Question

The University of California has two bonds outstanding. Both issues have the same credit rating, a face value of $1,000 and a coupon rate of 4%. Coupons are paid twice a year. Bond A matures in 1 year, while bond B matures in 30 years. The market interest rate for similar bonds is 12% (quoted as a semi-annual simple interest rate, so 6% per 6-month period). What is the price of Bond A? What is the price of Bond B? Now assume that yields increase to 15%. What is the price of bond A?

Answer 1

Face Value = $1,000

Annual Coupon Rate = 4.00%
Semiannual Coupon Rate = 2.00%
Semiannual Coupon = 2.00% * $1,000
Semiannual Coupon = $20

Answer a.

Time to Maturity = 1 year
Semiannual Period = 2

Annual YTM = 12.00%
Semiannual YTM = 6.00%

Current Price = $20 * PVIFA(6.00%, 2) + $1,000 * PVIF(6.00%, 2)
Current Price = $20 * (1 - (1/1.06)^2) / 0.06 + $1,000 * (1/1.06)^2
Current Price = $20 * 1.83339 + $1,000 * 0.89000
Current Price = $926.67

Answer b.

Time to Maturity = 30 years
Semiannual Period = 60

Annual YTM = 12.00%
Semiannual YTM = 6.00%

Current Price = $20 * PVIFA(6.00%, 60) + $1,000 * PVIF(6.00%, 60)
Current Price = $20 * (1 - (1/1.06)^60) / 0.06 + $1,000 * (1/1.06)^60
Current Price = $20 * 16.16143 + $1,000 * 0.03031
Current Price = $353.54

Answer c.

Time to Maturity = 1 year
Semiannual Period = 2

Annual YTM = 15.00%
Semiannual YTM = 7.50%

Current Price = $20 * PVIFA(7.50%, 2) + $1,000 * PVIF(7.50%, 2)
Current Price = $20 * (1 - (1/1.075)^2) / 0.075 + $1,000 * (1/1.075)^2
Current Price = $20 * 1.79557 + $1,000 * 0.86533
Current Price = $901.24