Portfolio Diversification Instructions: Complete the models of Problem 1 and 2.
ID: 2786524 • Letter: P
Question
Portfolio Diversification Instructions: Complete the models of Problem 1 and 2. Problem 1: INPUTS USED IN THE MODEL: P0 $50.00 Net Ppf $30.00 Dpf $3.30 D0 $2.10 g 7% B-T rd 10% Skye's beta 0.83 Market risk premium, RPM 6.0% Risk free rate, rRF 6.5% Target capital structure from debt 45% Target capital structure from preferred stock 5% Target capital structure from common stock 50% Tax rate 35% Flotation cost for common 10% a. Calculate the cost of each capital component, that is, the after-tax cost of debt, the cost of preferred stock (including flotation costs), and the cost of equity (ignoring flotation costs). Use both the DCF method and the CAPM method to find the cost of equity. Cost of debt: B-T rd × (1 – T) = A-T rd Cost of preferred stock (including flotation costs): Dpf / Net Ppf = rpf Cost of common equity, DCF (ignoring flotation costs): D1 / P0 + g = rs Cost of common equity, CAPM: rRF + b × RPM = rs b. Calculate the cost of new stock using the DCF model. D0 × (1 + g) / P0 × (1 – F) + g = re c. What is the cost of new common stock based on the CAPM? d. Assuming that Gao will not issue new equity and will continue to use the same capital structure, what is the company's WACC? wd 45.0% wpf 5.0% ws 50.0% 100.0% wd × A-T rd + wpf × rpf + ws × rs = WACC e. Suppose Gao is evaluating three projects with the following characteristics: (1) Each project has a cost of $1 million. They will all be financed using the target mix of long-term debt, preferred stock, and common equity. The cost of the common equity for each project should be based on the beta estimated for the project. All equity will come from reinvested earnings. (2) Equity invested in Project A would have a beta of 0.5. The project has an expected return of 9.0%. (3) Equity invested in Project B would have a beta of 1.0. The project has an expected return of 10.0%. (4) Equity invested in Project C would have a beta of 2.0. The project has an expected return of 11.0%. Analyze the company’s situation and explain why each project should be accepted or rejected. Beta rs rps rd(1 – T) WACC Expected return on project Project A 0.5 Project B 1.0 Project C 2.0 Problem 2: Following is information for the required returns and standard deviations of returns for A, B, and C. Here are the expected returns and standard deviations for stocks A, B, and C: Stock ri si A 7.0% 33.11% B 10.0% 53.85% C 20.0% 89.44% Here is the correlation matrix: A B C A 1.0000 0.1571 0.1891 B 0.1571 1.0000 0.1661 C 0.1891 0.1661 1.0000 a. Suppose a portfolio has 30 percent invested in A, 50 percent in B, and 20 percent in C. What are the expected return and standard deviation of the portfolio? wA = 30% wB = 50% wC = 20% rp = Portfolio variance = sp = b. The partial model lists 66 different combinations