Question

The Pioneer Petroleum Corporation has a bond outstanding with an $60 annual interest payment, a market price of $880, and a maturity date in eight years. Assume the par value of the bond is $1,000.
Find the following:________.
(Use the approximation formula to compute the approximate yield to maturity and use the calculator method to compute the exact yield to maturity. Do not round intermediate calculations. Input your answers as a percent rounded to 2 decimal places.)
A) Coupon rate %
B) Current yield %
C) Approximate yield to maturity %
D) Exact yield to maturity %

Answer 1

Answer:

A) Coupon rate %

coupon rate = coupon / par value = $60 / $1,000 = 0.06 = 6%

B) Current yield %

current yield = coupon / bond's market price = $60 / $880 = 0.06818 = 6.82%

C) Approximate yield to maturity %

Approximate YTM = {coupon + [(face value - market value)/n] / [(face value + market value)/2] = {60 + [(1,000 - 880)/8] / [(1,000 + 880)/2] = 75 / 940 = 0.07978 x 100 = 7.98%

D) Exact yield to maturity = 8.096%

I used a financial calculator to determine the exact YTM, but you can also do it by solving the following equation:

Price = [coupon / (1 + r)] + [coupon / (1 + r)²] + [coupon / (1 + r)³] + [coupon / (1 + r)⁴] + [coupon / (1 + r)⁵] + [coupon / (1 + r)⁶] + [coupon / (1 + r)⁷] + [(coupon + face value) / (1 + r)⁸]

880 = [60 / (1 + r)] + [60 / (1 + r)²] + [60 / (1 + r)³] + [60 / (1 + r)⁴] + [60 / (1 + r)⁵] + [60 / (1 + r)⁶] + [60 / (1 + r)⁷] + [1,060 / (1 + r)⁸]