000) (10000) (10000) EBIT 22000 23600 25280 27044 28896 -Taxes (40%) (8800) (9440) (10112) (10818) (11558) EBIT after taxes 13200 14160 15168 16226 17338 +Depreciation 10000 10000 10000 10000 10000 -CAPX 50000 FCF -50000 23200 24160 25168 26226 27338 PV @ 8.2% -50000 21442 20637 19869 19135 18434 NPV $49,516

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Page 36 of 56 Question 37 Pilot Inc . has a cost of capital of 10% and a marginal corporate tax rate of 40%. Pilot Inc . is considering the introduction of a Magic Ink Pen ( MIP ). You are given the following facts: • A marketing study, which has cost the company $3,000, shows that annual sales of MIP are expected to be $600,000 in each of the 2 years that the MIP would be in the market. • The new machine to produce the MIP would cost $800,000 and would be sold for $200,000 in year 2. • Pilot Inc ., a Canadian firm, follows the CCA depreciation method. The new machine has a CCA rate of 30%. [ Pilot Inc. has numerous other assets in the same asset pool.] Calculate the incremental FCF of launching the MIP in year 2 including the CCA tax shield. Solution UCC 2 = 400,000 x (1-0.3) + 400,000 =$680,000 ( See table below .) CCA 2 = 680,000 x 0.3 = $204,000 CCA Tax Shield 2 = 204,000 x 0.4 = $81,600 FCF 2 ( Including CCA Tax Shield ) = 600,000 x (1-0.4) +200,000 + 81,600 = $641,600 For your information : CAPX UCC CCA CCA Tax Shield 0 800,000 1 400,000 120,000 48,000 2 680,000 204,000 81,600

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Page 37 of 56 Question 38 Boston Hydro (BH) is negotiating the purchase of a new piece of equipment for its current operations. You are given the following facts: - The new equipment costs $100,000 and would replace the existing equipment that has a current market value of $35,000 if sold today. - The new equipment would increase sales by $65,000 per year. The new equipment would be depreciated in straight-line at the rate of $30,000 per year, and would be sold for $50,000 in year 3. - The existing equipment could last for another 3 years, and after the 3 years could be sold for $14,000. The current book value of the existing equipment is $50,000 and it would be depreciated in straight-line at the rate of $10,000 per year. - The new equipment would only require $4,000 in net working capital, while the existing equipment requires $6,000 in net working capital. - BH’s marginal tax rate is 40% and i ts required rate of return is 10% Calculate the NPV of buying the new equipment Solution FCF (0) = - 100,000 + 35,000 – 0.4 x (35,000 – 50,000) – (4,000 – 6,000) = – $57,000 FCF (1) = FCF (2) = 65,000 x (1-0.4) + 0.4 x (30,000 – 10,000) = $47,000 FCF (3) = 65,000 x (1-0.4) + 0.4 x (30,000 – 10,000) + (4,000 – 6,000) + 50,000 – 0.4 x [50,000 – 10,000*] – 14,000 + 0.4 x [14,000 – 20,000**] = $62,600 *Book Value of the New Machine at time 3 = 100,000 – 3 x 30,000 = 10,000 **Book Value of the Existing Machine at time 3 = 50,000 – 3 x 10,000 = 20,000 603 , 71 $ 1 . 1 600 , 62 1 . 1 000 , 47 1 . 1 000 , 47 000 , 57 3 2 = + + + − = NPV

