Question

Crane Corp. has five-year semi-annual bonds outstanding that pay a coupon rate of 8.1 percent, these bonds are priced at $1,065.26. (Round answers to 2 decimal places, e.g. 15.25%.)

What is the yield to maturity on these bonds? Assume semiannual coupon payments. What is the effective annual yield?

Answer 1

Answer:
Face Value = $1,000
Current Price = $1,065.26

Annual Coupon Rate = 8.1%
Semiannual Coupon Rate = 4.05%
Semiannual Coupon = 4.05% * $1,000
Semiannual Coupon = $40.50

Time to Maturity = 5 years
Semiannual Period to Maturity = 10

Let Semiannual YTM be i%

$1,065.26 = $40.50 * PVIFA(i%, 10) + $1,000 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -1065.26
PMT = 40.50
FV = 1000

I = 3.27%

Semiannual YTM = 3.27%
Annual YTM = 2 * 3.27%
Annual YTM = 6.54%

Effective Annual Yield = (1 + Semiannual YTM)^2 – 1
Effective Annual Yield = (1 + 0.0327)^2- 1
Effective Annual Yield = 0.0665 or 6.65%