Question

A 25-year maturity bond with par value $1,000 makes semiannual coupon payments at a coupon rate of 8%.

a. Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is $950. (Round your intermediate calculations to 4 decimal places. Round your answers to 2 decimal places.)

Bond equivalent yield to maturity	%
Effective annual yield to maturity	%

Answer 1

Par Value = $1,000
Current Price = $950

Annual Coupon Rate = 8.00%
Semiannual Coupon Rate = 4.00%
Semiannual Coupon = 4.00% * $1,000
Semiannual Coupon = $40

Time to Maturity = 25 years
Semiannual Period = 50

Let Semiannual YTM be i%

$950 = $40 * PVIFA(i%, 50) + $1,000 * PVIF(i%, 50)

Using financial calculator:
N = 50
PV = -950
PMT = 40
FV = 1000

I = 4.24%

Semiannual YTM = 4.24%

Equivalent YTM = 2 * Semiannual YTM
Equivalent YTM = 2 * 4.24%
Equivalent YTM = 8.48%

Effective YTM = (1 + Semiannual YTM)^2 - 1
Effective YTM = (1 + 0.0424)^2 - 1
Effective YTM = 1.0866 - 1
Effective YTM = 0.0866 or 8.66%