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Page 38 of 56 Question 39 Year Return on Security A Return on Security B 2009 -10% 21% 2008 20% 30% 2007 5% 7% 2006 -5% -3% 2005 2% -8% 2004 9% 25% Using the above historical information i) Estimate the sample average return on Security A and B. ii) Estimate the sample variance of the return on Security A and B. iii) Estimate the sample covariance and correlation between Security A and B. Solution i) T A A At t 1 T B B Bt t 1 1 10 20 5 5 2 9 R R R 3.5% T 6 1 21 30 7 3 8 25 R R R T 6 12% = = − + + − + + = = = = + + − − + = = = =   ii) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 T 2 A A At 2 2 t 1 2 2 2 T 2 2 B B Bt t 1 0.1 0.035 0.2 0.08 0.05 0.035 1 1 Var(R ) R R T 1 5 0.05 0.035 0.02 0.035 0.09 0.035 0.01123 0.21 0.12 0.3 0.12 1 1 Var(R ) R R 0.07 0.12 T 1 5 = =   − − +     − + − +   = − = −   − − + −     + −   = − + − + = − = − −   ( ) ( ) ( ) 2 2 2 0.03 0.12 0.08 0.12 0.25 0.12 0.02448       + − − +     − − + −   =

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Page 39 of 56 iii) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) A B A B A,t B,t t 0.1 0.035 0.21 0.4 0.2 0.035 0.3 0.12 0.05 0.035 0.07 0.12 1 1 Cov(R , R ) (R R )(R R ) 0.05 0.035 0.03 0.12 T 1 5 0.02 0.035 0.08 0.12 0.09 0.035 0.25 0.12 0.00794 C Correlation − − − + − − + − − + = − − = − − − − + − − − − + − − =                   =  ovariance Variance of A Variance of B 0.479 =

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Page 40 of 56 Question 40 State Probability Return on Security A Return on Security B Boom 0.3 12% -2% Normal 0.6 8% 2% Bust 0.1 4% 6% Use the information above to answer the following questions: i) What is the expected return on Security A and B? ii) What is the standard deviation of the return on Security A and B? iii) What is the covariance and the correlation between Security A and B? iv) What is the expected return and the standard deviation on a portfolio with weights of 60% in Security A and 40% in Security B? Solution i) % 8 . 8 04 . 0 1 . 0 08 . 0 6 . 0 12 . 0 3 . 0 ) ( =  +  +  = A R E % 2 . 1 06 . 0 1 . 0 02 . 0 6 . 0 ) 02 . 0 ( 3 . 0 ) ( =  +  + −  = B R E ii) % 4 . 2 ) 088 . 0 04 . 0 ( 1 . 0 ) 088 . 0 08 . 0 ( 6 . 0 ) 088 . 0 12 . 0 ( 3 . 0 ) ( 2 2 2 = −  + −  + −  = A R SD % 4 . 2 ) 012 . 0 06 . 0 ( 1 . 0 ) 012 . 0 02 . 0 ( 6 . 0 ) 012 . 0 02 . 0 ( 3 . 0 ) ( 2 2 2 = −  + −  + − −  = B R SD iii) % 0576 . 0 ) 012 . 0 06 . 0 ( ) 088 . 0 04 . 0 ( 1 . 0 ) 012 . 0 02 . 0 ( ) 088 . 0 08 . 0 ( 6 . 0 ) 012 . 0 02 . 0 ( ) 088 . 0 12 . 0 ( 3 . 0 − = −  −  + + −  −  + − −  −  = AB Cov 1 0.024 0.024 0.000576 - − =  = = B A AB AB     iv) % 8 . 5 ) ( ) ( ) ( =  +  = B B A A P R E w R E w R E ( ) % 5 . 0 000576 . 0 4 . 0 6 . 0 2 024 . 0 4 . 0 024 . 0 6 . 0 2 ) ( 2 2 2 2 2 2 2 2 = −    +  +  = = + +  = AB B A B B A A P w w w w R SD   

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Page 41 of 56 Question 41 Mary has $20,000 in her bank account. She plans to borrow an additional $10,000 from the bank at the risk free rate of 3%. Mary also plans to short-sell $5,000 worth of Sony stocks and invest all (i.e., $35,000) in Samsung . Sony ’s expected return is 6% and Samsung ’s expected return is 8%. Calculate the expected return of Mary’s portfolio. Solution 50 . 0 000 , 20 000 , 10 25 . 0 000 , 20 000 , 5 75 . 1 000 , 20 000 , 35 : Weights Portfolio $20,000 5,000 - 10,000 ,000 5 3 Value Portfolio − = − = − = − = = = = − = − Free Risk Sony Samsung w w w % 11 % 3 ) 50 . 0 ( % 6 ) 25 . 0 ( % 8 75 . 1 ) E(R P =  − +  − +  =

