WACC AND NPV - WACC and NPV PDF

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WACC and NPV...

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Och, Inc., is considering a project that will result in initial after-tax cash savings of $1.85 million at the end of the first year, and these savings will grow at a rate of 3 percent per year indefinitely. The company has a target debt-equity ratio of .65, a cost of equity of 11 percent, and an after tax cost of debt of 4.3. percent. The cost saving proposal is somewhat riskier than the usual projects the firm undertakes; management uses the subjective approach and applies an adjustment factor of +2 percent to the cost of capital for such risky projects. Under what circumstances should the company take on the project? We have debt-equity ratio, so we can calculate the weightage average cost of capital (WACC) of firm with the help of following formula WACC = wd *rd + we * re Where, Weight of debt wd = 0.85/ (1+0.85) = 0.85/1.85 Weight of equity we = 1/ (1+0.85) = 1/1.85 After-tax cost of debt, rd = 5.3% And the cost of equity, re = 12.5% WACC = (0.85/1.85)* 5.3% + (1/1.85)*12.5% = 9.19% As the project is riskier than the usual projects of the firm therefore an adjustment of 2% are required for additional risk. Therefore Project’s risk adjusted discount rate = WACC + adjustment factor of +2% = 9.19% + 2% = 11.19% What is the maximum initial cost the company would be willing to pay for the project is the present value the cash inflows. For present value calculations the cash flows are discounted at Project’s risk adjusted discount rate of 11.19%. The cash inflows are a growing perpetuity therefore the PV of a growing perpetuity can be calculated in same manner as we use in dividend growth model. PV of future Cash Flows = After-tax cash savings at the end of the first year / (k –g) Where, After-tax cash savings at the end of the first year = $1.85 million Project’s risk adjusted discount rate, k = 11.19% per year And perpetual growth rate of cash flow, g = 3% per year Therefore, PV of future Cash Flows = $1,850,000/ (0.1119 – 0.03) = $22,583,305.84 Therefore the maximum initial cost the company would be willing to pay for the project is $22,583,305.84 Calculating Cost of Equity: The Nixon Corporation’s common stock has a beta of .95. If the risk-free rate is 2.7 percent and the expected return on the market is 10 percent, what is the company’s cost of equity capital? Beta of the stock = β = .95

Risk-free rate of return = RF = 2.7 % Expected return on the market = RM = 10% The company's cost of equity capital is calculated using the CAPM Equation, given by the following equation: Cost of equity capital = RE = RF + β*(RM-RF) = 2.7% + .95*(10% - 2.7%) = 9.64 % Answer -> Cost of equity capital = 9.64 % Calculating Cost of Debt

One Step, Inc., is trying to determine its cost of debt. The firm

has a debt issue outstanding with 17 years to maturity that is quoted at 95 percent of face value. The issue makes semiannual payments and has a coupon rate of 6 percent. What is the company’s pretax cost of debt? If the tax rate is 21 percent, what is the aftertax cost of debt? Keys to use in a financial calculator: 2nd I/Y 2 FV 1000 PV -920 PMT 30 N 34 CPT I/Y Pretax cost of debt = 6.49% 2) After tax cost of debt = 0.0649 (1 - 0.23) After tax cost of debt = 5%

Calculating WACC Mullineaux Corporation has a target capital structure of 70 percent common stock and 30 percent debt. Its cost of equity is 10.9 percent and the cost of debt is 5.7 percent. The relevant tax rate is 23 percent. What is the company’s WACC?

Taxes and WACC

Miller Manufacturing has a target debt-equity ratio of .40. Its cost of

equity is 11.8 percent and its cost of debt is 6.5 percent. If the tax rate is 21 percent, what is the company’s WACC? The formula for calculating the weighted average cost of capital is = WACC = [ Ke * We ] + [ ( Kd * ( 1- t ) ) * Wd ] Ke = Cost of equity ; We = Weight of equity ; Kd = Cost of debt ; Wd = Weight of debt ; t = Income tax rate As per the information available in the question we have Ke = 11.8 % ; Kd = 6.5 % ; t = 23 % = 0.23 ; Debt - equity ratio = 0.30 : 1 Thus weight of debt = 0.30 / ( 1 + 0.30 ) = 0.30 / 1.30 = 0.2308 weight of equity = 1 / ( 1 + 0.30 ) = 1 / 1.30 = 0.7692 Therefore We = 0.7692 ; Wd = 0.2308 Applying the above values in the formula we have = [ 11.8 * 0.7692 ] + [ ( 6.5 * ( 1 – 0.23 ) ) * 0.2308 ] = [ 11.8 * 0.6452 ] + [ ( 6.5 * 0.77 * 0.3548 ] = [ 9.0769 + 1.1550 ] = 10.2319 %

= 10.23 % ( when rounded off to two decimal place ) Thus the WACC of the company is = 10.23 % WACC Kose, Inc., has a target debt-equity ratio of .38. Its WACC is 10.1 percent and the tax rate is 25 percent. a. If the company’s cost of equity is 12 percent, what is its pretax cost of debt? b. If instead you know that the after tax cost of debt is 6.4 percent, what is the cost of equity?

