# 3.7 Capital Structure - Solutions

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## 3.7 Capital Structure - Solutions

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- 2
- School:
- University of Texas at Austin
- Course:
- Fin 320f - Foundations of Finance

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FIN 320F Foundations of Finance 3.7 Capital Structure - Solutions 1. A company has two items in its capital structure: long-term debt and equity. The after-tax cost of the debt is 5% and the required rate of return on the equity is 15%. a) Assume the long-term debt represents 50% of the total capital structure and the equity represents 50% of the total capital structure. What is the Weighted Average Cost of Capital (WACC)? WACC = (Proportion of debt × Cost of debt) + (Proportion of equity × Cost of equity) WACC = (0.50 × 5%) + (0.50 × 15%) = 2.5% + 7.5% = 10% b) Assume the long-term debt rises to 60% of the total capital structure so the equity falls to 40% of the total capital structure. What is the WACC? WACC = (0.60 × 5%) + (0.40 × 15%) = 3% + 6% = 9% c) Did the WACC rise or fall when the debt ratio rose? Why? When a greater proportion of debt is used (when the debt ratio rises), the WACC goes down. Debt has a lower required rate of return than equity does; that is, debt is cheaper than equity. Thus, adding debt into the capital structure lowers the average cost of capital. d) In part a, notice that the WACC is equal to the mean (that is, the WACC equals the arithmetic average of the two costs). Why is that true in part a, but not true in part b? The weighted average equals the mean average whenever all of the proportions are the same. In item a, each proportion equaled 50%. In item b, the proportions were unequal. 2. Our new company has three capital structure components: a long-term loan, with an after- tax cost of 6%; some long-terms bonds, with an average cost of 5%; and equity, with an expected cost of 18%. The loan represents 12% of the total capital, the bonds represent 24% of the total, and equity represents the remainder. What is the company’s WACC? Total capital = 100%. 100% – 12% – 24% = 64%. Equity is 64% of total capital. WACC = (0.12 × 6%) + (0.24 × 5%) + (0.64 × 18%) = 0.72% + 1.2% + 11.52% = 13.44% 3. A different company has three capital structure components: $500,000 that it received by taking out a 15-year mortgage loan, $2,500,000 that it obtained when it issued 5-year bonds, and $9,000,000 in total equity. a) How much total capital does the firm have? $500,000 $2,500,000 $9,000,000 $12,000,000 The firm has a total of $12 million in capital b) What is each component’s proportion to the total? $500,000 ÷ $12,000,000 =0.041667 = the proportion of loan-related debt $2,500,000 ÷ $12,000,000 =0.208333 = the proportion of bond-related debt $9,000,000 ÷ $12,000,000 =0.750000 = the proportion of equity $12,000,000 1.000000 SourceDocument.docx Page 1

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