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**Cost of Capital Chapter 14 Notes to the Instructor:**

The PowerPoints are designed for an introductory finance class for undergraduates with the emphasis on the key points of each chapter Each chapter’s PowerPoint is designed for active learning by the students in your classroom Not everything in the book’s chapter is necessarily duplicated on the PowerPoint slides There are two finance calculators used (when relevant). You can delete the slides if you don’t use both TI and HP business calculators Animation is used extensively. You can speed up, slow down or eliminate the animation at your discretion. To do so just open a chapter PowerPoint and go to any slide you want to modify; click on “Animations” on the top of your PowerPoint screen tools; then click on “Custom Animations”. A set of options will appear on the right of your screen. You can “change” or “remove” any line of that particular slide using the icon on the top of the page. The speed is one of the three options on every animation under “timing”. Effort has been made to maintain the basic “7x7” rule of good PowerPoint presentations. Additional problems and/or examples are available on McGraw-Hill’s Connect. McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.

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**Chapter Outline The Cost of Capital – Overview The Cost of Equity**

The Cost of Debt The Cost of Preferred Stock The Weighted Average Cost of Capital (WACC) Divisional and Project Costs of Capital Floatation Costs relative to WACC

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**Why the Cost of Capital Is Important**

We know that the return earned on assets depends on the risk of those assets The return to an investor is the same as the cost to the company Lecture Tip: Students often find it easier to grasp the intricacies of cost of capital estimation when they understand why it is important. A good estimate is required for: -good capital budgeting decisions – neither the NPV rule nor the IRR rule can be implemented without knowledge of the appropriate discount rate -financing decisions – the optimal/target capital structure minimizes the cost of capital -operating decisions – cost of capital is used by regulatory agencies in order to determine the “fair” return in some regulated industries (e.g. utilities)

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**Why the Cost of Capital Is Important**

Our cost of capital provides us with an indication of how the market views the risk of our assets 4. Knowing our cost of capital can also help us determine our required return for capital budgeting projects Lecture Tip: Students often find it easier to grasp the intricacies of cost of capital estimation when they understand why it is important. A good estimate is required for: -good capital budgeting decisions – neither the NPV rule nor the IRR rule can be implemented without knowledge of the appropriate discount rate -financing decisions – the optimal/target capital structure minimizes the cost of capital -operating decisions – cost of capital is used by regulatory agencies in order to determine the “fair” return in some regulated industries (e.g. utilities)

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**The Cost of Equity Business risk Financial risk**

The cost of equity is the return required by equity investors given the risk of the cash flows from the firm: Business risk Financial risk

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**Dividend growth model (aka: the Gordon Model) 2. SML, or the CAPM**

The Cost of Equity There are two major methods for determining the cost of equity: Dividend growth model (aka: the Gordon Model) 2. SML, or the CAPM

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**The Dividend Growth Model (The Gordon Model)**

Start with the dividend growth model formula and rearrange to solve for RE Remind students that D1 = D0(1+g) You may also want to take this time to remind them that return is comprised of the dividend yield (D1 / P0) and the capital gains yield (g)

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**Dividend Growth Model Example**

Suppose that your company is expected to pay a dividend of $1.50 per share next year. There has been a steady growth in dividends of 5.1% per year and the market expects that to continue. The current price is $25. What is the cost of equity?

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**Example: Estimating the Dividend Growth Rate**

One method for estimating the growth rate is to use the historical average: Year Dividend Percent Change (1.30 – 1.23) / 1.23 = 5.7% (1.36 – 1.30) / 1.30 = 4.6% (1.43 – 1.36) / 1.36 = 5.1% (1.50 – 1.43) / 1.43 = 4.9% Our historical growth rates are fairly close, so we could feel reasonably comfortable that the market will expect our dividend to grow at around 5.1%. Note that when we are computing our cost of equity, it is important to consider what the market expects our growth rate to be, not what we may know it to be internally. The market price is based on market expectations, not our private information. So, another way to estimate the market consensus estimate is to look at analysts’ forecasts and take an average. Lecture Tip: It is noted in the text that there are other ways to compute g. Rather than use the arithmetic mean, as in the example, the geometric mean (which implies a compound growth rate) can be used. OLS regression with the log of the dividends as the dependent variable and time as the independent variable is also an option. Another way to estimate g is to assume that the ROE and retention rate are constant. If this is the case, then g = ROE*retention rate. Lecture Tip: Here’s a good real-world exercise to illustrate real-world growth rates. You can assign this as homework, or do it in class if your classroom has Internet access. Go to screen.yahoo.com/stocks.html and find the “Analysts Estimates Est. 5 Yr EPS growth” box, and use up more than 30%. In August of 2008, using the S&P 500 index stocks found 91 stocks. A search of the S&P 600 (small-cap stocks) found 135 stocks (more small-cap stocks were expected to have very high growth rates than large-cap stocks). Average = ( ) / 4 = 5.1%