Finding the WACC

Given the following information for Huntington Power Co., find the

WACC. Assume the company’s tax rate is 21 percent. Debt: 17,000 4.9 percent coupon bonds outstanding, $2,000 par value, 20 years to maturity, selling for 105 percent of par; the bonds make semiannual payments. Common stock: 425,000 shares outstanding, selling for $67 per share; the beta is .88. Market: 7 percent market risk premium and 3.5 percent risk-free rate. Market Value of 1 bond = 2000 x 1.05 = $2,100 Annual coupon payment = 2000 x 4.9% = $98 Semi annual coupon payment = 98 / 2 = $49 Number of coupon payments = 20 x 2 = 40 Using a financial calculator, PV = -2,100 FV = 2,000 N = 40 PMT = 49 Computing I/Y = 2.2588% Cost of debt = 2.2588 x 2 = 4.518% After tax cost of debt = 4.518 x (1 - tax rate) = 4.518 x (1 - 0.21) = 3.569% Cost of equity = Risk free rate + beta x Market risk premium = 3.5 + 0.88 x 7 = 9.66% Total market value of debt = number of bonds x market value of bonds = 17,000 x 2,100 = $35,700,000 Total Market value of equity = share price x number of shares = 425,000 x 67 = $28,475,000 Total Market value = 35,700,000 + 28,475,000 = $64,175,000 Weight of Debt = (35,700,000 / 64,175,000) = 55.63% Weight of Equity = 100 - Weight of Debt = 44.37% WACC = Weight of debt x After tax cost of debt + Weight of equity x cost of equity = 0.5563 x 3.569 + 0.4437 x 9.66 = 6.27%

Finding the WACC Titan Mining Corporation has 6.4 million shares of common stock outstanding and 175,000 6.2 percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $53 per share and has a beta of 1.15; the bonds have 25 years to maturity and sell for 106 percent of par. The market risk premium is 6.8 percent, T-bills are yielding 3.1 percent, and the company’s tax rate is 22 percent. a. What is the firm’s market value capital structure? b. If the company is evaluating a new investment project that has the same risk as the firm’s typical project, what rate should the firm use to discount the project’s cash flows? a.

Market value of equity E = Number of shares * stock price = 6.4 million *$53 = $339.20 million

Market value of debt D = Debt outstanding * selling at % of par = 175,000 * $1000* 106% = $185,500,000 Firm’s market value capital structure = Market value of debt D + Market value of equity E (D +E)= $185,500,000 + $339,200,000 = $524,700,000 = $524.70 million b.

We need to find the YTM on bond issues

Before tax cost of debt is bond’s yield; we have following formula for calculation of bond’s yield Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n Where Price of the bond P0 = $1060 (106% of 1000) M = value at maturity, or par value = $1000 C = coupon payment = 6.2%/2 of $1000 = $31 semiannual coupon n = number of payments = 25 years *2 = 50 i = interest rate, or yield to maturity =? Now we have, $1060 = $31 * [1 – 1 / (1+i) ^50] /i + $1000 / (1+i) ^50 We got the value of i = 2.87% Therefore YTM of bond = 2 *2.87%= 5.74% Tax rate = 22% Therefore After tax cost of debt rd = 5.74% *(1-0.22) = 4.48% re= the firm's cost of equity = risk free rate (rf) + β of stock * risk premium on the market = 3.1% + 1.15 * 6.8% = 10.92% Weighted Average Cost of Capital (WACC) WACC = [E/ (E+D)] * re + [D/ (E+D)] * rd Where, re is the cost of equity rd is the after-tax cost of debt E is the value of common equity D is the value of debt WACC = ($339,200,000/$524,700,000) * 10.92% + ($185,500,000 /$524,700,000) * 4.48% = 7.06% + 1.58% =8.64% Therefore, the Weighted Average Cost of Capital (WACC) is 8.64%...