A firm has outstanding common stock valued at $67 a share. The firm also has convertible bonds which have a $1,000 par value, a 7.5 percent, semi-annual coupon, and a time to maturity of 11 years. The bonds have a conversion ratio of 15. Comparable, non-convertible bonds have a yield to maturity of 8.2 percent. What is the intrinsic value of this bond?

Question

Quizplus · Accepted Answer

The intrinsic value of the bond is the present value of the future cash flows, plus the present value of the conversion value. The future cash flows are the semi-annual coupon payments and the par value at maturity. The conversion value is the number of shares that the bond can be converted into, multiplied by the current stock price.The semi-annual coupon payment is $1,000 * 7.5% / 2 = $37.50. The par value at maturity is $1,000. The number of shares that the bond can be converted into is $1,000 / $67 = 14.93. The current stock price is $67.The present value of the future cash flows is:PV = $37.50 * (1 - (1 + 8.2% / 2)^(-22)) / (8.2% / 2) + $1,000 * (1 + 8.2% / 2)^(-22) = $949.90The present value of the conversion value is:PV = 14.93 * $67 * (1 - (1 + 8.2% / 2)^(-22)) / (8.2% / 2) = $7.47The intrinsic value of the bond is the sum of the present value of the future cash flows and the present value of the conversion value:IV = $949.90 + $7.47 = $957.37

A Firm Has Outstanding Common Stock Valued at $67 a Share