Question

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

First we have to calculate value of bond today

Coupon = 100,000 * 2% = 2000.

Time to maturity = 20 years

YTM = 12%

Value of bond using financial calculator

=[N = 20 ; I/Y = 12% ; PV = ? ; PMT = 2000 ; FV = 100000]

= R25,305.56

Let x be the equal amount to be withdrawn for 2 years

Present value of 'x' should equal to 23,305.56

Present value = future value / (1+r)^n

25,305.56 = x + (x/(1+10%))

2.1x = 25305.56*(1+10%)

x = 27,836.12/ 2.1

Equal annual amounts (x) = $13,255.30

(In case of any further clarification please comment)

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