FIN3403 Ch.14
To use the dividend growth model we must come up with an estimate for the growth rate, or "g".
(1) Use historical growth rates (2) use analysts forecasts of future growth rates.
The Capital Structure Weights
E- equity to stand for the market value of the firms equity. We calculate by taking the # of shares outstanding x the price per share. We will use D for the market value of the firm's debt. For long term: market price of a single bond x the number of bonds outstanding. we use the symbol V for value to stand for the combined market value of the debt and equity: V=E+D Percentage of total capital represented by the debt adn equity: 100%= E/V + D/V Can be interpreted just like the portfolio weights often called the capital structure weights.
The Dividend Growth Model
Easiest way. under the assumption that the firm dividend will grow at a constant rate, g, the price per share of the stick, P0, can be written as: P0= (D0 x (1+g)) / (Re-g) this = D1/ Re-g D0 is the dividend just paid and D1 is the next periods projected dividend. Re is required return on equity) Re= D1/ P0+g Re can be interpreted as the firms cost of equity capital because it is the shareholders require on the stock.
Cost of Equity
Estimated using dividend growth model. Company could grow in the future. they are in a stable position Pe=(D1/P0)+g
Discount rate
I/Y or the "R" in the formulas. The discount rate should be the cost of capital to the company. it is the return their required to make in order to buy the bond.
Cost of Capital
What the interest rate is from a firm's point of view.
To make the right decision as president:
examine what the capital markets have to offer and use the information found to figure out the project's cost of capital.
The cost of capital depends primarily on the use of the funds, not the source
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The return an investor in a security receives is the cost of that security to the company that issued it.
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Jimmy Johns has 1.4 million shares of stock outstanding. stock currently sells at $20 per share. firm debt is publicly traded. it was recently quoted at 93% of face value. it has a total face value of 5 million. its current price to yield 11%. risk free rate is 8%. market risk prem is 34%. What is the WACC?
1. Cost of equity: 8%+.74 x 7%=13.18% TV of equity: 1.4mill x $20= $28 mill pretax cost of debt is current yield on outstanding debt= 11% debt sells for 93% of face value so current market value is .93 x 5mill= 4.65 mill total market value of equity and debt together is 28 mill+ 4.65 mill= 32.65 the percentage of equity used by JJ is 28 mill/32.65 mill= 85.76% The perctenage of debt is 1-.8576= 14.24% WACC= (see equation above) WACC=.8576 x 13.18% +.1424 x 11% x (1-.34) WACC =12.34%
SML Approach: Advantages and Disadvantages
Adv- explicity adjusts for risk and it is applicable to companies other than those with steady dividend growth so it may be more useful Dis- it requires the estimation of the market risk premium and the beta coefficient. So, the estimates are poor and the cost of equity will be inaccurate. Different time periods and different stocks and makrets could result in very different estimates: 7 percent is based on about 100 years. We rely on the past to predict the future when we use this approach, similar to the dividend growth model.
Dividend growth model: Advantages and Disadvantages
Adv- it is simple. Dis- it is only applicable to companies that pay dividends so its many times useless. Also , the assumption is that the dividend grows at a constant rate. this will never be exactly the case. it is only really applicable to cases in which reasonably steady growth is likely to occur. Also, the estimated cost of equity is very sensitive to the estimated growth rate. So, the approach does not explicitly consider risks. (pg.462) Unlike the SML approach there is NO direct adjustment for the riskiness of the investment.
What would you need in order to decide whether to go ahead and renovate a warehouse. it would cost 50 mill but could save 12 mill per year after taxes for the next 6 years.
Familiar with capital budgeting You would determine the relevant cash flows, discount them, and if the NPV is positive, take it on. If NPV is negative, scrap it. So far so good, but what do you use as the discount rate?
WACC
Cost of equity Cost of preferred stock Cost of debt Capital Structure Weights All variables should be current market values- costs and dollars
suppose Greater States Public Service a large public utility, paid a dividend of $4 per share last year. The stock currently sells for $60 per share. You estimate that the dividend will grow steadily at a rate of 6% per year into the indefinite future. What is the cost of equity capital for Greater States?
