L33. Cost of capital Flashcards
Learning outcomes
a. Calculate and interpret the weighted average cost of capital (WACC) of a company
b. Describe how taxes affect the cost of capital from different capital sources
c. Describe the use of target capital structure in estimating WACC and how target capital structure weights may be determined
d. Explain how the marginal cost of capital and the investment opportunity schedule are used to determine the optimal capital budget
e. Explain the marginal cost of capital’s role in determining the net present value of a project
f. Calculate and interpret the cost of debt capital using the yield-to-maturity approach and the debt-rating approach
g. Calculate and interpret the cost of noncallable, nonconvertible preferred stock
h. Calculate and interpret the cost of equity capital using the capital asset pricing model approach, the dividend discount model approach, and the bond-yield-plus risk-premium approach
i. Calculate and interpret the beta and cost of capital for a project
j. Describe uses of country risk premiums in estimating the cost of equity
k. Describe the marginal cost of capital schedule, explain why it may be upward-sloping with respect to additional capital, and calculate and interpret its break-points
l. Explain and demonstrate the correct treatment of flotation costs
Cost of capital
If company invests in projects that produce return in excess of the cost of capital, the company has created value. But if the company invests and its return are less than cost of capital, company has destroyed value
- cost of capital is not observable but estimated
- cost of capital is the rate of return that the suppliers of capital (bondholders and owners) require as compensation for their contribution of capital OR the opportunity cost of funds for the suppliers of capital
- component cost of capital is the rate of return required by suppliers of capital for an individual source of a company’s funding such as debt or equity
- marginal cost = what it would cost to raise additional funds for potential investment project
Weighted average cost of capital (WACC)
Also referred to as the marginal cost of capital (MCC) because it is the cost that a company incurs for additional capital
WACC = WdRd (1-t) + WpRp + WeRe
Wd = proportion of debt that company uses when raising new funds Rd = before tax marginal cost of debt t = marginal tax rate Wp = proportion of preferred stock that company uses when raising new funds Rp = marginal cost of preferred stock We = proportion of equity that company uses when raising new funds Re = marginal cost of equity
- marginal cost of debt financing is the cost of debt after considering the allowable deduction for interest on debt based on country’s tax law
Target capital structure
- the capital structure that a company is striving to obtain
- used to determine what weights to use for the proportion of each source of capital
- Debt: deductible for tax purposes
- Preferred stock: dividends are paid after tax, no tax treatment
- Common stock: dividends are paid after tax, no tax treatment
Few ways to determine what is the company target capital structure
- assume current structure (at market value weights) represent the target
- examine past trends
- use averages of competitors
EG. based on 1 If company has following market values for its capital Bonds = 5 million PS = 1 million CS = 14 million Total = 20 million
Then the weights will be
Bonds = 5/20 = 0.25
PS = 1/20 = 0.05
CM = 14/20 = 0.7
Eg. based on 3
debt / Equity
Competitor A - 25m / 50m
Competitor B - 101m / 190m
Competitor C - 40m / 60m
For debt = (25/75 + 101/291 + 40/100) / 3 = 0.3601
For equity = (50/75 + 190/291 + 60/100) / 3 = 0.6399
Practice Qns for WACC
Given the following info about a firm
- debt to equity ratio = 50%
- tax rate = 40%
- cost of debt = 8%
- cost of equity = 13%
What is the WACC?
Solution
Convert D/E to the weight for debt
0.50 / 0.5+ 1 = 1/3
if debt = 1/3, then equity = 2/3
Sub into WACC formula
= 1/3 (0.08) x (1-0.40) + 2/3(0.13) = 0.1026 or 10.3%
Practice Qns for WACC
Analyst gathered following info about a company
Source of capital Proportion Marginal aftertax cost
Debt 50% 6%
PS 10% 10%
CM 40% 15%
IRR of 2 projects
- warehouse project = 8%
- equipment project = 12%
Which project should be accepted?
