Question

You are a bond trader. You are considering buying a bond with a coupon rate of 8.4% that matures in 17 years and has semiannual payments. The bond price is now trading for $829.52. Par value is $1,000. The bond can be called in 7 years for $1,084. What is the yield to maturity (YTM)? What is the yield to call (YTC)? Please answer in annual yield in percentage with two decimal places.

Answer 1

Answer a.

Face Value = $1,000
Current Price = $829.52

Annual Coupon Rate = 8.40%
Semiannual Coupon Rate = 4.20%
Semiannual Coupon = 4.20% * $1,000
Semiannual Coupon = $42.00

Time to Maturity = 17 years
Semiannual Period to Maturity = 34

Let Semiannual YTM be i%

$829.52 = $42 * PVIFA(i%, 34) + $1,000 * PVIF(i%, 34)

Using financial calculator:
N = 34
PV = -829.52
PMT = 42
FV = 1000

I = 5.291%

Semiannual YTM = 5.291%

Annual YTM = (1 + Semiannual YTM)^2 - 1
Annual YTM = (1 + 0.05291)^2 - 1
Annual YTM = 1.1086 - 1
Annual YTM = 0.1086 or 10.86%

Answer b.

Call Value = $1,084
Current Price = $829.52
Semiannual Coupon = $42.00

Time to Call = 7 years
Semiannual Period to Call = 14

Let Semiannual YTC be i%

$829.52 = $42 * PVIFA(i%, 14) + $1,084 * PVIF(i%, 14)

Using financial calculator:
N = 14
PV = -829.52
PMT = 42
FV = 1084

I = 6.475%

Semiannual YTC = 6.475%

Annual YTC = (1 + Semiannual YTC)^2 - 1
Annual YTC = (1 + 0.06475)^2 - 1
Annual YTC = 1.1337 - 1
Annual YTC = 0.1337 or 13.37%