1. The car you like costs $35,000. You are trying to decide whether you should lease or buy the vehicle.
If you lease the car from the dealer, you must pay $1,700 today, and $400 per month for the next 3 years. At the end of the 3-year lease (3 years from today), you will return the vehicle to the dealer.
If you buy the car, you will obtain a three-year, $35,000 loan @ 6% per year, compounded monthly. The loan will be repaid over the next 36 months (36 monthly payments, beginning one month from today). Three years from today, you will be able to sell the car for $22,000 (resale price).
a) What is the monthly payment on the car loan?
b) Should you buy, or lease the car? Why? Be sure to provide quantitative justification for you answer.
c) What resale price three years from today would make you indifferent between buying and leasing?
2. Storageco just paid (earlier today) a dividend of $4.00 per share. The company will increase its dividend by 20 percent next year (so, at t = 1, the dividend will be $4.80). Thereafter, each year they will reduce the dividend growth rate by 5 percentage points (15%, 10%…) until it reaches the industry average of 5 percent dividend growth. The company will then keep this constant (5%) growth rate, forever. The required return for the stock is 13%.
a) At what price should Storageco stock sell today (now)?
b) At what price should Storageco stock sell two years from today (t=2) – the instant before the t=2 dividend?
3. The Hawk Corp. has a 6 percent coupon bond outstanding. The Dove Corp. has a 14 percent coupon bond outstanding. Both bonds make semi-annual coupon payments, and mature in 10 years. The par value of the Hawk Corp. bond is $1,000. The par value of the Dove Corp. bond is $500.
a) Calculate the price of each bond assuming they are priced to provide a yield to maturity (ytm) of 10 percent.
b) Interest rates suddenly change and the ytm of each bond rises by 4 percent. Calculate the new price of each bond.
c) What does this problem tell you about the interest rate risk of lower coupon bonds (provide quantitative justification for your answer)?
4. An investment pays $1,000 every 3rd year, forever, beginning one year from today (so the cash flows occur at t = 1, 4, 7,……).
a) What is the value (today) of this investment if the appropriate discount rate is 8% per year (compounded annually)?
b) What is the value (today) of this investment if the appropriate discount rate is 8% per year (compounded semi-annually)?
c) What is the value (today) of this investment if the appropriate discount rate is 8% per year (compounded quarterly)?