Suppose that the firm of Example 17.6 has a value of \(\$ 200,000\) instead of \(\$ 100,000\). Perhaps this makes the bond more secure. What, in fact, is the value of the bond in this case?

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Example 17.6 Figure 17.7 shows an example using the same HiTech firm and its bond, except that now we have included a modest yearly coupon of $10 (thousand). We first generate the firm value lattice going forward, as in Figure 17.3. We convert the last column to equity by the formula E = max (0, V-F- C), where V is the firm value, F is the face value of the bond, and C is the coupon. For example, the top node in the last column is 3989-800-10=3179 (see figure 17.3). Next we evaluate earlier values of equity by going backward. The value of E at any prior node is Enew = max [0, (qE" + (1-9)Ed)/R) - C], where, of course, E" and Ed are the upper and lower next-period values of equity, respectively. When we get back to the starting point, the value is the value of equity there. The value of the debt (the bond) is the difference between total value of $1,000 (thousands) and the equity. Hence, the bond value is $1,000 - $389.3 = $610.7 (as compared to