1. [2] Investment X offers to pay you $4,200 per year for eight years, whereas Investment Y offers to pay you $6,100 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 5 percent? If the discount rate is 15 percent?
2. [3] The Brasher doubloon, which was featured in the plot of the Raymond Chandler novel, The High Window, was sold at auction in 2014 for $4,582,500. The coin had a face value of $15 when it was first issued in 1787 and had been previously sold for $430,000 in 1979. At what annual rate did the coin appreciate from its minting to the 1979 sale? What annual rate did the 1979 buyer earn on his purchase? At what annual rate did the coin appreciate from its minting to the 2014 sale?
3. [2] You are trying to save to buy a new $500,000 Ferrari. You have $50,000 today that can be invested at your bank. The bank pays 4.5% annual interest on its accounts. How long will it be before you have enough to buy the car?
4. [2] You are still committed to owning a $500,000 Ferrari. If you believe you mutual fund can achieve an annual rate of return of 15% and you now want to buy the car in 10 years (on the day you turn 30), how much must you invest today?
5. [4] The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $30,000 per year forever. If the required return on this investment is 7%, how much will you pay for the policy? Suppose instead a sales associate told you the policy costs $754,000. At what interest rate would this be a fair deal?
6. [2] You have just won the lottery and will receive $1,500,000 in one year. You will receive payments for 30 years, and the payments will increase by 1.5% per year. If the appropriate discount rate is 3.2%, what is the present value of your winnings?
7. [4] You took a $350,000 mortgage from Truist. You term is 30 years with monthly payments, and your payment is $1,600 per month. What must be your annual quoted rate (APR)? After paying the loan for 5 years, youre allowed to pay a Balloon Payment, i.e., a single amount to pay off the entirety of the loan. What is this amount? (Hint: i.e., what is the PV of this mortgage after 5 years?)
8. [6] Both Bond Sam and Bond Dave have 7.3 percent coupons, make semiannual payments, and are priced at par value (which is $1,000). Bond Sam has 3 years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2%, what is the percentage change in the price of Bond Sam? Of Bond Dave? If rates were to suddenly fall by 2% instead, what would the percentage change in the price of Bond Sam be then? Of Bond Dave? Illustrate your answers by graphing bond prices versus YTM. What does this problem tell you about the interest rate risk of long-term bonds?