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Page 42 of 56 Question 42 You own a portfolio consisting of the following shares. Security Weights Beta Expected Return 1 20% 1.00 16% 2 30% 0.85 14% 3 15% 1.20 20% 4 25% 0.60 12% 5 10% 1.60 24% If the risk-free rate is 7 percent and expected return on the market portfolio is 15.5 percent: a) Calculate the expected return and the beta for your portfolio. b) Evaluate which of the stocks are relatively overpriced and which ones are relatively underpriced. Solution a) % 8 . 15 24 . 0 1 . 0 12 . 0 25 . 0 20 . 0 15 . 0 14 . 0 3 . 0 16 . 0 2 . 0 ) ( =  +  +  +  +  = P R E 945 . 0 60 . 1 1 . 0 60 . 0 25 . 0 20 . 1 15 . 0 85 . 0 3 . 0 1 2 . 0 =  +  +  +  +  = P  b) Security Beta Expected Return i f i r R E  − ) ( Evaluation 1 1.00 16% 9 Undervalued 2 0.85 14% 8.2 Overvalued 3 1.20 20% 10.8 Undervalued 4 0.60 12% 8.3 Overvalued 5 1.60 24% 10.6 Undervalued Market portfolio 1 15.5 8.5 Benchmark Note : According to the CAPM, for all assets, it should hold the following relation: %. 5 . 8 % 7 % 5 . 15 ) ( ) ( = − = − = − f Mkt i f i r R E r R E  Therefore, for example, for Security 2, % 5 . 8 % 2 . 8 85 . 0 % 7 % 14 ) (  = − = − i f i r R E  , which implies that Security 2’s return of 14% is too low, that is, Security 2 is overvalued.

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Page 43 of 56 Question 43 You hold three stocks in your portfolio, Stocks A, B and C. The portfolio beta is 1.50. Stock A contributes 20 percent of the dollar value of your holdings and has a beta of 1.25. If you sell all of your holdings in Stock A, and replace it with an equal investment in Stock D with a beta of 1.00, what is the beta of the new portfolio (Stocks B, C and D)? Solution Before: 5625 . 1 8 . 0 25 . 1 2 . 0 5 . 1 8 . 0 8 . 0 8 . 0 8 . 0 8 . 0 25 . 1 2 . 0 5 . 1 =  − =       +        + +  = C C B B C C B B w w w w     After selling A and including D: 45 . 1 5625 . 1 8 . 0 1 2 . 0 8 . 0 8 . 0 8 . 0 1 2 . 0 =  +  =       + +  = C C B B New w w   

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Page 44 of 56 Question 44 Dot.com is considering replacing its existing machine. The new machine costs $260,000 and would replace the existing machine. The new machine would be sold for $20,000 after 10 years. During those 10 years, the new machine would depreciate in straight line from $260,000 to $20,000 at the rate of $24,000 per year. During the 10 years that the new machine would be operating, the new machine would increase before-tax sales by $80,000 per year. The new machine would also increase before-tax operating costs by $30,000 per year. The old machine was acquired 5 years ago for $90,000 and it has a current market value of $40,000. The old machine could last for another 10 years, and after 10 years would be worth $20,000. During those 10 years, the old machine would depreciate in straight line from $40,000 to $20,000 at the rate of $2,000 per year. Dot.com has profitable ongoing operations all in the same line of business. Dot.com has 5 million outstanding shares of common stock selling for $20 per share. The required return on Dot.com common stock is 25 percent. Dot.com also has 1 million shares of preferred stock. A share of preferred stock pays a $5 annual dividend and currently trades at $50. Dot.com has no debt and its tax rate is 40 percent. Calculate the NPV of buying the new machine. Solution Calculate FCF: Incremental FCF (Year 0) = -260K +40K -0.4 (40K-40K) = -$220K Incremental FCF (Years 1-9) = (80K-30K) (1-0.4) + 0.4 (24K-2K) = $ 38.8K Incremental CF (Year 10) = (80K-30K) (1-0.4) + 0.4 (24K-2K) + 20K -0.4(20K-20K) - 20K + 0.4(20K-20K) = $38.8K Calculate WACC: Market value of common equity = 5,000K x 20 = $100,000K Market value of preferred stock = 1,000K x 50 = $50,000K % 10 50 5 = = = pfd pfd P Div r

