Answer to Question #137922 in Finance for Thabiso

Question

2.5 (6 points) Marie Snell recently inherited some bonds (face value R100 000) from her father, and soon thereafter she became engaged to Sam Spade, a University of Florida marketing graduate. Sam wants Marie to cash in the bonds so the two of them can use the money to "live like royalty" for two years in Monte Carlo. The 2 percent annual coupon bonds mature on January 1, 2024, and it is now January 1, 2004. Interest on these bonds is paid annually on December 31 of each year, and new annual coupon bonds with similar risk and maturity are currently yielding 12 percent. If Marie sells her bonds now and puts the proceeds into an account which pays 10 percent compounded annually, what would be the largest equal annual amounts she could withdraw for two years, beginning today

Answer 1

solution

Proceeds from sale of the bonds

face value $F=100,000$

Coupon $C= 0.02*100,000=2,000$

Time to maturity $t=10 \ years$

Interest$\ r=0.12$

Present value

$$PV= C* \frac{1-(1+r)^{-t}}{r} + \frac{F}{(1+r)^t}$$

$$PV= 2,000* \frac{1-(1+0.12)^{-10}}{0.12} + \frac{100,000}{(1+0.12)^{10}}$$

$$11,300.4461 + 32,197.3237= 43,497.7698$$

She will receive 43,497.7698 from the sale of the bonds.

Investing so that they can withdraw beginning today:

$$PV= C* \frac{1-(1+r)^{-t}}{r} (1+r)$$

$$43,497.7698= C* \frac{1-(1+0.10)^{-2}}{0.10} (1+0.1)$$

$$1.9091*C=43,497.7698$$

$$C=22,784.5461$$

answer: they can make equal withdrawals of $R\ 22,784.5461$