Athabasca University



Slide #1: Lecture 14 – WACC CalculationWelcome to Lecture 14: Weighted Average Cost of Capital (WACC) Calculation. Slide #2: Topics coveredThese are the eight topics we will cover in this lecture. We will start by describing a numerical example that we will use throughout this lecture. We will then move on to defining the variables needed to calculate the WACC. We then calculate the cost of debt, cost of equity, and cost of preferred equity based on the information given in our numerical example. Also based on this information, we calculate the market value capital structure weights. We will then have enough data to calculate the WACC (weighted average cost of capital). Last but not least, you are provided with a practice question that you can do after completing this lecture. Slide #3: Numerical example used throughout this lectureHere is the information for the numerical example. This company’s capital structure is made up of debt, common equity, and preferred equity. The data is given for each part of the capital structure. Debt:# bonds = 5,000Coupon rate = 8% per annumPayments = Semi-annualFace value = $1,000Bond price = $976.87Time to maturity = 6 yearsCommon equity:# shares outstanding = 2,000,000Price per share = $2.50Beta = 1.5Risk-free rate = 3%Market return = 7%Preferred equity:# shares = 100,000Dividend per share = $1.5Price per share = $10.50Slide #4: Variables needed to calculate WACCWe are asked to calculate the weighted average cost of capital, using the formula:WACC = wCSRCS + wPSRPS + wDRD(1 – T)To use this formula, we will need the following data:The weight on common equity, denoted by wCS The weight on preferred equity, denoted by wPS The weight on debt, denoted by wD The cost of capital on common equity, denoted by RCSThe cost of capital on preferred equity, denoted by RPSThe cost of capital on debt, denoted by RDThe marginal corporate tax rate, denoted by T Slide #5: Cost of debtLet’s start with the cost of debt. The data given for bonds in the previous slide is shown here again:Debt:# bonds = 5,000Coupon rate = 8% per annumPayments = Semi-annual (2)Face value = $1,000Bond price = $976.87Time to maturity = 6 yearsWe are given these six numbers:- The number of bonds outstanding is 5,000. - The coupon rate is 8% per year, and coupons are paid semi-annually, i.e., every 6 months. So we know that the number of payments each year is 2.- Each bond has a face value of $1,000 and a price of $976.87. - The bonds will mature in 6 years’ time. We can use the information given to solve for the bond yield but, first, we must calculate the coupon-payment per payment-period, which is equal to the coupon rate (8%) multiplied by the face-value ($1,000) divided by the number of payments per year (2). In this case, we have 0.08 multiplied by 1000 divided by 2, which gives us $40:Coupon payment = 0.08 x $1,000 / 2 = $40 We must also calculate the number of coupon payments remaining, which is equal to the number of years till maturity multiplied by the number of payments per year. This gives us 6 multiplied by 2 equals 12. We now have all the information needed to calculate the bond yield. For expediency’s sake, let’s use a financial calculator to help us calculate the bond yield. Enter the numbers for PMT = -40 FV = -1000 PV = 976.87N = 12And then ask the financial calculator to compute the I/Y or r. The answer should be 0.0425. Note that this is the yield for half a year (Note also that the number of compounding periods for bonds in Canada is usually 2 per year. This is why we multiply the semi-annual rate of 0.0425 by 2.), and therefore the annual yield is equal to 0.0425 multiplied by 2, which gives us 8.5%. So, the cost of debt (RD) is 8.5%.Slide #6: Cost of common equityFor the common equity, we are given: # shares outstanding = 2,000,000Price per share = $2.50Beta = 1.5Risk-free rate = 3%Market return = 7%With the SML, we can calculate the cost of common equity as the risk-free rate, plus the risk premium multiplied by the beta: RCS = Rf + Beta(E(RM) – Rf)Plugging in the numbers, we get RCS = 0.03 + 1.5(0.07 – 0.03) = 0.09 or 9%. So, the cost of common equity (RCS) is 9%.Slide #7: Cost of preferred equityFor the preferred equity, we are given: # shares = 100,000Dividend per share = $1.5Price per share = $10.50The cost of preferred equity is calculated as the dividend per share divided by the price per share, which gives us 0.14285714, or 14.285714%:Cost of preferred equity= preferred equity yield= RPS= Dividend per share / Price per share = 1.5/10.5= 0.14285714 = 14.285714% Where did we get this formula for calculating the cost of preferred equity? Remember that the preferred equity can be considered a perpetuity, and the present value of a perpetuity is calculated as PV = C/r. In this case, we have PV = price per share = 10.50, and C = Dividend per share = 1.5. We can therefore use the PV(perpetuity) formula to derive our r, where r = C/PV = Dividend per share / Price per share. Slide #8: Capital structure weightsNext, we calculate the capital structure weights. Before we can do that, though, we must calculate the market value of debt, market value of common equity, and market value of preferred equity. Market values are fairly easy to calculate. We