Question

Yield To Maturity. A firm’s bonds have a maturity of 10 years with a $1,000 face value, have an 8% semiannual coupon, are callable in 5 years at $1,050, and currently sell at a price of $1,100. What are their nominal yield to maturity and their nominal yield to call? Show detailed calculations

Answer 1

Answer a.

Face Value = $1,000
Current Price = $1,100

Annual Coupon Rate = 8.00%
Semiannual Coupon Rate = 4.00%
Semiannual Coupon = 4.00% * $1,000
Semiannual Coupon = $40

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Let Semiannual YTM be i%

$1,100 = $40 * PVIFA(i%, 20) + $1,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -1100
PMT = 40
FV = 1000

I = 3.309%

Semiannual YTM = 3.309%
Annual YTM = 2 * 3.309%
Annual YTM = 6.62%

Answer b.

Call Value = $1,050
Current Price = $1,100
Semiannual Coupon = $40

Time to Call = 5 years
Semiannual Period to Call = 10

Let Semiannual YTC be i%

$1,100 = $40 * PVIFA(i%, 10) + $1,050 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -1100
PMT = 40
FV = 1050

I = 3.244%

Semiannual YTC = 3.244%
Annual YTC = 2 * 3.244%
Annual YTC = 6.49%