Chapter 6: Measuring and Calculating Interest Rates and Financial Asset Prices Problems and Issues 1. Suppose a 10-year bond is issued with an annual coupon rate of 8 percent when the market rate of interest is also 8 percent. If the market rate rises to 9 percent, what happens to the price of this bond? What happens to the bond’s price if the market rate falls to 6 percent? Explain why. 2. Preferred stock for XYZ Corporation is issued at par $50 per share. If stockholders are promised a $4 annual dividend, what was the stock’s dividend yield at time of issue? If the stock’s market price has risen to $60 per share, what is its dividend yield? 3. You plan to borrow $2,000 to take a vacation and want to repay the loan in a year. The banker offers you a simple interest rate of 12 percent with repayments in two equal installments, 6 months and 12 months from now. What is your total interest bill? What is the APR? Would you prefer an add-on interest rate with one payment at the end of the year? If the bank applied the discount method to your loan, what are the net proceeds of the loan? What is your effective rate of interest rate? 4. An investor is interested in purchasing a new 20-year government bond carrying a 5 percent annual coupon rate with interest paid twice a year. The bond’s current market price is $875 for a $1,000 par value instrument. If the investor buys the bond at the going price and holds it to maturity, what will be his or her yield to maturity? Suppose the investor sells the bond at the end of 10 years for $950. What is the investor’s holding-period yield? 5. Calculate the bank discount rate of return (DR) and the YTM-equivalent return for the following money market instruments: a. Purchase price, $96; par value, $100; maturity, 90 days. b. Purchase price, $96; par value, $100; maturity, 180 days. c. Purchase price, $97.50; par value, $100; maturity, 270 days. d. Purchase price, $975; par value, $1,000; maturity, 270 days. 6. You have just placed $1,500 in a bank savings deposit and plan to hold that deposit for eight years, earning 2 percent per annum. If the bank compounds interest daily, what will be the total value of the deposit in eight years? How does your answer change if the bank switches to monthly compounding? Quarterly compounding? 7. You decide to take out a 30-year mortgage loan to buy the home of your dreams. The home’s purchase price is $120,000. You manage to scrape together a $20,000 down payment and plan to borrow the balance of the purchase price. Hardy Savings and Loan Association quotes you a fixed annual loan rate of 6 percent. What will your monthly payment be? How much total interest will you have paid at the end of 30 years? What would your monthly payment be if you could increase your down payment to $50,000? 8. A depositor places $5,000 in a credit union deposit account for a full year but then withdraws $1,000 after 270 days. At the end of the year, the credit union pays her $150 in interest. What is this depositor’s daily average balance and APY? 9. A commercial loan extended to CIBER-LAND Corporation for $2.5 million assesses an interest charge of $250,000 up front. Using the discount loan method of calculating loan rates, what is the effective interest rate on this loan? Suppose that instead of deducting the interest owed up front, the company’s lender agrees to extend the full $2.5 million and add the amount of interest owed to the face of CIBER’s note. What, then, is the loan’s effective interest rate?10. Bill Evans won a cash prize of $100,000 in a charity fund-raising event. He decided to invest the money for the next 5 years to help pay for his son’s college education. His financial adviser gave him two options for investing. Option A is invest all of money in stock mutual fund tied to the S&P 500. Option B is to buy a speculative stock, Advent-2 that has paid no dividends with 50 percent of Bill’s winnings and a 10-year T-note--a zero-coupon security--with the remainder. The adviser gave Bill three potential scenarios that could affect the value of these two investment portfolios. a. Scenario 1: The S&P 500 will appreciate 10 percent in each of the first two years, and then grow at a 3 percent rate in the last three years, during which time the price of Avent-2 is expected to double in the first year and remain flat in the last four years, while the yield on the T-note falls from its current 4 percent to 2 percent. b. Scenario 2: The S&P 500 will appreciate 10 percent in each of the upcoming five years, Advent-2 will increase by 20 percent each year, and the yield on the T-note will remain unchanged at 4 percent. c. Scenario 3: The S&P 500 will appreciate 3 percent in the first two years and 5 percent in subsequent three years, while the price of Advent-2 will fall by 10 percent in of each the first two years and then remain flat thereafter, as the yield on the T-note rises from 4 to 7 percent. Use a spreadsheet to compute the future value after five years of the $100,000 investment under Option A and Option B for each of the three scenarios. Can you say whether Option A or Option B is better investment