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Page 45 of 56 % 20 2 . 0 25 . 0 50 100 100 1 . 0 50 100 50 = =  + +  + =  + +  + = E pfd r P E E r P E P WACC Calculate NPV: 331 , 57 ) 2 . 0 1 ( 1 1 2 . 0 800 , 38 000 , 220 10 − =         + − + − = NPV

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Page 46 of 56 Question 45 Presto has an equity beta of 2.0, a target debt to value ratio of 28%, and its debt is virtually risk-free. Presto is considering investing in a new line of Italian pre-cooked food. Launching this new line would require today (i.e., year 2010) an investment of $15 million in CAPX, and of $5 million in inventory. In the table below you will find the investment’s projections for the n ext 3 years (i.e., 20011-2013). After the year 2013, the firm’s cash -flows will continue growing at 2% indefinitely. Year 2010 2011 2012 2013 Sales $15,000 $15,000 $18,000 Manufacturing Costs $3,000 $4,000 $5,000 Marketing Costs $1,000 $0 $0 Depreciation $1,500 $1,600 $1,500 Inventory $5,000 $5,200 $5,400 $5,600 A/R $1,000 $1,200 $1,200 CAPX $15,000 $2,500 $600 $2,500 All data is in thousands of dollars Currently, the government interest rate is 3% and the marginal tax rate is 40%. Below you will find historical information on annual holding-period securities returns for selected securities and market indexes: Years S&P 500 Index Government Bonds 2000-2010 4% 5% 1929-2010 14% 8% Calculate the NPV of the project.

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Page 47 of 56 Solution First, we calculate the FCF associated to the new line of Italian pre-cooked food the project : Year ( in housands of $ ) 2010 2011 2012 2013 Sales $15,000 $15,000 $18,000 Manufacturing Costs $3,000 $4,000 $5,000 Marketing Costs $1,000 $0 $0 EBITD $11,000 $11,000 $13,000 EBITD (1-T) $6,600 $6,600 $7,800 Depreciation $1,500 $1,600 $1,500 Depreciation x T $600 $640 $600 Inventory $5,000 $5,200 $5,400 $5,600 A/R $1,000 $1,200 $1,200 NWC $5,000 $6,200 $6,600 $6,800 Change in NWC $5,000 $1,200 $400 $200 CAPX $15,000 $2,500 $600 $2,500 FCF -$20,000 $3,500 $6,240 $5,700 Second, we calculate Presto’s WACC : % 15 ) 08 . 0 14 . 0 ( 2 0.03 = −  + = − + = ) r (r β r r f M E f E % 3 . 11 28 . 0 ) 4 . 0 1 ( 03 . 0 72 . 0 15 . 0 1 =  −  +  =  − +  = V D ) T ( r V E r r C D E WACC Notice that, as discussed in class, (i) to calculate the cost of equity we use the current government interest rate of 3%; and (ii) to calculate the market risk premium we use a long-term historical average ( i.e. , 14% minus 8%). Third, we calculate Presto’s TV in 2013 : K 516 , 62 $ 02 . 0 113 . 0 ) 02 . 0 1 ( 700 , 5 ) 1 ( 2013 2013 = − +  = − + = K g r g FCF TV WACC Finally, we calculate NPV of the project : M M M M M M 659 . 37 $ 113 . 1 516 . 62 113 . 1 7 . 5 113 . 1 240 . 6 113 . 1 5 . 3 20 NPV 3 3 2 = + + + + − =

