AFIN1002 Tutorial 8_Week 9_solutions

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Apr 3, 2024

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1 AFIN1002 Tutorial 8 Solutions 1) What factors determine the beta of a share? Define and describe each. ANSWER Beta measures the responsiveness of a security's returns to movements in the market. Beta is determined by the cyclicality of a firm's revenues. This cyclicality is magnified by the firm's operating and financial leverage. The following three factors will impact the firm’s beta. (1) Revenues. The cyclicality of a firm's sales is an important factor in determining beta. In general, share prices will rise when the economy expands and will fall when the economy contracts. As we said above, beta measures the responsiveness of a security's returns to movements in the market. Therefore, firms whose revenues are more responsive to movements in the economy will generally have higher betas than firms with less cyclical revenues. (2) Operating leverage. Operating leverage is the percentage change in earnings before interest and taxes (EBIT) for a percentage change in sales. A firm with high operating leverage will have greater fluctuations in EBIT for a change in sales than a firm with low operating leverage. In this way, operating leverage magnifies the cyclicality of a firm's revenues, leading to a higher beta. (3) Financial leverage. Financial leverage arises from the use of debt in the firm's capital structure. A levered firm must make fixed interest payments regardless of its revenues. The effect of financial leverage on beta is analogous to the effect of operating leverage on beta. Fixed interest payments cause the percentage change in net income to be greater than the percentage change in EBIT, magnifying the cyclicality of a firm's revenues. Thus, returns on highly levered stocks should be more responsive to movements in the market than the returns on stocks of firms with little or no debt in their capital structures.

2 2) Apollo Limited is a diversified conglomerate with major businesses in the information technology, retail, and mining industries. The company’s CEO, Leo Cavalier believes the pet food business has significant growth opportunities. Leo has explained that Apollo Limited uses the firm’s weighted average cost of capital as the required rate of return for evaluating all projects. Leo wants your help in estimating the firm's weighted average cost of capital. The firm has 10 million shares outstanding and expects to pay a dividend at the end of the year of $4 per share. Analysts expect dividends to grow at 3% per year in perpetuity. The firm’s beta is 1. 2. The risk-free interest rate is 4%, and the market risk premium is 6%. The firm has bonds outstanding with a face value of 300 million, maturity of 10 years and coupon rate of 4% payable annually. The bonds are currently trading at a yield of 5% compounded annually. The firm’s marginal tax rate is 30%. a) What is the firm’s cost of equity? b) What is the firm’s market value of equity? c) What is the market value of the firm’s bonds? d) What is the market value of the firm? e) What is the firm’s weighted average cost of capital? f) Comment on the current practice of using the firm’s weighted average cost of capital as the required return for evaluating all projects. ANSWER a) 𝑟 ? = 4% + 1.2 × 6% = 11.2% b) 𝑃 0 = ? 1 𝑟 𝐸 −𝑔 = 4 0.112−0.03 = $48.78 ? = $48.78 × 10 million shares = $487.8𝑚 c) ? = 12𝑚 × 1 0.05 (1 − 1 (1+0.05) 10 ) + 300𝑚 (1+0.05) 10 = $276.835𝑚 d) 𝑉 = ? + ? = 487.8𝑚 + 276.835𝑚 = $764.635𝑚 e) 𝑟 𝑊𝐴?? = 5%(1 − 0.3) × 276.835 764.635 + 11.2% × 487.8 764.635 = 8.412% f) The WACC for the firm can be used as the discount rate for a project if the project has (1) the same systematic risk as the average systematic risk of the firm’s existing projects; and (2) the debt-equity ratio remains constant. It is unlikely that projects across these diversified industries will have the same systematic risk. Therefore, the firm should consider using a project specific WACC.