of portfolio weights. For each combination of weights, find the required return and standard deviation. If you would like a return of 10.50 percent, what is the smallest standard deviation that you must accept? Why? Portoflio # wA wB wC Variance sp rp 1 0.0 0.0 1.0 2 0.0 0.1 0.9 3 0.0 0.2 0.8 4 0.0 0.3 0.7 5 0.0 0.4 0.6 6 0.0 0.5 0.5 7 0.0 0.6 0.4 8 0.0 0.7 0.3 9 0.0 0.8 0.2 10 0.0 0.9 0.1 11 0.0 1.0 0.0 12 0.1 0.0 0.9 13 0.1 0.1 0.8 14 0.1 0.2 0.7 15 0.1 0.3 0.6 16 0.1 0.4 0.5 17 0.1 0.5 0.4 18 0.1 0.6 0.3 19 0.1 0.7 0.2 20 0.1 0.8 0.1 21 0.1 0.9 0.0 22 0.2 0.0 0.8 23 0.2 0.1 0.7 24 0.2 0.2 0.6 25 0.2 0.3 0.5 26 0.2 0.4 0.4 27 0.2 0.5 0.3 28 0.2 0.6 0.2 29 0.2 0.7 0.1 30 0.2 0.8 0.0 31 0.3 0.0 0.7 32 0.3 0.1 0.6 33 0.3 0.2 0.5 34 0.3 0.3 0.4 35 0.3 0.4 0.3 36 0.3 0.5 0.2 37 0.3 0.6 0.1 38 0.3 0.7 0.0 39 0.4 0.0 0.6 40 0.4 0.1 0.5 41 0.4 0.2 0.4 42 0.4 0.3 0.3 43 0.4 0.4 0.2 44 0.4 0.5 0.1 45 0.4 0.6 0.0 46 0.5 0.0 0.5 47 0.5 0.1 0.4 48 0.5 0.2 0.3 49 0.5 0.3 0.2 50 0.5 0.4 0.1 51 0.5 0.5 0.0 52 0.6 0.0 0.4 53 0.6 0.1 0.3 54 0.6 0.2 0.2 55 0.6 0.3 0.1 56 0.6 0.4 0.0 57 0.7 0.0 0.3 58 0.7 0.1 0.2 59 0.7 0.2 0.1 60 0.7 0.3 0.0 61 0.8 0.0 0.2 62 0.8 0.1 0.1 63 0.8 0.2 0.0 64 0.9 0.0 0.1 65 0.9 0.1 0.0 66 1.0 0.0 0.0 Portfolio Diversification Instructions: Complete the models of Problem 1 and 2. Problem 1: INPUTS USED IN THE MODEL: P0 $50.00 Net Ppf $30.00 Dpf $3.30 D0 $2.10 g 7% B-T rd 10% Skye's beta 0.83 Market risk premium, RPM 6.0% Risk free rate, rRF 6.5% Target capital structure from debt 45% Target capital structure from preferred stock 5% Target capital structure from common stock 50% Tax rate 35% Flotation cost for common 10% a. Calculate the cost of each capital component, that is, the after-tax cost of debt, the cost of preferred stock (including flotation costs), and the cost of equity (ignoring flotation costs). Use both the DCF method and the CAPM method to find the cost of equity. Cost of debt: B-T rd × (1 – T) = A-T rd Cost of preferred stock (including flotation costs): Dpf / Net Ppf = rpf Cost of common equity, DCF (ignoring flotation costs): D1 / P0 + g = rs Cost of common equity, CAPM: rRF + b × RPM = rs b. Calculate the cost of new stock using the DCF model. D0 × (1 + g) / P0 × (1 – F) + g = re c. What is the cost of new common stock based on the CAPM? d. Assuming that Gao will not issue new equity and will continue to use the same capital structure, what is the company's WACC? wd 45.0% wpf 5.0% ws 50.0% 100.0% wd × A-T rd + wpf × rpf + ws × rs = WACC e. Suppose Gao is evaluating three projects with the following characteristics: (1) Each project has a cost of $1 million. They will all be financed using the target mix of long-term debt, preferred stock, and common equity. The cost of the common equity for each project should be based on the beta estimated for the project. All equity will come from reinvested