ABC Corporation has a $1,000 par value, 6% coupon callable convertible bond quoted with a price of 108. The conversion ratio is 12.5. This bond matures in 20 years. The common stock is currently trading at $79.50. The call price is 106. Comparable non-convertible and non-callable bonds sell for 92.

-The minimum price of this convertible bond is

Question

-The minimum price of this convertible bond is

Quizplus · Accepted Answer

The minimum price of a convertible bond can be calculated using the following formula:

Minimum convertible bond price = Maximum [Conversion Value, Straight Value] / (1 + Required Rate of Return / Conversion Ratio)

where, 
Conversion Value = Current stock price x Conversion Ratio
Straight Value = Bond value without conversion feature

Conversion Value = 79.50 x 12.5 = $993.75
Straight Value = 60 (coupon rate) x 1000 (par value) / 6% (required rate of return) = $1,000
Maximum [Conversion Value, Straight Value] = $1,000

Required rate of return = 6% (coupon rate) + (108 - 1000) / 20 (remaining years to maturity) + (1000 - 79.50 x 12.5) / 20 (remaining years to conversion) = 6.17%

Minimum convertible bond price = $1,000 / (1 + 6.17% / 12.5) = $993.75

Therefore, the best choice is B.

ABC Corporation Has a $1,000 Par Value, 6% Coupon Callable