The Blanco River Company plans to sell a 12% coupon, twenty-year convertible bon

Question

The Blanco River Company plans to sell a 12% coupon, twenty-year convertible bond for $1,014 (par value $1,000). The bond is callable at $1,080 in the first year, and the call price declines by $4 each year thereafter. The bond may be converted into twenty shares of stock that currently sell for $40 per share. The stock price is expected to increase at a rate of 7% each year. Nonconvertible bonds with the same degree of risk would yield 13%. Investors expect the firm to call the convertibles if and when the conversion value exceeds the par value by about 20%.

What rate of return can investors expect to receive if they purchase the bonds for $1,014?

Explanation / Answer

Yield to Maturity (YTM):

YTM is the Yield (Return) the bond gives to the bond holder provided to hold bod till maturity.

Formula :

YTM =        INTEREST AFTER TAX + AMORTIZATION                 

                 0.6 x SUBCRIPTION PRICE + 0.4 x MATURITY VALUE

Amortization = Maturity value - Subcription price / n

Interest after tax = $1000 X 12%= $120/- (I assume 12% interst rate is after tax effect)

YTM = 120 + (100-1014) / 20

            0.6 X 1014 + 0.4 X 1000

        = 119.3

            1008.4

        = 11.8%

If bond trading at premium, Return from the bond is less than Coupon rate because capital loss arodes the coupon.

In the given problem bond trading at $1014 more than par value ($1000). So yield 11.84% less than

interest rate is 12%

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