An Optimal Capital Structure for the Company - Essay Example

?Topic: Finance 6 Page No Solution: a. The after-tax cost of capital can be calculated by the following formula: Kd = (I/P T) Where, Kd = after-tax cost of debt I = interest in dollars P = principal amount borrowed T = effective tax rate (Droms & Wright, 2010, p.209) Thus from the given data, Kd = (8.5%) (1-0.30) = 5.95% b. The cost of preferred stock is calculated by the following formula: Kp = Dp / [Pp (1-F)] Where, Kp = cost of preferred stock Dp = preferred dividend Pp= preferred stock price F= floatation cost (Brigham & Daves, 2009, p.330). From the data, Kp = 9/91 = 9.89% c. Cost of common stock (at constant growing rate) can be calculated by the following formula: Ks = (D1/P0) + g Where, Ks = cost of common stock D1 = Dividend at the end of the first year P0 = price of the stock at the beginning of the first year g = growth rate (Gitman, 2007, p.448). From the data, Ks = (0.75/15) + 0.06 = 11% d. Calculation of Weighted Average Cost of Capital (WACC): Capital Component Percentage of capital structure Cost Product (Percentage?Cost) Debt 0.35 5.95% 2.08% Preferred Stock 0.05 9.89% 0.49% Common Stock 0.60 11% 6.60% WACC 9.17% Page 1 No. 2 Solution: Cost of retained earnings (Kre) = Ke (1-f) Where, Kre = cost of retained earnings Ke = cost of equity f = floatation cost (Kapil, 2011, p.278). Ke = (2.10/34) + 0.06 = 12% From the given data, Kre = 0.12 (1-2.38) = (16.56%) (negative) Cost of new common stock (Kn) = (D1/Nn) + g Where, Kn = cost of new issues of common stock D1 = Dividend at the end of first year Nn = net proceeds from the sale of new common stocks g = constant growth rate (Gitman, 2007, p.448) From the given data, Kn = (2.10/34) + 0.06 = 12.18% Page 1 No.3 Solution: a. Calculation of WACC: Debt/Assets After Tax Cost of Debt Cost of equity Cost of capital 0% 8% 12% 0% 10 8 12 2.00 20 8 12 4.00 30 8 13 6.30 40 9 14 9.20 50 10 15 12.5 60 12 16 16.8 Total WACC 50.8 Total weighted cost of debt=20.6% Total weighted cost of equity=30.2% b. Pro-forma Balance Sheet determining an optimal capital structure: Assets $100 Debt $30.2 Equity $68.6 WACC= kd (1-t) (d/v) +ke (e/v) V= $100 WACC=50.85 Kd =20.65% Ke=30.2% Let d=x E=100-x An optimal capital structure for the company may be obtained by increasing the debt level to 30 percent and declining the portion of equity to 70 percent. The original balance sheet reflects 10 percent debt and 90 percent equity. It may here be observed that companies in general tend to lessen their amounts of debts and increase equity amounts or make investments. In the long run in the business operations of any company, the concept of remaining free of debt may not pay well for the business profits. Instead it may be preferable to base a company’s capital structure on the cost of capital for the company. Thus, borrowing money for a long term and reinvesting the amounts in business projects is expected to generate profits for the company. Hence, an optimal structure may reflect on 30-40 percent of debt and the rest in equity for the firm (Kennon, 2011). c. A company may alter its capital structure and buy certain amounts of equity in exchange for new debt thus substituting debt for equity. This would not have any effect on the cost of capital of the company since the overall cost of capital employed does not change. The transaction remains neutral both for the company as well as the investor (Vernimmen & Quiry, 2009, p.448). d. If a company uses too much of debt financing, then the financial condition of the company may be in a difficult situation. This is primarily because in the long run, the company may lose its value and that tends to increase the cost of capital of the firm. An optimal capital structure of a firm largely depends on the business risk of the firm; greater the risk higher is the possibility for the company to obtain its optimal capital structure (Drake & Fabozzi, 2010, p.178). Page 3 No.1 Solution: