Sample Final Exam FINA-635
Professor Nisan Langberg
Instructions
You have three hours to complete this exam. Please write your answers clearly in the body of the exam. You may use a simple/financial calculator only. You may bring two A4 sheets to the exam.
Question 1 [5 points]: You wish to borrow $10,000 from your bank for one year. Which alternative shall you choose?
(a) 4.25% APR compound quarterly
(b) 4.25% EAR
Question 2 [5 points]: What is the YTM on a 3 year zero-coupon bond with face value $100,000 and price $83,962?
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 1.24?
Question 4 [15 points]: Fast Track Bikes, Inc., is thinking of developing a new composite road bike. An initial investment of $1,000,000 is required (at time t=0). Profits are expected to be $70,000 this year (at time t=1) and will grow at rate of 3% afterwards forever. Fast Track Bikes has a cost of capital of 12%.
(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)?
Question 5 [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 $45,000 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 4%, 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.
Question 6 [20 points]: NDF, Inc., expects earnings at the end of this year (at time t=1) of $10 per share, and it plans to pay an annual dividend to shareholders of $4 (also at time t=1). NDF has new projects with an expected return on investment of 12% 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 $100.
(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=1 of $2.5 instead of $4). What would its current stock price be under the new payout policy?
Question 7 [25 points]: You have just purchased a home and taken out a $500,000 mortgage. The mortgage has a 30-year term with monthly payments and an APR compounded monthly of 5%.
(a) What is the required monthly payment?
(b) What is the loan outstanding after 5 years (you have just made your 60th payment)?
(c) What would be the loan outstanding after 5 years if during the first 5 years of this mortgage you have voluntarily increased the monthly payment by $100 (above the required payment on the mortgage)?
Good Luck!