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Chapter 4: Q17BP (page 283)
The Clearinghouse Sweepstakes has just informed you that you have won \(1 million. The amount is to be paid out at the rate of \)20,000 a year for the next 50 years. With a discount rate of 10 percent, what is the present value of your winnings?
The present value is $198,296.29.
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Look at Table 10-1 again, and now assume interest rates in the market (yield to maturity) increase from 9 to 12 percent.
a. What is the bond price at 9 percent?
b. What is the bond price at 12 percent?
c. What would be your percentage return on the investment if you bought when rates were 9 percent and sold when rates were 12 percent?
Using Table 10-1, assume interest rates in the market (yield to maturity) are 14 percent for 20 years on a bond paying 10 percent.
a. What is the price of the bond?
b. Assume five years have passed and interest rates in the market have gone down to 12 percent. Now, using Table 10-2 for 15 years, what is the price of the bond?
c. What would your percentage return be if you bought the bonds when interest rates in the market were 14 percent for 20 years and sold them 5 years later when interest rates were 12 percent?
Dr. Harold Wolf of Medical Research Corporation (MRC) was thrilled with the response he had received from drug companies for his latest discovery, a unique electronic stimulator that reduces the pain from arthritis. The process had yet to pass rigorousFederal Drug Administration (FDA) testing and was still in the early stages ofdevelopment, but the interest was intense. He received the three offers described in the following paragraph. (A 10 percent interest rate should be used throughout this analysisunless otherwise specified.)
Offer I\(1,000,000 now plus \)200,000 from year 6 through 15. Also if the productdid over \(100 million in cumulative sales by the end of year 15, he wouldreceive an additional \)3,000,000. Dr. Wolf thought there was a 70 percentprobability this would happen.
Offer IIThirty percent of the buyer鈥檚 gross profit on the product for the next fouryears. The buyer in this case was Zbay Pharmaceutical. Zbay鈥檚 gross profitmargin was 60 percent. Sales in year one were projected to be \(2 millionand then expected to grow by 40 percent per year.
Offer IIIA trust fund would be set up for the next eight years. At the end of thatperiod, Dr. Wolf would receive the proceeds (and discount them back tothe present at 10 percent). The trust fund called for semiannual paymentsfor the next eight years of \)200,000 (a total of $400,000 per year).
The payments would start immediately. Since the payments are coming at thebeginning of each period instead of the end, this is an annuity due. Assumethe annual interest rate on this annuity is 10 percent annually (5 percent semiannually).Determine the present value of the trust fund鈥檚 final value. Hint:See the section on Annuities Due.
Required: Find the present value of each of the three offers and indicatewhich one has the highest present value.
Exodus Limousine Company has $1,000 par value bonds outstanding at 10 percent interest. The bonds will mature in 50 years. Compute the current price of the bonds if the percent yield to maturity is
a. 5 percent.
b. 15 percent.
North Pole Cruise Lines issued preferred stock many years ago. It carries a fixed dividend of $6 per share. With the passage of time, yields have soared from the original 6 percent to 14 percent (yield is the same as required rate of return).
a. What was the original issue price?
b. What is the current value of this preferred stock?
c. If the yield on the Standard & Poor鈥檚 Preferred Stock Index declines, how will the price of the preferred stock be affected?
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