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The SML Approach Use the following information to compute our cost of equity: Risk-free rate, Rf Market risk premium, E(RM) – Rf Systematic risk of asset, You will often hear this referred to as the Capital Asset Pricing Model Approach as well. www: Click on the web surfer to go to finance.yahoo.com. Both betas and 3-month T-bills are available on this site. To get betas, enter a ticker symbol to get the stock quote, then choose key statistics. To get the T-bill rates, click on “Rates” under Bonds on the home page.

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**Example - SML Suppose your company has: an equity beta of .58**

the current risk-free rate is 6.1% the expected market risk premium is 8.6% The similarity is completely dependent on estimates of the risk-free rate and market risk premium. What is the cost of equity using the SML valuation technique? RE = (8.6) = 11.1%

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How Did We Do? Since we came up with similar numbers using both the dividend growth model (11.1%) and the SML approach (11.1%), we should feel good about our estimate!

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**Example – Cost of Equity**

Our company has a beta of 1.5. The market risk premium is expected to be 9%, and the current risk-free rate is 6%. We have used analysts’ estimates to determine that the market believes our dividends will grow at 6% per year and our last dividend was $2. Our stock is currently selling for $15.65. What is our cost of equity using the SML? RE = 6% + 1.5(9%) = 19.5%

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**Example – Cost of Equity**

Our company has a beta of 1.5. The market risk premium is expected to be 9%, and the current risk-free rate is 6%. We have used analysts’ estimates to determine that the market believes our dividends will grow at 6% per year and our last dividend was $2. Our stock is currently selling for $15.65. Since the two models are reasonably close, we can assume that our cost of equity is probably around 19.5%. Again, though, this similarity is a function of the inputs selected and is not indicative of the true similarity that could be expected. What is our cost of equity using the DGM? RE= [2(1.06) / 15.65] = 19.55%

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Cost of Debt The cost of debt is the required return on our company’s debt We usually focus on the cost of long-term debt or bonds (as opposed to short-term debt like notes payable) Point out that the cost of debt is rarely the coupon interest rate as the coupon rate was the cost of debt for the company when the bond was issued. We are interested in the rate we would have to pay on newly issued debt, which could be very different from past rates.

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Cost of Debt The required return is best estimated by computing the yield-to-maturity on the existing long-term debt (the YTM). The computation of the YTM was presented in the chapter on Bond Valuation Lecture Tip: Consider what happens to corporate bond rates and mortgage rates as the Federal Reserve board changes the fed funds rate. If the Federal Reserve raises the fed funds rate by a quarter point, virtually all bond rates, from government to municipal to corporate, will increase after this action.

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**Example: Cost of Debt: computing the YTM**

Suppose we have a corporate bond issue currently outstanding that has 25 years left to maturity. The coupon rate is 9%, and coupons are paid semiannually. The bond is currently selling for $ per $1,000 bond. What is the cost of debt?

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**HP 12-C 25 years/2 = 50 periods = N $-908.72 = PV**

$90/2 = $45 = Payment (PMT) YTM = i = ? $1,000 = FV 5.00 (x2 = 10%) Remind students that it is a trial and error process to find the YTM if they do not have a financial calculator or spreadsheet application. 14-18

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**TI BA II Plus $ -908.72 = PV $1,000 = FV YTM = I/Y = ?**

25 yrs/2 = 50 payments = N 5%(5 x 2 = 10% $ = PV $90/2 = $45 (PMT) $1,000 = FV Remind students that it is a trial and error process to find the YTM if they do not have a financial calculator or spreadsheet application. YTM = I/Y = ? 1st 2nd 14-19

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**Capital Structure Weights**

To compute the WACC, we first need the weights of each source of funds: namely debt, preferred stock and equity

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**Capital Structure Weights**

Let’s simplify with an example of just debt and equity. We often use the market value of both debt and equity

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**Capital Structure Valuation**

Debt’s Market Value = (# of outstanding bonds ) x (the market price of one bond) Equity’s Market Value = (# shares of outstanding common stock) x (the market price of one share of common stock) Note that for bonds we would find the market value of each bond issue and then add them together. Also note that preferred stock would just become another component of the equation if the firm has issued it.