Assuming the cost of capital to be 10% and 12% the NPVs can be calculated on the costs and cash flows as given in the data. At 10%, NPV = $ 1102.98 At 12%, NPV = $ 2079.77 IRR = 10(1102.98/(1102.98+2079.77))*2 = 6.93% Thus the internal rate of return for the investment is 6.93%. Page 4 No.2 Solution: The cash flow data given is as follows: Year Cash flow(A) in $ Cash flow (B) in $ Discounting factor at 10% 1 300 200 0.91 2 200 200 0.83 3 100 200 0.75 a. Investment costs = $480 NPV of A = $30.13 NPV of B = $15.79 Based on the NPV of the investments, A should be selected since it has the higher NPV than B thus expected to give higher returns. b. Calculations of IRR: For A, NPV at 10%= $30.13 NPV at 12%= $16.49 IRR= 10(30.13/(30.13+16.49))*2 = 12.93% For B, NPV at 10%= $15.79 NPV at 12% = $0.33 IRR = 10(15.79/(15.79+0.33))*2 = 19.59% In this case the IRR is higher in case of investment B, hence based on IRR; B would be preferred as the investment. Thus the answer does not match with that of part a. c. If the cost of capital is 14%: NPV of A = $3.99 NPV of B = $13.75 NPV at 14% also can be seen to be higher in case of investment B; hence B would be preferred. Page 4 No. 3 Solution: a. Calculation of NPV of the investments: NPV = CF0 + {(CF1/(1+R)) + (CF2/(1+R)2)+…… + CFn(1+R)n Year Cash flow(A) in $ Cash flow (B) in $ Cash flow (C) in $ Discounting factor at 8% 1 1100 3600 - 0.93 2 1100 - - 0.86 3 1100 - 4562 0.79 NPV of Investment A at 8%= $152.96 NPV of Investment B at 8% = $308.64 NPV of Investment C at 8% = $575.43 b. The NPV of investment C being the highest should be taken up by the firm since this is expected to give the higher rates of return to the company. c. Calculation of IRR: For investment A: NPV at 8%=$152.96 NPV at 10%=240.42 IRR = 8 (152.96/(152.96+240.42))*2 = 6.22% For investment B: NPV at 8%=$308.64 NPV at 10%=$ 247.93 IRR = 8(308.64/(308.64+247.93))*2 = 8.87% For Investment C: NPV at 8%=$575.43 NPV at 10%=$388.63 IRR= 8(575.43/(575.43+388.63)*2 = 9.55% d. The internal rate of return for Investment C being the highest should be selected by the firm since that would give the highest return to the company as it is higher than the cost of capital. e. Depending on both the NPV and IRR values the investment C should be selected by the company since the rates of return in both these can be expected to be higher than the other investments. f. If the $3600 from investment B was reinvested by the company at 10%, then the NPV for the three investments would be as follows: NPV of A = $785.88 NPV of B = $297.52 NPV of C = $156.82 In this case the NPV for Investment is the highest hence A should be adopted by the firm. When the rate is 14%: NPV of A = $917.72 NPV of B = $387.81 NPV of C = $456.82 Also, in this case A should be selected by the company since it has the highest NPV. g. NPV of A at 10%=$240.42 NPV of A at 12%=$319.63 IRR = 10(240.42/(240.42+319.63)*2 = 8.58% h. Payback method: the payback period method denotes the number of years required for the cash flows to become equal to the initial project cost. That is to say, through this method, the initial investment is overcome as benefits of cash. This helps in decision making as that project is selected that has the shortest payback period (Nadar, 2009, pp.205-206). Page 4 No.4 Solution: Year Cash flow (A) in $ Cash flow (B) in $ Discount rates at 9% 1 10,000 0 0.92 2 25,000 22,000 0.84 3 30,000 48,000 0.77 Initial investment = $50,000 NPV for A at 9% = $15,854.24 NPV for B at 9% =$5120.89 Calculations of IRR: NPV for A at 11%=$1112.89 NPV for B at 11%=$2660.25 IRR for A=9(15854.24/(15854.24+1112.89))*2 = 16.81% IRR for B=9(5120.89/(5120.89+2660.25))*2 = 9.21% Thus depending on the NPV and IRR values the investment A would be preferred by the firm as these reflect higher returns than B. If the cost of capital was 14%: NPV for A = $1528.28 NPV for B = $ 590.42 Even in this case investment A would be chosen over B since its NPV is higher. Page 