3 3) Jackson Limited has 25 million shares outstanding, and its most recent dividend was $0.50 per share. Analysts expect the growth rate in dividends to be 4.4% per year in perpetuity. The risk-free interest rate is 5%, and the market risk premium is 7%. The beta of Jackson Limited is 1.2. The tax rate is 30%. The firm's debt represents a bond with 12 years to maturity and a face value of $90 million. The coupon rate on the bond is 12.5% payable annually. The face value of the bond is paid at maturity. The market yield on 12-year bonds with the same credit rating as Jackson is 11% compounding annually. Management is planning to invest $20 million to acquire a new business, and they expect to finance the business using the same proportion of debt and equity for Jackson at market values. The internal rate of return for the business has been calculated at 12%. The new business is unrelated to Jackson ’s current business. While Jackson operates furniture stores, the business it intends to acquire is a dairy farm on the south coast of New South Wales. The beta for companies in the dairy farming industry is 1.8, and the debt-equity ratio for the industry is 0.9. a) What is the weighted average cost of capital of Jackson Limited? Would management accept the venture at this cost of capital? b) What is the appropriate cost of capital for this venture? Should the acquisition be undertaken? ANSWER a) 𝑟 ? = 5% + 1.2 × 7% = 13.4% 𝑃 0 = ? 1 𝑟 ? − 𝑔 = ? 0 (1 + 𝑔) 𝑟 ? − 𝑔 0.50 × 1.044 0.134 − 0.044 = $5.80 ? = $5.80 × 25 million shares = $145𝑚 𝑟 ? = 11% ? = 11.25𝑚 × 1 0.11 (1 − 1 (1+0.11) 12 ) + 90𝑚 (1+0.11) 12 = $98.765𝑚 𝑉 = ? + ? = 98.765𝑚 + 145𝑚 = $243.765𝑚 𝑟 𝑊𝐴?? = 11%(1 − 0.3) × 98.765 243.765 + 13.4% × 145 243.765 = 11.091% Given the internal rate of return of 12% for the new venture, management would accept the project if they used the weighted average cost of capital for Jackson Limited. This is because the IRR of 12% exceeds the cost of capital of 11.091%. Hence, the NPV is positive at this cost of capital.

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4 b) Given that the new venture is unrelated to Jackson’s current business, the project's systematic risk is different from that of the firm. The beta that applies to the dairy farming industry should be used to capture the business risk in this venture. However, the reported beta for dairy farming will incorporate both the business and financial risks of the industry, the latter reflected in the D/E ratio for the industry. To estimate the pure business risk in dairy farming, we need to calculate the unlevered beta for the industry. This can then be used to estimate the required return to equity for Jackson, incorporating the D/E ratio that is optimal for Jackson. Given Jackson intends to finance the venture in the same proportion as the market values of debt and equity in its balance sheet, we can calculate the weighted average cost of capital that applies to the new venture, and then determine if the investment should proceed. Here are the calculations: Beta for dairy farming industry = 1.80 D/E for the dairy farming industry = 0.9. Unlevered beta for dairy farming = 𝛽 𝑈 = 𝛽 𝐿 [1+(1−𝑡 𝑐 )(?/?)] = 1.8 [1+(1−0.3)0.9] = 1.104294 The unlevered beta of 1.104294 represents the true business risk of the industry. Now use this beta to estimate the relevant beta for Jackson for this venture, using the D/E ratio that applies to Jackson. The D/E for Jackson, based on the answer to (1) above: D/E = 98.765 / 145 = 0.681138 𝛽 𝐿 = 𝛽 𝑈 [1 + (1 − 𝑡 𝑐 )(?/?)] = 1.104294[1 + (1 − 0.3)0.681138] = 1.631 Now we can calculate the required return to equity for the venture: 𝑟 ? = 5% + 1.631 × 7% = 16.417% The WACC for the new venture is: 𝑟 𝑊𝐴?? = 11%(1 − 0.3%) × 98.765 243.765 + 16.417% × 145 243.765 = 12.885% The new venture should in fact be rejected because the internal rate of return of 12% is less than the weighted average cost of capital of 12.885%. Hence the NPV is negative at this cost of capital. Management would have made a poor investment decision if they had used the weighted average cost of capital for Jackson because this did not incorporate the true business risk of the new venture.