It is now the beginning of a year. Jared is considering the purchase of a 7.5 pe

Question

It is now the beginning of a year. Jared is considering the purchase of a 7.5 percent (coupon rate), 15-year bond that is presently priced to yield 11 percent (i.e. market interest rate is 11 percent). Based on extensive analysis of market interest rates, he thinks rates will fall so that at the end of this year the market yield of this issue will drop to 9 percent. If his expectations are correct, what kind of realized return will Jared earn by purchasing the bond today and selling the bond at the end of the year? (Assuming annual interest payments)

Question options:

a)

b)

c)

d)

e)

a)

23.95%

b)

25.07%

c)

26.74%

d)

28.05%

e)

18.03%

Explanation / Answer

Beginning of the year:

Face Value of Bond = $1,000
Annual Coupon = 7.50%*$1,000 = $75
Time to Maturity = 15 years
Annual Yield = 11%

Purchase Price = $75 * PVIFA(11%, 15) + $1,000 * PVIF(11%, 15)
Purchase Price = $75 * (1 - (1/1.11)^15) / 0.11 + $1,000 / 1.11^15
Purchase Price = $748.32

End of the year:

Face Value of Bond = $1,000
Annual Coupon = 7.50%*$1,000 = $75
Time to Maturity = 14 years
Annual Yield = 9%

Selling Price = $75 * PVIFA(9%, 14) + $1,000 * PVIF(9%, 14)
Selling Price = $75 * (1 - (1/1.09)^14) / 0.09 + $1,000 / 1.09^14
Selling Price = $883.21

Realized Return = (Selling Price + Coupon - Purchase Price) / Purchase Price
Realized Return = ($883.21 + $75 - $748.32) / $748.32
Realized Return = 28.05%

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