PROBLEM SET 5: INTEREST RATES, AMORTIZING LOANS, BOND VALUATION, STOCK VALUATION 1. A typical credit card agreement quotes an interest rate of 18 percent APR. Monthly payments are required. What is the actual interest rate you pay on such a credit card? 2.
After carefully going over your budget, you have determined you can afford to pay €632 per month toward a new sports car. You call up your local bank and find out that the going rate is 1 percent per month for 48 months. How much you can borrow? 3. You ran a little short on your spring break vacation, so you put €1,000 on your credit card.You can only afford to make the minimum payment of €20 per month. The interest rate on the credit card is 1.
5 percent per month. How long will you need to pay off the €1,000? 4. Suppose you borrow €10,000. You are going to repay the loan by making equal
com/groupon-3059/">annual payments for five years. The interest rate on the loan is 14 percent per year. Prepare an amortization schedule for the loan. How much interest will you pay over the life of the loan? 5. You have recently finished your Master degree and you want to purchase a new BMW immediately. The car costs about €21,000.
The bank quotes an interest rate of 15 percent APR for a 72-month loan with a 10 percent down payment. What will your monthly payment be? What is the effective interest rate on the loan? 6. A bond has a 10 percent coupon rate and a €1,000 face value. Interest is paid semiannually, and the bond has 20 years to maturity. If investors require a 12 percent yield, what is the bond’s value? What is the effective annual yield on the bond? 7.
A bond carries an 8 percent coupon, paid semiannually. The par value is €1,000, and the bond matures in six years.If the bond currently sells for €911. 37, what is its yield to maturity? What is the effective annual yield? 8. Company X is expected to pay dividends of $5. 50 a share in 1 year’s time and $5.
80 a share in 2 years’ time, after which its stock is expected to sell at $91. If the market capitalization rate is 10%, what is the current stock price? 9. IBM’s dividend is expected to be $3 next year. If the shareholders require a return of 15 percent and the current share price is $80 what rate of dividend growth must they be expecting? 10.The current earnings of B&S Video are $2 per share, and it has just paid an annual dividend of 40 cents.
You forecast that the company will continue to plow back 80 percent of its earnings for the next 5 years and that both earnings and dividends will grow at 25 percent a year over that period. From year 6 on, you expect the payout ratio to be increased to 50 percent and that this will reduce the subsequent long-term growth rate to 8 percent. If the capitalization rate for this stock is 15 percent, calculate (a) its price, (b) its price-earnings ratio, (c) the present value of its growth opportunities.