earnings. (2) Equity invested in Project A would have a beta of 0.5. The project has an expected return of 9.0%. (3) Equity invested in Project B would have a beta of 1.0. The project has an expected return of 10.0%. (4) Equity invested in Project C would have a beta of 2.0. The project has an expected return of 11.0%. Analyze the company’s situation and explain why each project should be accepted or rejected. Beta rs rps rd(1 – T) WACC Expected return on project Project A 0.5 Project B 1.0 Project C 2.0 Problem 2: Following is information for the required returns and standard deviations of returns for A, B, and C. Here are the expected returns and standard deviations for stocks A, B, and C: Stock ri si A 7.0% 33.11% B 10.0% 53.85% C 20.0% 89.44% Here is the correlation matrix: A B C A 1.0000 0.1571 0.1891 B 0.1571 1.0000 0.1661 C 0.1891 0.1661 1.0000 a. Suppose a portfolio has 30 percent invested in A, 50 percent in B, and 20 percent in C. What are the expected return and standard deviation of the portfolio? wA = 30% wB = 50% wC = 20% rp = Portfolio variance = sp = b. The partial model lists 66 different combinations of portfolio weights. For each combination of weights, find the required return and standard deviation. If you would like a return of 10.50 percent, what is the smallest standard deviation that you must accept? Why? Portoflio # wA wB wC Variance sp rp 1 0.0 0.0 1.0 2 0.0 0.1 0.9 3 0.0 0.2 0.8 4 0.0 0.3 0.7 5 0.0 0.4 0.6 6 0.0 0.5 0.5 7 0.0 0.6 0.4 8 0.0 0.7 0.3 9 0.0 0.8 0.2 10 0.0 0.9 0.1 11 0.0 1.0 0.0 12 0.1 0.0 0.9 13 0.1 0.1 0.8 14 0.1 0.2 0.7 15 0.1 0.3 0.6 16 0.1 0.4 0.5 17 0.1 0.5 0.4 18 0.1 0.6 0.3 19 0.1 0.7 0.2 20 0.1 0.8 0.1 21 0.1 0.9 0.0 22 0.2 0.0 0.8 23 0.2 0.1 0.7 24 0.2 0.2 0.6 25 0.2 0.3 0.5 26 0.2 0.4 0.4 27 0.2 0.5 0.3 28 0.2 0.6 0.2 29 0.2 0.7 0.1 30 0.2 0.8 0.0 31 0.3 0.0 0.7 32 0.3 0.1 0.6 33 0.3 0.2 0.5 34 0.3 0.3 0.4 35 0.3 0.4 0.3 36 0.3 0.5 0.2 37 0.3 0.6 0.1 38 0.3 0.7 0.0 39 0.4 0.0 0.6 40 0.4 0.1 0.5 41 0.4 0.2 0.4 42 0.4 0.3 0.3 43 0.4 0.4 0.2 44 0.4 0.5 0.1 45 0.4 0.6 0.0 46 0.5 0.0 0.5 47 0.5 0.1 0.4 48 0.5 0.2 0.3 49 0.5 0.3 0.2 50 0.5 0.4 0.1 51 0.5 0.5 0.0 52 0.6 0.0 0.4 53 0.6 0.1 0.3 54 0.6 0.2 0.2 55 0.6 0.3 0.1 56 0.6 0.4 0.0 57 0.7 0.0 0.3 58 0.7 0.1 0.2 59 0.7 0.2 0.1 60 0.7 0.3 0.0 61 0.8 0.0 0.2 62 0.8 0.1 0.1 63 0.8 0.2 0.0 64 0.9 0.0 0.1 65 0.9 0.1 0.0 66 1.0 0.0 0.0Explanation / Answer
a) Cost of debt: AT rd = BT rd x (1 - tax rate) = 10% x (1 - 35%) = 6.5%
b) Cost of preferred stock = 3.3 / 30 = 11%
c) Cost of equity (using DCF) = D0 x (1 + g) / P0 + g = 2.1 x 1.07 / 50 + 7% = 11.49%
d) Cost of equity (using CAPM) = Rf + beta x MRP = 6.5% + 0.83 x 6% = 11.48%
e) Cost of equity (using DCF and flotation) = D0 x (1 + g) / P0 x (1 - f) + g = 2.1 x 1.07 / (50 x (1 - 10%)) + 7% = 11.99%
f) WACC = wd x rd x (1 - tax) + we x re + wps x kps
= 45% x 6.5% + 5% x 11% + 50% x 11.48%
= 9.215%