Question

An 8% semiannual coupon bond matures in 5 years. The bond has a face value of $1,000 and a current yield of 8.3765%.

What is the bond's price? Do not round intermediate calculations. Round your answer to the nearest cent.
$

What is the bond's YTM? (Hint: Refer to Footnote 7 for the definition of the current yield and to Table 7.1.) Do not round intermediate calculations. Round your answers to two decimal places.
   %

Answer 1

• yearly coupon rate = 8%;
• Semi-annual coupon rate = 8%/2 = 4%
• semi-annual coupon amount = (4% * 1000) = $40
• Years to maturity = 5; Number of compounding periods = 5* 2 = 10
• Face value = $1000

a) Bond Price:

• Current yield = Coupon amount / Bond price
• 8.3765% = $80 / Bond price
• Bond price = $80/ 0.083765 = $955.05

b) YTM

YTM is the average yield to maturity at which present value of coupons and present value of face amount at maturity will be equal to the current bond's price.

$955.05 = $40/(1+y)^1 + $40/(1+y)^2 + ....+ $40/(1+y)^10

Solving for y, we get y = 4.57% (semi-annual yield)

Annual YTM = 4.57% * 2 = 9.14% (answer)