Question

Your broker calls with an offer on a corporate bond that he feels is perfect for your portfolio. The bond has 7 years remaining to maturity, semi-annual payments, and a coupon rate of 5.5%. Given today’s yield curve, you estimate that the yield on a comparable Treasury security is 2.2%. What are the present values of the annuity stream, principal repayment, and the maximum value you’d be willing to pay for the bond?

A) $368.60, $857.99 and $1,226.59

B) $368.60, $737.37 and $1,105.59

C) $355.02, $857.99 and $1,213.01

D) $355.02, $737.37 and $1,092.39

Answer 1

1)

Coupon = (0.055 * 1000) / 2 = 27.5

Number of periods = 7 * 2 = 14

Rate = 2.2% / 2 = 1.1%

Present value of annuity stream = Coupon * [1 - 1 / (1 + r)ⁿ] / r

Present value of annuity stream = 27.5 * [1 - 1 / (1 + 0.011)¹⁴] / 0.011

Present value of annuity stream = 27.5 * [1 - 0.85799] / 0.011

Present value of annuity stream = 27.5 * 12.90971

Present value of annuity stream = $355.02

2)

Present value of principal payment = FV / (1 + r)ⁿ

Present value of principal payment = 1000 / (1 + 0.011)¹⁴

Present value of principal payment = 1000 / 1.16551

Present value of principal payment = $857.99

3)

Value = $355.02 + $857.99

Value = $1,213.01