Question

Rich McDonald, CFA, is evaluating his investment alternatives in Ytel Incorporated by analyzing a Ytel convertible bond and Ytel common equity. Characteristics of the two securities are given in the following exhibit:

a. Calculate, based on the exhibit, the

i. Current market conversion price for the Ytel convertible bond.

ii. Expected one-year rate of return for the Ytel convertible bond.

iii. Expected one-year rate of return for the Ytel common equity.

One year has passed and Ytel’s common equity price has increased to $51 per share. Also, over the year, the yield to maturity on Ytel’s nonconvertible bonds of the same maturity increased, while credit spreads remained unchanged.

b. Name the two components of the convertible bond’s value. Indicate whether the value of each component should decrease, stay the same, or increase in response to the:

i. Increase in Ytel’s common equity price.

ii. Increase in bond yield.

Short answer

Answer

a. (i) $39.20 (ii) 18.88% (iii) 28.57%

b. (i) Increase in option value, no change in bond value

(ii) decline in bond value

Step-by-step solution

Calculation of current market conversion price ‘a (i)’

Market Conversion price = market price of convertible bond / conversion ratio

= $980 x 25 (given)

= $39.20

Calculation of expected one year return of bond ‘a (ii)’

Coupon = Par Value x Coupon Rate

=$1,000 x 4%

=$40

Expected return = [(End of year price + coupon) / current price ] – 1

= [($1,125 + $40) / 980] – 1 (given)

= 0.1888

= 18.88%

Calculation of expected one year return of equity ‘a (iii)’

Expected Return = [(End of Year Price + Dividend) / Current Price ] – 1

= [($45 + $0) / 35] – 1 (given)

= 0.2857

= 28.57%

Explanation on increase in common equity price ‘b (i)’

It would increase the option value while retaining the same value of the bond. It is because the call option becomes deep “in the money” when the $51 per share equity price is compared with convertible conversion price.

Explanation on increase in bond value ‘b (ii)’

Since the increase in interest rates lead to the decline in bond value, it would lead to increase in the option value while decrease in the straight bond value.