D1= D0 x (1+g) = 4 x 1.06 = $4.24 given this, the cost of equity, Re is: Re= D1/P0 + g = 4.24/60 + .06 = 13.07% The cost of equity is thus 13.07 %.
Preferred stock Ex: on april 4th, alabama power co had two issues of ordinary preferred stock wtih a $100 par value on NYSE. One issue paid $4.64 annually per share and sold for $92.25 per share. The other paid $4.92 per share annually and sold for $95 per share. What is the cost of preferred stock?
First issuer: Rp= D/P0 = $4.64/92.25 = .0503 or 5.03 Second issuer: Rp= D/Po =$4.64/92.25 = .0518 or 5.18% So alabamas cost of preferred stock appears to be about 5.1 percent.
CAPM or capital asset pricing model
Provides the expected (future) required return that someone needs to make from investing in the asset. Appropriate if valuing common equity (dividend discount model) Appropriate is firm is 100% financed with equity AND the project has similar risk as the company. Most firms are not 100% equity financed. Many projects have different risk than the firm
SML: An estimate of the market risk premium based on large common stocks is about 7%. The US treasury bill is about .10 percent. Abercrombie and fitch had an estimated beta of 1.85 we could use Abercrombie and Fitch's cost of equity as:
Raf= Rf+BafX(Rm-Rf) = .10%+ 1.85 x 7% = 13.05%
Taxes and the weighted Average Cost of Capital
The interest paid by a company is deductible in tax purposes. Payments to stockholders, such as dividends are not. So, the gov pays some of the interest.
Total market value of a company's stock is calculated as $200 million and the total market value of the company's debt were calculated as $50 million.
The combined value would be $250 mill. of this total, E/V= $200 mill/ 250 mill which is 80%. 80% of the firm's financing would be equity and the remaining 20% would be debt.
Weighted Average Cost of Capital
The cost of capital for the firm as a while and is otherwise seen as the required return on the overall firm. a firm will normally raise capital in a variety of forms and these different forms will have different costs associated with them.
Unlike a firm's cost of equity, its cost of debt can normally be observed either directly or indirectly.
The cost of debt is simply in the interest rate the firm must pay on new borrowing and we can observe interest rates in the financial markets. For example, if the firm already has bonds outstanding, the yeild to maturity of those bonds is the market-required rate on the firm's debt. (pg.465)
Divisional Cost of Capital
Two divisions: one could be risky, one may not be. imagine if the average was taken of the too in a single WACC cutoff. The risker division would tend to have greater returns and would be awarded greater funds. the potential of the less glam operation could end up being ignored.
Suppose the stock in Alpha Air Freight has a beta of 1.2. The market risk prem is 7 percent and the risk free rate is 6 percent. Alphas dividend was $2 per share, and the dividend is expected to grow at 8% indefiitely. The stock currently sells for $30. What is Alpha's cost of equity capital
USING SML: Re= Rf+ Be x (Rm-Rf) = 6% + 1.2 x 7% =14.4 This suggests that 14.4 % is Alphas cost of equity. USING DIVIDEND GROWTH MODEL: projected div is Do x (1+g)= $2 x 1.08 = $2.16 expected return is Re= D1/Po +g = $2.16/30 +.08 = 15.2% The two estimates are reasonably close so we might just average them to be 14.8.
Divisional and Project Costs of Capital
Using WACC as the discount rate for future cash flows is only appropriate when the proposed investment is similar to the firm's existing activities. Ex: if we are in pizza biz and and are thinking about opening a new location, then the WACC is the discount rate to use. same for retailer thinking of a new store, manufacturer thinking of a new product, or consumer products expanding its market. A desirable investment is one that plots above the SML. Using the WACC for all types of projects can result in the firms incorrectly accepting relatively risky projects and incorrectly rejecting relatively safe ones.
To estimate Re using the dividend growth model:
We need P0, D0, and g^2.
Implementing the SML Approach
We need: Risk free rate- Rf an estimate of the market risk premium- Rm-Rf. and estimate of the relative Beta, Be.
When we say the return on the investment is 10%, what do we mean?
