Question

Wesimann Co. issued 12-year bonds a year ago at a coupon rate of 7.2 percent. The bonds make semiannual payments and have a par value of $1,000. If the YTM on these bonds is 5.5 percent, what is the current bond price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

$1,138.92

Explanation:

Current bond price can be calculated present value (PV) of cash flows formula below:

Current price or PV of bond = C{[1 - (1 + i)^-n] ÷ i} + {M × (1 + i)^-n} ...... (1)

Where:

Face value = $1,000

r = coupon rate = 7.2% annually = (7.2% ÷ 2) semiannually = 3.6% semiannually

C = Amount of semiannual interest payment = Face value × r

C = $1,000 × 3.6% = $36

n = number of payment periods remaining = (12 - 1) × 2 = 22

i = YTM = 5.5% annually = (5.5% ÷ 2) semiannually = 2.75% semiannually  = 0.0275 semiannually

M = value at maturity = face value = $1,000

Substituting the values into equation (1), we have:

PV of bond = 36{[1 - (1 + 0.0275)^-22] ÷ 0.0275} + {1,000 × (1 + 0.0275)^-22}

PV of bond = $1,138.92.

Therefore, the current bond price is $1,138.92.