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Page 48 of 56 Question 46 One-year European call options are available on Dot.com stock with an exercise price of $100. Dot.com stock is now selling at $90 per share. Assume that on exercise day Dot.com shares sell at one of two possible prices: $80 or $120. If the Treasury bill rate is 4%. a) How much would you pay for one call option on Dot.com stock? b) How many shares along with the risk-free asset do you need to replicate the call option on Dot.com stock? c) How much would you pay for one put option on Dot.com stock? Solution a) S U = 120 S D = 80 S 0 = 90 r f = 4% C U = max {0, (120 – 100)} = 20 C D = max {0, (80 – 100)} = 0 54 . 6 $ ) 80 120 ( ) 04 . 1 ( 120 0 80 20 90 80 120 0 20 ) ( ) 1 ( 0 0 = −   −  −  − − = −  + − −  − − = D U T f U D D U D U D U S S r S C S C S S S C C C b) 5 . 0 80 120 0 20 = − − = − − D U D U S S C C Need half a share along with the risk-free asset per call option. c) Using the put-call parity relation: 69 . 12 $ 04 . 1 100 90 54 . 6 1 0 0 0 = + − = + + − = T f ) r ( K S C P

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Page 49 of 56 Question 47 Dot.com's assets are currently worth $900. In one year, they will be worth either $600 or $1200. The risk-free interest rate is 5%. Suppose Dot.com has an outstanding debt issue with a face value $500. a) What is the value of equity? b) What is the value of debt? Solution a) The stock is a call option on the firm's assets with strike price equal to the debt's face value. Therefore, for the formula to value financial options: C D = 100 ; C U = 700 ; K= 500 S D = 600 ; S U = 1,200 ; S 0 = 900 81 . 423 $ ) 600 1200 ( ) 05 . 0 1 ( 1200 100 600 700 900 600 1200 100 700 ) ( ) 1 ( 0 0 = −  +  −  −  − − = = −  + − −  − − = D U T f U D D U D U D U S S r S C S C S S S C C C b) D = $900 – 423.81= $476.19

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Page 50 of 56 Question 48 A one-year European call option on one share of Dot.com with an exercise price of $50 is currently trading at $10, and a one-year European put option on one share of Dot.com with an exercise price of $50 is currently trading also at $10. Fill the tables below for the profit of the following portfolios as a function of the stock price at maturity. a) Buy one call and one put option (a long straddle). b) Short one call and one put option (a short straddle). Solution a) Buy one call and one put option (a long straddle) S T Profit from buying a call Profit from buying a put Profit from buying a call and a put 0 -10 (= 0-10) 40 (= 50-10) 30 (= -10+40) 20 -10 (= 0-10) 20 (= 30-10) 10 (= -10+20) 30 -10 (= 0-10) 10 (= 20-10) 0 (= -10+10) 40 -10 (= 0-10) 0 (= 10-10) -10 (= -10+0) 50 -10 (= 0-10) -10 (= 0-10) -20 (= -10-10) 60 0 (= 10-10) -10 (= 0-10) -10 (= 0-10) 70 10 (= 20-10) -10 (= 0-10) 0 (= 10-10) 80 20 (= 30-10) -10 (= 0-10) 10 (= 20-10) 100 40 (= 40-10) -10 (= 0-10) 30 (= 40-10)

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Page 51 of 56 Long Straddle: Buy a Call and a Put Buy a put with an exercise price of $50 for $10 $40 A Long Straddle only makes money if the stock price moves $20 away from $50. $40 $0 -$20 $50 Buy a call with an exercise price of $50 for $10 -$10 $30 $60 $30 $70 S T Profits b) Short one call and one put option (a short straddle) S T Profit from short a call Profit from short a put Profit from shorting a call and a put 0 10 (=10-0) -40 (= 10-50) -30 (= 10-40) 20 10 (=10-0) -20 (= 10-30) -10 (= 10-20) 30 10 (=10-0) -10 (= 10-20) 0 (= 10-10) 40 10 (=10-0) 0 (= 10-10) 10 (= 10+0) 50 10 (=10-0) 10 (= 10-0) 20 (= 10+10) 60 0 (= 10-10) 10 (= 10-0) 10 (= 0+10) 70 -10 (= 10-20) 10 (= 10-0) 0 (= -10+10) 80 -20 (= 10-30) 10 (= 10-0) -10 (= -20+10) 100 -40 (= 10-50) 10 (= 10-0) -30 (= -40+10)

