Question

An investor purchases a 30-year municipal bond for $960. The bond’s coupon rate is 8 percent and, it still had 16 years remaining until maturity. If the investor holds the bond until it matures and collects the $1000 par value from the municipality and his marginal tax rate is 34 percent, what will be his (effective) yield to maturity?

Answer 1

Face Value = $1,000
Current Price = $960

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4%*$1,000
Semiannual Coupon = $40

Time to Maturity = 16 years
Semiannual Period to Maturity = 32

Let semiannual YTM be i%

$960 = $40 * PVIFA(i%, 32) + $1,000 * PVIF(i%, 32)

Using financial calculator:
N = 32
PV = -960
PMT = 40
FV = 1000

I = 4.23%

Semiannual YTM = 4.23%

Effective YTM = (1 + Semiannual YTM)^2 - 1
Effective YTM = (1 + 0.0423)^2 - 1
Effective YTM = 1.0423^2 - 1
Effective YTM = 1.0864 - 1
Effective YTM = 0.0864
Effective YTM = 8.64%