Lowell Inc. has bonds which mature in 10 years, and have a face value of $1,000. The bonds have a 10 percent quarterly coupon (i. e., the nominal coupon rate is 10 percent). The bonds may be called in five years. The bonds have a nominal yield to maturity of 8 percent and a yield to call of 7.5 percent. What is the call price on the bonds? a. $1,048.34b. $ 379.27c. $1,025.00d. $1,136.78e. $1,036.77

a. $1,048.34

Explanation:

approximate YTC = {coupon + [(call price - current market price)/n]} / [(call price + current market price)/2]

we must first determine the current market price using YTM:

PV of face value = $1,000 / 1.02⁴⁰ = $452.89

PV of coupon payments = $25 x 27.355 (PV annuity factor, 2%, 40 periods) = $683.88

market price = $1,136.77

I will now try options a, c and e to check which one results in a YTC of 7.5%

option a) YTC = {25 [(1,048.34 - 1,136.77)/20]} / [(1,048.34 + 1,136.77)/2] = 20.5785 / 1,092.555 = 0.018835207 x 4 (quarterly payments) = 7.5% ✓

option c) YTC = {25 [(1,025 - 1,136.77)/20]} / [(1,025 + 1,136.77)/2] = 19.4115 / 1,080.885 = 0.017958894 x 4 (quarterly payments) = 7.184% X

option e) YTC = {25 [(1,036.77 - 1,136.77)/20]} / [(1,036.77 + 1,136.77)/2] = 20 / 1,086.77 = 0.018403157 x 4 (quarterly payments) = 7.3613% X

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