A firm's bonds have a maturity of 12 years with a $1,000 face value, have an 8% semiannual coupon, are callable in 6 years at $1,055.84, and currently sell at a price of $1,106.22. What are their nominal yield to maturity and their nominal yield to call

Annual YTM = 6.67%

Annual YTC = 6.60%

Explanation:

Nominal yield to maturity

Face Value = $1,000

Current Price = $1,106.22

Semiannual Coupon Rate = 8.00%/2 =  4.00%

Semiannual Coupon = 4.00% * $1,000 = $40

Semiannual Period to Maturity = 12*2 = 24

Let Semiannual YTM be i%

$1,106.22 = $40 * PVIFA(i%, 24) + $1,000 * PVIF(i%, 24)

Using MS Excel

N = 24 , PV = -1,106.22 , PMT = 40 , FV = 1000

Semiannual YTM = Rate(24, -1106.22, 40, 1000)

Semiannual YTM = 0.033489859

Semiannual YTM = 3.335%

Annual YTM = 3.335% * 2

Annual YTM = 6.67%

Nominal yield to call

Call Value = $1,055.84

Current Price = $1,106.22

Semiannual Coupon = $40

Time to Call = 6 years

Semiannual Period to Call = 12

Let Semiannual YTC be i%

$1,106.22 = $40 * PVIFA(i%, 12) + $1,055.84* PVIF(i%, 12)

N = 12 , PV = -1,106.22, PMT = 40 , FV = 1,055.84

Using MS Excel

Semiannual YTC = Rate(12, -1106.22, 40, 1,055.84)

Semiannual YTC = 0.033004545

Semiannual YTC = 3.30%

Annual YTC = 3.30% * 2

Annual YTC = 6.60%

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