FINA 6A35 - Solutions for Sample Final Exam

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1 FINA 6A35 - Solutions for Sample Final Exam September 26, 207 Question [5 points]: Consider a project that requires a current investment of $,000,000 at time t=0 and yields annual cash flows of $250,000 at the end of each year for the next ten years, i.e., at time t=,2,30. What statement is appropriate for this project? (a) It meets the 5year payback rule. (b) It does not meet the 5year payback rule. The annual cash flows of $250,000 add up to $,000,000 by the end of year, which is less than 5 years. Hence the project meets the 5-year payback rule (Option (a)). Question 2 [5 points]: Identify each of the following risks as either systematic risk or diversifiable risk: (a) The risk that the CEO of your firm is killed in a plane accident. (b) The risk that the economy slows, decreasing demand for your firm s products. (c) The risk that your best employees will be hired away. (d) The risk that the new product you expect your R&D division to produce will not materialize. (a) Diversifiable (b) Systematic (c) Diversifiable (d) Diversifiable Question 3 [5 points]: Suppose the market risk premium is 6% and the risk-free interest rate is 2.7%. What is the expected annual return of investing in Microsoft s stock according to the CAPM if its beta is.2? CAPM Equation: r a = r f + β a (r m r f ) for security a

2 r m r f = 6% r f = 2.7% β a =.2 Return on Microsoft s stock: r Microsoft = (6) = 0.% Question [5 points]: Fast Track Bikes, Inc., is thinking of developing a new composite road bike. An initial investment of $,000,000 is required (at time t=0). Profits are expected to be $70,000 this year (at time t=) and will grow at rate of 3% afterwards forever. Fast Track Bikes has a cost of capital of 2%. (a) What is the IRR of this investment? (b) Is it a good idea for Fast Track Bikes to invest in this project (what is the NPV of the project)? Part (a): IRR? Part (b): NPV? 70, 000, 000, 000 = IRR , , 000 IRR =, 000, 000 IRR = 0% 70, 000 P V profit = 2% 3% = 777, <, 000, 000 = P V cost NP V < 0. Do not invest. 2

3 Question 5 [20 points]: Your firm needs to decide how many new coffee shops to open in a small town and whether they should be all inclusive or coffee only: the difference is that an all inclusive coffee shop sells sandwiches as well as coffee and pastries while the coffee only shop sells only coffee and pastries but no sandwiches. The appropriate cost of capital for your firm is 0%. Coffee Only shop: Costs $300,000 to build, requires 2 trained workers, and generates annual cash flows of $6,000 at the end of each year for 5 years. All-inclusive shop: Costs $50,000 to build, requires trained workers, and generates annual cash flows of $69,000 at the end of each year for 5 years. (a) What is the NPV of opening one coffee only shop? (b) What is the NPV of opening one all inclusive shop? (c) How many shops and of what kind would you build if you hand only 8 trained workers? Part (a): Coffee only shop: Part (b): All inclusive shop: Part (c): How many shops? NP V = P V (Benefits) P V (Costs) 6, 000 ( NP V = ) 300, (.) 5 NP V = $39, , 000 NP V = 9, NP V = P V (Benefits) P V (Costs) 69, 000 ( NP V = ) 50, (.) 5 NP V = $528, , 000 NP V = 7, 89.9 (A): Coffee only shop requires 2 workers each. P I A = NP V A #W orkers = 9, = $2, (B): All inclusive shop requires workers each. P I B = NP V B #W orkers = 7, 89.9 = $8,

4 P I A > P I B = Open shops of Coffee only type. Question 6 [25 points]: You are saving for retirement. To live comfortably, you decide you will need to save $2 million by the time you are 65. Today is your 30th birthday and you have accumulated $5,000 in savings so far. You decide that starting at the end of this year and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is %, how much must you set aside each year to make sure that you will have a total of $2 million in your savings account on your 65th birthday. We know that the present value of all future payments plus the $5,000 already saved must be equal to the present value of the final savings of $2,000,000: 2, 000, 000 = C ( ) + 5, 000 ( + r) n r ( + r) n 2, 000, 000 = C ( ) + 5, 000 (.0) (.0) , , 000 = 8.66C C = $2, Question 7 [20 points]: NDF, Inc., expects earnings at the end of this year (at time t=) of $0 per share, and it plans to pay an annual dividend to shareholders of $ (also at time t=). NDF has new projects with an expected return on investment of 2% per year. Suppose that NDF will maintain the same dividend payout rate, retention rate, and return on new investments in the future and will not change its number of outstanding shares. NDF s current (at time t=0) stock price is $00. (a) Based on the market price of NDF s stock, what is the NDF s equity cost of capital? (b) Suppose that NDF instead used a payout rate of 25% forever (will pay a dividend at time t= of $2.50 instead of $). What would its current stock price be under the new payout policy?

5 Part (a) EPS = 0 Div = ROI = 2% P = 00 Retention Rate = 60% g = 60%*2% = 7.2% 00 = Div r E g 00 = r E r E = r E =.2% Part(b) Div = 0.25(0) = $2.50 Retention Rate = 75% g = 75%*2% = 9% New price = Div r E g New price = New price = New price = $3.6 5

Midterm Exam Suggested Solutions

JEM034 Corporate Finance Winter Semester 2017/2018 Instructor: Olga Bychkova Date: 7/11/2017 Midterm Exam Suggested Solutions Problem 1. 4 points) Which of the following statements about the relationship