Question

In: Finance

what is the yield to call of a bond that has a coupon rate of a...

what is the yield to call of a bond that has a coupon rate of a 10.25% payable semiannually, a yield to maturity of 9.75%. The bond has 12 years to maturity, 3 years to call and the call premium is two year's interest?

Solutions

Expert Solution

Face Value = $1,000

Annual Coupon Rate = 10.25%
Semiannual Coupon Rate = 5.125%
Semiannual Coupon = 5.125% * $1,000
Semiannual Coupon = $51.25

Calculation of Current Price:

Time to Maturity = 12 years
Semiannual Period = 24

Annual YTM = 9.75%
Semiannual YTM = 4.875%

Current Price = $51.25 * PVIFA(4.875%, 24) + $1,000 * PVIF(4.875%, 24)
Current Price = $51.25 * (1 - (1/1.04875)^24) / 0.04875 + $1,000 / 1.04875^24
Current Price = $1,034.92

Calculation of YTC:

Call Premium = 4 * Semiannual Coupon
Call Premium = 4 * $51.25
Call Premium = $205.00

Call Price = Face Value + Call Premium
Call Price = $1,000 + $205
Call Price = $1,205

Time to Call = 3 years
Semiannual Period = 6

Let Semiannual YTC be i%

$1,034.92 = $51.25 * PVIFA(i%, 6) + $1,205 * PVIF(i%, 6)

Using financial calculator:
N = 6
PV = -1034.92
PMT = 51.25
FV = 1205

I = 7.236%

Semiannual YTC = 7.236%
Annual YTC = 2 * 7.236%
Annual YTC = 14.47%


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