Question

Hens has a 7.4% coupon bond on the market with 9 years to maturity. The bond makes semi-annual payments and currently sells for 96% of par (presume $1,000 face/par). What is the current yield? The Yield to Maturity? The Effective Annual Yield? Please show full work.

Answer 1

Face Value = $1,000

Current Price = 96% * Face Value
Current Price = 96% * $1,000
Current Price = $960

Annual Coupon Rate = 7.40%
Semiannual Coupon Rate = 3.70%
Semiannual Coupon = 3.70% * $1,000
Semiannual Coupon = $37

Time to Maturity = 9 years
Semiannual Period = 18

Calculation of Current Yield:

Current Yield = Annual Coupon / Current Price
Current Yield = $74 / $960
Current Yield = 0.0771 or 7.71%

Calculation of Yield to Maturity:

Let Semiannual YTM be i%

$960 = $37 * PVIFA(i%, 18) + $1,000 * PVIF(i%, 18)

Using financial calculator:
N = 18
PV = -960
PMT = 37
FV = 1000

I = 4.016%

Semiannual YTM = 4.016%

Annual YTM = 2 * Semiannual YTM
Annual YTM = 2 * 4.016%
Annual YTM = 8.03%

Calculation of Effective Annual Yield:

Effective Annual Yield = (1 + Semiannual YTM)^2 - 1
Effective Annual Yield = (1 + 0.04016)^2 - 1
Effective Annual Yield = 1.0819 - 1
Effective Annual Yield = 0.0819 or 8.19%