Question

A HCA bond, maturing in 7 years, pays 8 percent interest on a $1,000 face value. However interest is paid semi-annually. If your required rate of return is 10 percent, what is the value of the bond? What is the value if the interest were paid annually?

Answer 1

When the interest is paid semi annually:

Coupon payment = 0.08 * 1000 = 80 / 2 = 40

Number of periods = 7 * 2 = 14

Interest rate = 0.10 / 2 = 0.05 or 5%

Value of bond = Coupon payment * [ 1 - 1 / ( 1 + R)ⁿ] / R + Face value / ( 1 + R)ⁿ

Value of bond = 40 * [ 1 - 1 / ( 1 + 0.05)¹⁴] / 0.05 + 1000 / ( 1 + 0.05)¹⁴

Value of bond = 40 * 9.898641 + 505.06795

Value of bond = $901.01

You can also find this using a finanical calculator: 2nd I/Y 2, FV 1000, PMT 40, N 14, I/Y 10, CPT PV

When interest is paid annually:

Number of periods = 7

rate = 10%

Coupon payment = 80

Value of bond = 80 * [ 1 - 1 / ( 1 + 0.1)⁷] / 0.1 + 1000 / ( 1 + 0.1)⁷

Value of bond = 80 * 4.868419 + 513.158118

Value of bond = $902.63

You can also find this using a finanical calculator: 2nd I/Y 1, FV 1000, PMT 80, N 7, I/Y 10, CPT PV