Solutions Guide: Please reword the answers to essay type parts so as to guarantee that your answer is an original. Do not submit as your own.
Piedmont Instruments Corporation has estimated the following costs of debt and equity capital for various fractions of debt in its capital structure. Debt Fraction ki ke with Financial Distress Costs and Without Agency Costs ke with Financial Distress Costs and Agency Costs 0.00 0.10 0.30 0.40 0.45 0.50 0.60 — 4.8% 4.9 5.0 5.2 5.7 7.0 12.00% 12.05 12.10 12.20 12.40 12.80 15.00 12.00% 12.05 12.20 12.60 13.40 14.80 18.00 a. Based on these data, determine the company’s optimal capital structure (i) with financial distress costs and without agency costs and (ii) with fi nancial distress and agency costs. b. Suppose the company’s actual capital structure is 50 percent debt and 50 percent equity. How much higher is ka at this capital structure than at the optimal value of ka, with financial distress and agency costs? c. Is it necessary in practice for the company to know precisely its optimal capital structure? Why?
a.ka = (fraction of equity) (ke) + (fraction of debt) (ki)
(i) With financial distress costs and without agency costs:
Debt Fraction
0.00ka = 12.0%
0.10ka = (0.9)(12.05) + (0.1)(4.8) = 11.33%
0.30ka = (0.7)(12.1) + (0.3)(4.9) = 9.94%
0.40ka = (0.6)(12.2) + (0.4)(5.0) = 9.32%
0.45ka = (0.55)(12.4) + (0.45)(5.2) = 9.16%
0.50ka = (0.5)(12.8) + (0.5)(5.7) = 9.25%
0.60ka = (0.4)(15.0) + (0.6)(7.0) = 10.2%
Therefore, the optimal capital structure is approximately 45% debt + 55% equity.
(ii.) With financial distress and agency costs:
Debt Fraction
0.00 ka = 12.0%
0.10ka = (0.9)(12.05) + (0.1)(4.8) = 11.33%
0.30ka = (0.7)(12.20) + (0.3)(4.9) = 10.01%
0.40ka = (0.6)(12.60) + (0.4)(5.0) = 9.56%
0.45ka = (0.55)(13.4) + (0.45)(5.2) = 9.71%
0.50ka = (0.5)(14.8) + (0.5)(5.7) = 10.25%
0.60ka = (0.4)(18.0) + (0.6)(7.0) = 11.4%
Therefore, the optimal capital structure is approximately
40% debt+ 60% equity.
b.50% - 50% = 10.25%
optimal = 9.56%
0.69%
c. No, because in practice the optimal portion of the ka curve is saucer-shaped, i.e., relatively flat. This problem shows that the ka values at 40% and 45% debt differ only slightly.