Question

1A) Compute the yield to maturity for a zero coupon bond with a maturity of 13 years and a face value of $1000. The bond is selling for $594.06. (Assume annual discounting.) (Round to 100th of a percent and enter as a percentage, e.g. 12.34% as 12.34)

1B) Your business manager forwards the following information to you. Your businesses earned a real rate of return of 4.4% last year and inflation for the same period was 1.6%. What was your nominal rate of return? (Note: nominal rates of return can be positive or negative.) (Use the exact method rather than the approximation method here.) (Round to 100th of a percent and enter as a percentage, e.g. 12.34% as 12.34.)

1C) What is the most we should pay for a bond with a par value of $1000, coupon rate of 7.4% paid semi-annually, and a remaining life of 19 years? The bond is rated BBB, with a yield to maturity of 6.7%. (Round your answer to the nearest penny.)

ANSWER

Answer 1

1A)

Yield to maturity = (Future value / initial value)^1/n - 1

Yield to maturity = (1000 / 594.06)^1/13 - 1

Yield to maturity = (1.683332)^1/13 - 1

Yield to maturity = 1.0409 - 1

Yield to maturity = 0.0409 or 4.09%

1B)

Real rate = [(1 + nominal rate) / (1 + inflation rate)] - 1

0.044 = [(1 + nominal rate) / (1 + 0.016)] - 1

1.044 = [(1 + nominal rate) /1.016]

1.060704 = 1 + nominal rate

Nominal rate = 0.0607 or 6.07%

1C)

Number of periods = 19 * 2 = 38

Semi annual YTM = 6.7% / 2 = 3.35%

Semi annual coupon = (7.4% of 1000) / 2 = 37

Price of bond = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Price of bond = 37 * [1 - 1 / (1 + 0.0335)^38] / 0.0335 + 1000 / (1 + 0.0335)^38

Price of bond = 37 * [1 - 0.285892] / 0.0335 + 285.891816

Price of bond = 37 * 21.316662 + 285.891816

Price of bond = $1,074.61