Question

The Guilford Corporation has a bond outstanding with a face value of $1,000 that reaches maturity in ten years. The bond certificate indicates that the stated coupon rate for this bond is 8.0% and that the coupon payments are made semiannually. Assuming the appropriate yield to maturity (YTM) on the Guilford bond is currently 11.1%, then the current price of this bond is closest to

a.

$979

b.

$652

c.

$1,142

d.

$816

e.

$438

Answer 1

Price of a bond is mathematically represented as: 1 1-- (1 + i)" PEC. - +- м. (1 + i)" where P is price of bond, with periodic coupon C, n periods to maturity, periodic YTM i and face value M.

For this question,

M = $1000, n = 10 * 2 = 20 semi-annual periods, C = 8% * $1000/2 = $40 semi-annually, i = 11.1%/2 = 5.55% (semi-annually)

$P = 40 * \frac{1-\frac{1}{(1 + 0.0555)^{20}}}{0.0555} + \frac{1000}{(1 + 0.0555)^{20}}$

P = 476.04 + 339.50

P = $815.54

P = $816