We usually mean that the investment will have a positive NPV but ONLY if it exceed 10%. So, in other words. the firm absolutely has to earn 10% on the investment just to compensate its investors for the use of capital that is needed to finance the project. This is also why we could pretty much say that 10 percent is the cost of capital associated with the investment.
Required Return
What the interest rate is from investors point of view.
Correct Discount rate
depends on the riskiness of the project to renovate the warehouse. it will have a positive NPV only if it's return exceeds what the financial markets offer on investments of similar risk. We called this the minimum required return the cost of capital associated with the project.
How to measure increase/ decrease of dividends
difference/ original cost. ex: it changes from 1.10 to 1.20 so .10/ 1.10= 9.09% increase. If we average the four growth rates, the result is 9, so we could use this as an estimate for the expected growth rate.
Pure Play
examine other investments outside the firm that are in the same risk class as the one we are considering. use market-required return on these investments as the discount rate. We will try to determine the cost of capital for investments by trying to locate some similar investments in the marketplace
(WACC) Weighted Average Cost of Capital
firms overall cost of capital. We calculate this by multiplying the capital structure weights by the associated costs and add them up. WACC= (E/V) x Re+(D/V)xRdx(1-Tc) WACC is the overall the firm must earn on its existing assets to maintain the value of its stock. We use this when we evaluate the cash flows from a proposed expansion of our existing operations.
Cost of Preferred Stock
preferred stock has a fixed dividend paid every period forever so a share os preferred stock is essentially a perpetuity. Rp= D/P0 D- fixed dividend P0= current price per share of the pref stock. Cost of preferred stock is = to the dividend yield on the preferred stock.
If a company cant repay the investors, then what?
that stock droppp because the company cant compensate the investors. Value would decline over time.
Beta
the measure of systematic risk. measured for equity.
A firm's overall cost of capital will reflect the required return on the firm's assets as a whole
the overall cost of capital will be a mix of returns needed to compensate it's creditors and those needed to compensate its stockholders. AKA a firms cost of capital will reflect both the cost of debt capital and the cost of equity capital.
Capital Structure
the particular mixture of debt and equity a firm chooses to employ. it is a managerial variable.
The SML approach
the required or expected return on a risky investment depends on three things: 1. the risk free rate, Rf 2. The market risk premium, E(Rm)-Rf. 3. The systematic risk of the asset relative to the average, called the beta coefficient, B Using SML we can write the expected return on the company's equity E(Re) as: E(Re)= Rf+BE X [E(Rm)-Rf] To make the SML approach consisent with the dividend growth model, we drop the Es denoting expectations and henceforth write the required return from the SML, Re as: Re= Rf+Be X (Rm-Rf)
The Cost of Debt
the return the firm's creditors demand on new borrowing.
How do we determine the overall cost of equity?
there is no way of directly observing the return that the firm's equity investors require on their investment. but, we can estimate it. There are two approaches to determining the cost of equity: 1. the dividend growth model approach 2. the security market line (SML) approach
A firm borrows $1 million at 9% interest. The corporate tax rate is 34%. What is the aftertax interest rate on this loan? The total interest bill will be 90,000 per year.
this is tax deductible so the 90,000 interest reduces the firms tax bill by .34x90,000= $30,600. The aftertax interest bill is thus 90,000-30600=$59,400. The aftertax interest rate is thus 59,400/1mill= 5.94% The aftertax interest rate is equal to the pretax rate x 1-tax rate. if we use Tc for the corporate tax rate, then the aftertax rate can be written as Rd x (1-Tc) or in this ex: 9% x (1-.34)= 5.94%
imagine- we are evaluating a risk free project. how do we determine the required rate of return?
we look at capital markets and observe the current rate offered by risk-free investments and use the rate to dscount the project's cash flows. The cost of capital for a risk free investment is the risk free rate. IF THE PROJECT IS RISKY (assuming all other information is unchanged) THE REQUIRED RETURN IS OBVIOUSLY HIGHER. or the cost of capital (IF RISKY) is GREATER than the risk free rate. also, the appropriate discount rate would exceed the risk free rate.
Why are taxes important?
when considering the required return on the investment. We want to know the value of the after tax cash flows from a project.
