Question

1.) A 9 year, 8% semi annual bond is selling for $1052.32. Calculate the bonds YTM.

2.) Assume that same bond is callable in 4 years with a call premium of $70. Calculate the bonds YTC.

3.) Say you buy the bond for $1052.32, but you plan to hold it for 3 years only. Using the term structure on interest rates, you estimate the YTM on the bond when you sell it to be 6.84%. Calculate what you expect your realized yield will be for the 3 year period.

Answer 1

Answer 1.

Face Value = $1,000
Current Price = $1,052.32
Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4%*$1,000 = $40
Semiannnual Period to Maturity = 18 (9 years)

Let Semainnual YTM be i%

$1,052.32 = $40 * PVIFA(i%, 18) + $1,000 * PVIF(i%, 18)

Using financial calculator:
N = 18
PV = -1052.32
PMT = 40
FV = 1000

I = 3.60%

Semiannual YTM = 3.60%
Annual YTM = 2 * 3.60%
Annual YTM = 7.20%

Answer 2.

Call Price = $1,070
Current Price = $1,052.32
Semiannual Coupon = $40
Semiannnual Period to Call = 8 (4 years)

Let Semainnual YTC be i%

$1,052.32 = $40 * PVIFA(i%, 8) + $1,070 * PVIF(i%, 8)

Using financial calculator:
N = 8
PV = -1052.32
PMT = 40
FV = 1070

I = 3.984%

Semiannual YTC = 3.984%
Annual YTC = 2 * 3.984%
Annual YTC = 7.97%

Answer 3.

Purchase Price = $1,052.32
Semiannual Coupon = $40
Semiannual Holding Period = 6 (3 years)

Selling Price = $40 * PVIFA(3.42%, 12) + $1,000 * PVIF(3.42%, 12)
Selling Price = $40 * (1 - (1/1.0342)^12) / 0.0342 + $1,000 / 1.0342^12
Selling Price = $1,056.31

Let semiannual holding period be i%

$1,052.32 = $40 * PVIFA(i%, 6) + $1,056.31 * PVIF(i%, 6)

Using financial calculator:
N = 6
PV = -1052.32
PMT = 40
FV = 1056.31

I = 3.858%

Semiannual Holding period yield = 3.858%
Annual Holding period yield = 2 * 3.858%
Annual Holding period yield = 7.72%