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**Capital Structure Valuation**

A firm’s market value is simply the added value of both the debt and the equity: V = D + E Note that for bonds we would find the market value of each bond issue and then add them together. Also note that preferred stock would just become another component of the equation if the firm has issued it.

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**Capital Structure Weights**

WD = D/V This is the % financed with debt WE = E/V This is the % financed with equity Finally, we generally ignore current liabilities in our computations. However, if a company finances a substantial portion of its assets with current liabilities, it should be included in the process. Lecture Tip: It may be helpful to mention and differentiate between the three types of weightings in the capital structure equation: book, market and target. It is also helpful to mention that the total market value of equity incorporates the market value of all three common equity accounts on the balance sheet (common stock, additional paid-in capital and retained earnings). Lecture Tip: The cost of short-term debt is usually very different from that of long-term debt. Some types of current liabilities are interest-free, such as accruals. However, accounts payable has a cost associated with it if the company forgoes discounts. The cost of notes payable and other current liabilities depends on market rates of interest for short-term loans. Since these loans are often negotiated with banks, you can get estimates of the short-term cost of capital from the company’s bank. The market value and book value of current liabilities are usually very similar, so you can use the book value as an estimate of market value.

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**Student Alert! WD + WE = 100% or WD + WPS + WE = 100%**

The capital structure weights must always add up to 100% WD + WE = 100% or WD + WPS + WE = 100%

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**Example: Capital Structure Weights**

Suppose you have a market value of equity equal to $500 million and a market value of debt equal to $475 million. What are the capital structure weights? V = $500 million + $475 million = $975 million wD = D/V = 475 / 975 = = 48.72% wE = E/V = 500 / 975 = = 51.28%

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**Taxes and the WACC Wait a minute!**

Debt and Equity are not equal in the eyes of the firm. Debt gets a tax advantage and Equity does not. We are concerned with after-tax cash flows, so we also need to consider the effect of taxes on the various costs of capital Dividends are not tax deductible, so there is no tax impact on the cost of equity

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**Taxes and the WACC Interest expense reduces our tax liability**

This reduction in taxes reduces our cost of debt Thus, our real cost of debt is actually the AFTER-TAX cost of debt or … After-tax cost of debt = RD(1-TC)

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**Taxes and the WACC WACC = WDRD(1-TC) + WE RE**

Our new equation for the WACC is: WACC = WDRD(1-TC) + WE RE This is one of the most powerful relationships in finance. Point out that if we have other financing that is a significant part of our capital structure, we would just add additional terms to the equation and consider any tax consequences. Lecture Tip: If the firm utilizes substantial amounts of current liabilities, equation 14.7 from the text should be modified as follows: WACC = (E/V)RE + (D/V)RD(1-TC) + (P/V)RP + (CL/V)RCL(1-TC) where CL/V represents the market value of current liabilities in the firm’s capital structure and V = E + D + P + CL.

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**Putting All the Pieces Together – WACC Example**

Equity Information: 50 million shares $80 per share Beta = 1.15 Market risk premium = 9% Risk-free rate = 5% Debt Information: $1 billion in outstanding debt (face value) Current quote = 110 Coupon rate = 9%, semiannual coupons 15 years to maturity Remind students that bond prices are quoted as a percent of par value The firm’s tax rate is 40%

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**WACC Example = 7.854% 1. What is the cost of debt?**

N = 30; PV = -1,100; PMT = 45; FV = 1,000; CPT I/Y = RD = 3.927(2) = 7.854% Point out that students do not have to compute the YTM based on the entire face amount. They can still use a single bond or they could also base everything on 100 (PV = -110; FV = 100; PMT = 4.5). 2. What is the cost of equity (using the CAPM)? RE = (9) = 15.35%

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**WACC Example RD (1 – TC) = 7.854 (1 - .40) = 4.712%**

What is the AFTER-TAX cost of debt? RD (1 – TC) = ( ) = 4.712%

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**WACC Example 4. What are the capital structure weights?**

Debt = 1 billion ($1.10) = $1.1 billion Equity = 50 million ($80) = $4 billion Value of the Firm = = $5.1 billion

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**WACC Example (Plug and Chug)**

Compute the Weighted Average Cost of Capital (the WACC) WACC = WDRD(1-TC) + WE RE WACC = (4.712%) (15.35%) = 13.06%

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Formulas Cost of Equity (Dividend Growth Model) Cost of Equity (CAPM)

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**Formulas (continued) WACC = WDRD(1-TC) + WE RE Rps = D_ P0**

Cost of Preferred Stock After-tax cost of debt = RD(1-TC) WACC = WDRD(1-TC) + WE RE

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