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# Calculating the Intrinsic Value of a Bond

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Twin Oaks Health Center has a bond issue outstanding with a coupon rate of 7 percent and four years remaining until maturity. The par value of the bond is \$1,000, and the bond pays interest annually.

a. Determine the current value of the bond if present market conditions justify a 14 percent required rate of return.

b. Now, suppose Twin Oaks' four-year bond had semiannual coupon payments. What would be its current value? (Assume a 7 percent semiannual required rate of return. However, the actual rate would be slightly less than 7 percent because a semiannual bond is slightly less risky than an annual coupon bond.)

c. Assume that Twin Oaks' bond had a semiannual coupon but 20 years remaining to maturity. What is the current value under these conditions? (Again, assume a 7 percent semiannual required rate of return, although the actual rate would probably be greater than 7 percent because of increased price risk.)

#### Solution Preview

Please refer attached file for better understanding of formulas.

a. Determine the current value of the bond if present market conditions justify a 14 percent required rate of return.

Required rate of return=rate=14%
Number of periods=nper=4
Coupon amount=pmt=1000*7%=\$70
Par Value of bond=fv=\$1,000
Type of paument=type=0 0 indicate end of period payments
Value of bond = present value of cash inflows=\$796.04 (Use PV function ...

#### Solution Summary

Solution describes the steps to find intrinsic value of a bond in different conditions with the help of formulas in MS Excel.

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## Rates of Return on Convertible Bond Investments

Fondren Exploration, Ltd., has 1,000 convertible bonds (\$1,000 par value) outstanding, each of which may be converted to 50 shares. The \$1 million worth of bonds has 25 years to maturity. The current price of the stock is \$26 per share. The firm's net income in the most recent fiscal year was \$270,000. The bonds pay 12 percent interest. The corporation has 150,000 shares of common stock outstanding. Current market rates on long-term nonconvertible bonds of equal quality are 14 percent. A 35 percent tax rate is assumed.

a.Compute diluted earnings per share.

b.Assume the bonds currently sell at a 5 percent conversion premium over conversion value (based on a stock price of \$26). However, as the price of the stock increases from \$26 to \$37 due to new events, there will be an increase in the bond price, and a zero conversion premium. Under these circumstances, determine the rate of return on a convertible bond investment that is part of this price change, based on the appreciation in value.

c.Now assume the stock price is \$16 per share because a competitor introduced a new product. Would the conversion value be greater than the pure bond value, based on the interest rates stated above? (See Table 16-3 in Chapter 16 to get the bond value without having to go through the actual computation.)

d.Referring to part c, if the convertible traded at a 15 percent premium over the conversion value, would the convertible be priced above the pure bond value?

e. If long-term interest rates in the market go down to 10 percent while the stock price is at \$23, with a 6 percent conversion premium, what would the difference be between the market price of the convertible bond and the pure bond value? Assume 25 years to maturity, and once again use Table 16-3 for part of your answer.

Table 16-3
Interest Rates and Bond Prices (the bond pays 12% interest)
------------------------------------------------------------------------------
Rate in the Market (%) - Yield to Maturity*
Years to Maturity 8% 10% 12% 14% 16%
1 1038.16 1018.54 1000 981.48 963.98
15 1345.52 1153.32 1000 875.54 774.48
25 1429.92 1182.36 1000 862.06 754.98