simply multiply the price per bond or per share by the number of bonds or shares outstanding. In the case of the debt, we have a bond price of $976.87 and 5000 bonds outstanding. That means that our market value of debt is: Market value of debt = MV(Debt)= Bond price x # bonds = $976.87 x 5,000= $4,884,348.71 For common equity, we have a share price of $2.50 and 2,000,000 common shares outstanding, which give us $5,000,000 in market value of common equity:Market value of common equity = MV(Common Equity)= Share price x # shares= $2.50 x 2,000,000= $5,000,000For the preferred equity, we have a preferred share price of $10.50 and the number of preferred shares outstanding of 100,000, which give us market value of preferred equity of $1,050,000:Market value of preferred equity = MV(Preferred Equity)= Preferred share price x # preferred shares= $10.50 x 100,000= $1,050,000 Slide #9: Capital structure weights (cont.)The market value of total assets is therefore equal to the sum of the market values of debt, common equity, and preferred equity. This gives us market value of total assets of $10,934,348.71:MV(Total Assets) = MV(Debt) + MV(Common equity) + MV(Preferred equity)= $4,884,348.71 + $5,000,000 + $1,050,000= $10,934,348.71Using these market values, we can then calculate the market value capital structure weights for this company using the formula:Weight on i = Market value of i / Market value of total assets The weight on debt is equal to the market value of debt divided by the market value of total assets, which gives us 0.44669773, or about 45 percent in debt:Weight on Debt = MV(Debt) / MV(Total Assets)= $4,884,348.71 / $10,934,348.71= 0.44669773 The weight on common equity is equal to the market value of common equity divided by the market value of total assets, which gives us 0.45727461, or about 46%:Weight on Common Equity = MV(Common Equity) / MV(Total Assets) = $5,000,000 / $10,934,348.71= 0.45727461 The weight on preferred equity is equal to the market value of preferred equity divided by the market value of total assets, which gives us 0.09602767, or about 9.6%: Weight on Preferred Equity= MV(Preferred Equity) / MV(Total Assets)= $1,050,000 / $10,934,348.71= 0.09602767This shows us that the debt and equity are almost of equal proportion in the capital structure. Notice that the sum of the capital structure weights must be equal to one. Slide #10: WACCThe weighted average cost of capital, or WACC, is calculated as the sum of the weights on each financing option multiplied by the cost of each financing option:WACC = wCSRCS + wPSRPS + wDRD(1 – T)The only tricky part here is for the cost of debt. Because interest expenses are tax-deductible (whereas dividends are not tax-deductible), we are interested in the after-tax cost of debt, or RD(1 – T). Having found the capital structure weights for common equity, preferred equity, and debt, as well as the cost of common equity, preferred equity, and debt, we can now calculate the WACC. Oops! Not so fast! First, we will need to identify the marginal corporate tax rate for the company. Let’s say that the tax rate is 40%. NOW we have all the information needed to calculate the WACC. Here, we have the weights: 0.45727461, 0.09602767, and 0.44669773. We have the cost of common equity of 0.09, the cost of preferred shares of 0.14285714, and the cost of debt of 0.085. And of course, for the cost of debt, because interest expenses are tax-deductible, we are interested in the after-tax cost of debt, or RD(1 – T). wCS = 0.45727461wPS = 0.09602767wD = 0.44669773RCS = 0.09RPS = 0.14285714RD = 0.085T = 40% = 0.4We plug all the numbers in, and we get an approximate WACC of 7.7655%:WACC = (0.45727461 x 0.09) + (0.09602767x 0.14285714) + (0.44669773 x 0.085 x (1 – 0.4))= 0.04115471 + 0.01371824 + 0.02278184 = 0.07765479= 7.765479%Slide #11: Three Cheers for practice!And now, three cheers for practice! Hip Hip Hooray! Here’s your practice question. See if you can get the WACC. ABC, Inc.’s capital structure is made up of debt, common equity, and preferred equity.The company has 10,000 coupon bonds outstanding, each with a maturity of 10 years, a face value of $1,000, and a coupon rate of 6%. Coupons are paid quarterly but interest is compounded semi-annually. The yield on this bond issue is 5.5%. There are 1 million common shares outstanding, each at a price of $6.00. The beta on these common shares is 0.9, the risk-free rate is 2% and the expected market return is 8%. There are 50,000 preferred shares outstanding. The preferred shares pay a constant dividend of $1.00 and has an estimated yield of 6.25%.If the marginal corporate tax rate is 35%, what is ABC’s WACC?Slide #12: Check answersHere are your check answers. Cheers! Cost of debt = RD = 0.055Cost of common equity = RCS = Rf + Beta(Rm – Rf) = 0.02 + 0.9(0.08 – 0.02) = 0.074Cost of preferred equity = RPS = 0.0625 MV(Debt) = $1,041.187451 x 10,000 = $10,411,874.51MV(Common Equity) = $6 x 1,000,000 = $6,000,000MV(Preferred Equity) = $16 x 50,000 = $800,000MV(Total Assets) = $17,211.874.51wD = 0.60492392wCS = 0.34859655wPS = 0.04647954WACC = 0.05032715 = 5.03%Slide #13: End of Lecture 14Here ends Lecture 14 on WACC Calculation. ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download