Question

1A) Mickey and Minnie just bought a zero coupon bond for $403.26, but they cannot recall when it matures. The yield to maturity equals 7.2%. Can you help Mickey and Minnie? The bond's face value is $1000. (Assume annual discounting) (Enter your answer in years and round to 2 decimal places.)

1B) Compute the current yield on a bond with a yield to maturity of 11.2%, a par value of $1000, a coupon rate of 5.9% paid semi-annually, a remaining life of 29 years? (Round to 100th of a percent and enter as a percentage, e.g. 12.34% as 12.34 and state as an annual rate.)

ANSWER

Answer 1

1A]

bond price = face value / (1 + YTM)ⁿ

where n = years to maturity

$403.26 = $1,000 / (1 + 7.2%)ⁿ

1.072ⁿ = ($1,000 / $403.26)

n = log_1.072($1,000 / $403.26)

n = 13.06

The bond will mature in 13.06 years

1B]

current yield = annual coupon payment / bond price

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 11.2%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 29 * 2 (29 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 5.9% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $546.86

current yield = annual coupon payment / bond price

current yield = ($1,000 * 5.9%) / $546.86

current yield = 10.79%