Question

Three years ago, you bought a 12% bond that had 7 years to maturity and a yield to maturity of 12%. Today (after the sixth interest payment), you sold the bond when it is yielding 13%. What is your annual rate of return for the three year period? All coupon payments are semi-annual, and the par value is $1,000.

Answer 1

Par Value = $1,000

Annual Coupon Rate = 12%
Semiannual Coupon Rate = 6%
Semiannual Coupon = 6% * $1,000
Semiannual Coupon = $60

At the time of purchase:

Time to Maturity = 7 years
Semiannual Period = 14

Annual YTM = 12%
Semiannual YTM = 6%

Price of Bond = $60 * PVIFA(6%, 14) + $1,000 * PVIF(6%, 14)
Price of Bond = $60 * (1 - (1/1.06)^14) / 0.06 + $1,000 / 1.06^14
Price of Bond = $1,000.00

At the time of sale:

Time to Maturity = 4 years
Semiannual Period = 8

Annual YTM = 13%
Semiannual YTM = 6.50%

Price of Bond = $60 * PVIFA(6.5%, 14) + $1,000 * PVIF(6.5%, 14)
Price of Bond = $60 * (1 - (1/1.065)^14) / 0.065 + $1,000 / 1.065^14
Price of Bond = $954.93

Calculation of holding period yield:

Purchase Price = $1,000.00
Selling Price = $954.93
Semiannual Coupon = $60
Semiannual Period = 6

Let Semiannual HPY be i%

$1,000.00 = $60 * PVIFA(i%, 6) + $954.93 * PVIF(i%, 6)

Using financial calculator:
N = 6
PV = -1000
PMT = 60
FV = 954.93

I = 5.343%

Semiannual HPY = 5.343%
Annual HPY = 2 * 5.343%
Annual HPY = 10.69%