Question

a) (5 points) Calculate the price of a $1000 face value five year coupon bond when the yield to maturity is 5%, and the coupon rate is 6%.

b) (5 points) Now suppose that the yield to maturity rises to 7%. Calculate the new price of this coupon bond.

c) (5 points) Suppose you purchased the bond at it original price (yield to maturity = 5%) held it for one year (collected one coupon payment) and sold it at the new price (part b). What is your rate of return?

Answer 1

Face value,M = $ 1,000

Coupon rate = 6%

YTM = 5%

P = 60(P/A, 5%,5) +1,000(P/F,5%,5)

=> P= 60 x- 1 - 1.05-5 0.05 - +1,000 x 1.05-5

Solving the above equation we get

Price = $ 1,043.30 (Approximately).

B. When YTM = 7%

P = 60(P/A, 7%,5) +1,000(P/F, 7%,5)

=> 1 - 1.07-5 P= 60 X – 0.07 - +1,000 x 1.07-5

Price = $ 958.99 (Approximately).

C. Price = $ 1,043.30

Received a coupon of $ 60.

Sold it for a price of $ 958.99

60 +958.99 – 1043.30 Rateofreturn = 1043.30

Rate of return = -24.31/1043.30 = - 0.0233

Rate of return = - 2.33 %

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