5 No.7 Solution: In order to decide on the capital budgeting alternative to be selected, two or more alternatives need to be analyzed that may provide a comparison between their NPVs and IRRs, and hence allow to decide on the alternative that may provide the firm with the higher returns. In the given problem, if the NPV of the alternative is calculated at 12% the NPV comes to $159.44. Since the NPV presents a positive value, it can be said that the alternative may be selected for the company’s capital budgeting policies. If the NPV of the project is calculated at 8%, then the NPV of the project comes to $171.47. Thus comparing these two alternatives at two different costs of capital, the second option would be more preferred by the company since its NPV is higher; hence can be expected to give higher returns. Page 7 No.11 Solution: The data of cash flows is given as follows: Year Investment Q cash flow(in $) Investment S cash flow (in $) Discount rates at 10% 1 1300 386 0.91 2 - 386 0.83 3 - 386 0.75 4 - 386 0.68 Investment cost for each = $ 1000 a. NPV of Investment Q= $165.29 NPV of Investment S= $ 203.24 According to the NPV of the two investments Q should be preferred since it reflects higher rates of return than S. b. Calculations of IRR: For Q: NPV at 10%= $165.29 NPV at 12%=143.49 IRR = 10(165.29/ (165.29+143.49))*2 = 10.71% For S: NPV at 10%= $ 203.24 NPV at 12% = $ 153.94 IRR = 10 (203.24/203.24+153.94))*2 = 11.38% Depending on the IRR values, investment Q would be more preferable than S reflecting higher returns for the company. c. If the $1300 of Q is reinvested, and earn 12 percent, and S is invested at 11.38%(IRR), then the NPVs of the two investments are as follows: NPV of Q = $124.36 NPV of S = $100.65 In this case also, the NPV of Q is higher than the S hence Q would be more preferred. If S’s capital were reinvested at 10 percent then NPV of Q = $124.36 NPV of S= $ 203.24 In this case S has a higher value than Q, hence S would be more preferred in this scenario. PG 6 no 10 solution Debt/Assets After Tax Cost of Debt Cost of equity Cost of capital 0% 5% 13 0 10 5 13 1.8 20 5 13 3.6 30 5 13 5.4 40 5 14 7.6 50 6 15 10.5 60 8 16 14.4 Total WACC 43.3 Total cost of debt= 12.8% Total cost of equity= 30.5% Optimum capital structure= cost of capital =43.3% Asset = $ 500 Let value of debt = x Value of equity = 500-x From the formulae, WACC= kd (1-t) (d/v) +ke (e/v) Kd= cost of Debt Ke= cost of equity Value of debt= $140 Value of Equity=$360 Assets $500 Debt $140 Equity $360 C. Cost of investment=$ 400 Cash flow= $133 Year=5 NPV= $100.26 As the NPV is positive so the project should be accepted Assets $400 Debt $230 Equity $170 Let value of debt = x Value of equity = 400-x From the formula WACC= kd (1-t) (d/v) +ke (e/v) Where, Kd= cost of Debt Ke= cost of equity Value of debt= $230 Value of Equity=$170 Total return on Asset= 20% of 400 = $80 Shareholders proportion in the Asset= 57.5% Shareholders return on Asset= (57.5% of $ 80) =$46 References 1) Brigham, E.F. & P.R. Daves. (2009), Intermediate Financial Management, Starnford: Cengage Learning 2) Drake, P.P. & F.J. Fabozzi (2010), The Basics of Finance: An Introduction to Financial Markets, Business Finance, and Portfolio Management, New Jersey: John Wiley and Sons 3) Droms, W.G. & Wright, J.O. (2010), Finance and Accounting for Nonfinancial Managers: All the Basics You Need to Know, New York: Basic Books 4) Gitman, L.J. (2007), Principles of Managerial Finance, 11/E, India: Pearson Education India 5) Kapil, S. (2011), Financial Management, India: Pearson Education India 6) Kennon, J. (2011), An Introduction to Capital Structure, About, available at: http://beginnersinvest.about.com/od/financialratio/a/capital-structure.htm (accessed on September 24, 2011) 7) Nadar, E.N. (2009), Managerial Economics, India: PHI Learning Pvt. Ltd. 8) Vernimmen, P. & P. Quiry (2009), Corporate Finance: Theory and Practice, New Jersey: John Wiley and Sons Read More