To calculate the after-tax cost of debt, multiply by (1 – T) as follows: (1 - 0.40) u 9.3594% = 5.6156% | 5.62%. 96. Cost of common equity: CAPM Answer: c Diff: E N k s = 5% + (6%)1.6 = 14.6%. 97. WACC Answer: b Diff: E N WACC = (0.40)(5.6156%) + (0.60)(14.6%) = 11.0062% | 11.0%.
Chapter 9 - Page 55 WEB APPENDIX 9A SOLUTIONS 9A-1. Risk and divisional costs of capital Answer: a Diff: E N The correct answer is statement a. The composite WACC will be the average of the two divisional WACCs. Since there is no debt, the WACC = k s . There is no cost of equity given, but it can be calculated from the beta, the risk-free rate, and the market risk premium using CAPM. The beta of the entire company is the weighted average of the two divisions’ betas (0.5 u 0.8 + 0.5 u 1.2 = 1.0). The firm’s cost of equity will be equal to 11% (k s = k RF + (RP M )b = 6% + 5% u 1.0 = 11%). Therefore, the WACC is 11%, and statement a is correct. Division B has a higher beta, therefore its cost of capital will be higher than A’s. Therefore, statement b is false. If both divisions were assigned the same hurdle rate, this rate would reflect the required return on projects with a beta of 1.0. Since Division A’s average projects have a beta of 0.8, they would tend to have a lower return. Therefore, fewer of them would meet the hurdle rate of 11%, and the company would choose too few of them. Conversely, the company would choose too many projects in Division B. Therefore, statement c is false. 9A-2. Risk and project betas Answer: d Diff: M 9A-3. SML and capital budgeting Answer: a Diff: M 9A-4. Project cost of capital Answer: c Diff: E Calculate the required return, k s , and compare to the expected return, s k ˆ . s k ˆ = 7%. k s = k RF + (k M - k RF )b = 7% + (10% - 7%)0.5 = 8.5%. k s > s k ˆ ; 8.5% > 7.0%; reject the investment. 9A-5. Project cost of capital Answer: e Diff: M Calculate the beta of the firm, and use to calculate project beta: k s = 0.16 = 0.10 + (0.05)b Firm . b Firm = 1.2. b Project = (b Firm )1.5. (b Project is 50% greater than current b Firm ) b Project = (1.2)1.5 = 1.8. Calculate required return on project, kProject, and compare to expected
Chapter 9 - Page 56 return: Project: k Project = 0.10 + (0.05)1.8 = 0.19 = 19%. Expected return = 0.18 = 18%. Since the required return is one percentage point greater than the expected return, the firm should not accept the new project. WEB APPENDIX 9B SOLUTIONS 9B-1. Pure play method Answer: b Diff: M 9B-2. Corporate WACC for firm with divisions Answer: c Diff: E N For Division A: k A = k RF + (k M – k RF )b A k A = 5% + (6%)0.8 k A = 9.8%. For Division B: k B = k RF + (k M – k RF )b B k B = 5% + (6%)1.5 k B = 14%. WACC = w A k A + w B k B = (0.50)(0.098) + (0.50)(0.14) = 0.119, or 11.9%. 9B-3. Pure play method Answer: b Diff: M Calculate the required return, k s , and use to calculate the WACC: k s = 10% + 1.38(5%) = 16.9%. WACC = 0.5(12.0%)(0.6) + 0.5(16.9%) = 12.05%. Compare expected project return, Project k ˆ , to WACC: But Project k ˆ = 13.0%. Accept the project since WACC k ˆ Project ! : 13.0% > 12.05%.