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Page 52 of 56 Short Straddle: Short a Call and a Put Short a put with exercise price of $50 for $10 $40 A Short Straddle only loses money if the stock price moves $20 away from $50. -$40 $0 -$30 $50 Short a call with an exercise price of $50 for $10 $10 $20 $60 $30 $70 S T Profits

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Page 53 of 56 Question 49 Draw on a graph the value of the following portfolios ( Portf T ) at maturity as a function of the price of the underlying stock ( S T ). 1) Buy a call option with strike price K C and a put option with strike price K P such that K P > K C . 2) Buy a share of the stock and short a call option with the same strike price K . Solution 1) Buy a call option with strike price K C and a put option with strike price K P > K C . Value Portfolio T Buy a Call Buy a Put K C K P S T K P

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Page 54 of 56 2) Buy a share of the stock and short a call option with strike price K . T Value Buy a share Portfolio T K S T Short a Call

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Page 55 of 56 Question 50 Dot.com has a beta of 1.7 and an expected return of 16.7 percent. Assume that the CAPM is true and that the risk-free rate is 7.6 percent. a) What is the market risk premium? b) Punto.com stock has a beta of 0.8. What is the expected return on Punto.com stock? c) Suppose you have invested $10,000 in both Dot.com and Punto.com, and the beta of the portfolio is 1.07. How much did you invest in each stock? What is the expected return on the portfolio? Solution a) % 353 . 5 ) ) ( ( ) ) ( ( 7 . 1 % 6 . 7 % 7 . 16 = −  − + = f M f M r R E r R E b) % 88 . 11 % 353 . 5 8 . 0 % 6 . 7 ) ( =  + = Punto R E c) 3 . 0 07 . 1 ) 1 ( 8 . 0 7 . 1 =  = −  +  Dot Dot Dot w w w & 7 . 0 = Punto w Hence $3,000 is invested in Dot.com and $7,000 in Punto.com. % 33 . 13 % 353 . 5 07 . 1 % 6 . 7 ) ( =  + = Portfolio R E Question 51 You have run a regression of returns of Nike against the S&P 500 Index using monthly returns over the last 5 years, and arrived at the following regression: 500 & 20 . 1 % 22 . 0 P S Nike R R  + = a) If the T-bill rate today is 6%, and the market risk premium is 5.5%, estimate the expected return for Nike. b) Now assume that you are an investor interested in buying stock in Nike. The current stock is $45 and you expect it to increase to $75 in five years. Assume that the stock does not pay dividends. In this stock a good investment?

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Page 56 of 56 Solution a) % 6 . 12 % 5 . 5 2 . 1 % 6 ) ( =  + = Nike R E b) ( ) 12.6% 10.76% 1 1 45 45 - 75 5  =  + =       + Annual Annual r r . Therefore, buying the stock would not be a good investment. Question 52 Mary has $25,000 in IBM equity, $8,000 in Dell equity and a loan of $13,000 from the bank at the risk-free rate of 5%. If IBM equity has a beta of 2 and Dell equity has a beta of 1.5, calculate the beta of Mary’s portfolio. a. 2.82 b. 3.10 c. 1.85 d. 3.50 e. 1.80 Solution Total Value of Mary’s Portfolio (V) = 25,000 + 8,000 – 13,000 = 20,000 25 . 1 000 , 20 000 , 25 = = IBM w 4 . 0 000 , 20 000 , 8 = = Dell w 65 . 0 000 , 20 000 , 13 − = − = − Free Risk w 10 . 3 0 65 . 0 5 . 1 4 . 0 2 25 . 1 =  −  +  =  +  +  = − − Free Risk Free Risk Dell Dell IBM IBM Portfolio w w w    

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