Solution
Find the WACC
0.5(0.06) + 0.1(0.1) + 0.4(0.15) = 10%
Accept project with higher IRR than cost which is equipment project
Capital budget decision making
- a company’s MCC may increase as additional capital is raised, whereas returns to a company’s investment opportunities are generally believed to decrease as the company makes additional investments as presented by investment opportunity schedule (IOS)
- IOS is a graphical depiction of a company’s investment opportunities ordered from highest to lowest expected return. A company’s optimal capital budget is found where the investment opportunity schedule intersects with the company’s marginal cost of capital
- -> optimal capital budget is that the amount of capital raised and invested at which the marginal cost of capital is = to the marginal return from investing
- with increase interest rate by central bank, MCC (higher cost of funding) curve will shift leftwards or upwards, IOS will move leftwards, or downwards therefore, lower optimal budget
- opposite effect for decrease IR
- for average risk project, use WACC as discount rate
- if risk is above/below average, upward/downward adjustment to WACC required
Cost of debt
- the cost of debt financing to a company when it issues a bond or takes out a bank loan
2 ways to determine the before tax cost of debt
- Yield to maturity approach (YTM)
- annual return that an investor earns on a bond if the investor purchases the bond today and holds it until maturity
P0 = {Sum of PMTs/[(1+rd/2)^t]} + FV/ [(1+rd/2)^n]
where P0 = current market price of bond
PMT = payments
rd = YTM
FV = maturity value of bond
- Debt-rating approach
- method used for estimating a company’s before tax cost of debt based upon a yield on comparably rated bonds for maturities that closely match that of the company’s existing debt
Eg.
company’s marginal tax = 35%
company’s rating is AAA and yield on debt with same debt rating and similar maturity is 4%, the company after tax cost of debt is
= 4(1-0.35) = 2.6%
Other issues
- fixed rate debt vs floating rate debt
a) company may issue floating rate debt in which adjust IR periodically accordingly to prescribed index such as Libor - debt with optionlike features
a) callable bond would have a yield > a similar noncallable bond as bondholders want to be compensated for the call risk associated with the bond - non rated debt
a) company do not have any rated bonds - leases
a) operating lease - agreement allowing lessee to use some asset for a period of time, like rental
b) finance lease or capital lease
should be included in cost of capital
Practice qns for YTM
Company X issues a 10 year, $1000 Face value, 5 percent semi annual coupon bond. Upon issue, bond sells at 1025. 1) What is the before tax cost of debt?
2) If the marginal tax rate is 35%, what is the after tax cost of debt?
Solution 1 FV = 1000 PMT = (1000* 5%) / 2 = 25 N = 10 * 2 = 20 PV = -1025 CPT I/Y = 2.342 Need to x 2 because this is based on semi annual, so before tax cost of debt is 4.68%
Solution 2
If marginal tax rate is 35%
then after tax cost of debt is
0.0468(1-0.35) = 0.03045 or 3.045%
Cost of preferred stock
- the cost that a company has committed to pay preferred stockholders as a preferred dividend when it issues preferred stock
- noncallable preferred stock that has a fixed dividend rate and no maturity date (fixed rate perpetual preferred stock) use below formula
Pp = Dp/Rp
where Pp = current preferred stock price per share
Dp = preferred stock dividend per share
Rp = cost of preferred stock
features for preferred stock
- call option
- cumulative dividends
- participating dividends
- adjustable rate dividends
- convertibility into common stock
Cost of common equity
- rate of return required by a company’s common shareholders
- company may increase common equity through the reinvestment of earnings (retained earnings) or through the issuance of new shares of stock
- approaches used for estimating cost of equity includes
1. capital asset pricing model
2. dividend discount model
3. bond yield plus risk premium method
Capital asset pricing model
- CAPM
- basic relationship from capital asset pricing model theory that the expected return on a stock, E(R) is the sum of the risk free rate of interest, Rf, and a premium for bearing the stock’s market risk B(Rm-Rf)
E(R) = Rf + B[E(Rm) - Rf]
where B = sensitivity of stock i to changes in market return
E(Rm) = expected return on the market
E(Rm) - Rf = expected market risk premium
- risk free asset = asset that has no default risk
- common proxy for the risk free rate is the yield on a default free government debt instrument
- eg if we are evaluating a project with a 10 years life, we may use the rate on the 10 year treasury bond
- the expected risk premium is the premium that investors demand for investing in a market portfolio relative to a risk free rate
- usually use an estimate of the equity risk premium (ERP) for the expected risk premium ie E(Rm) - Rf
- priced risk = risk for which investors demand compensation for bearing
- multi factor models include all other risks not captured in CAPM like inflation, business cycle etc
3 ways to estimate equity risk premium
- Historical equity risk premium approach
- based on assumption that the realised equity risk premium observed over a long period of time is a good indicator of the expected equity risk premium
- compiling historical data to find average rate of return
- limitations 1) level of risk of stock index may change
over time 2) risk aversion of investors may change over time 3) sensitive to method of estimation and. historical period covered
- Dividend discount model approach
- implemented using Gordon Growth model (aka the constant growth dividend discount model)
Re = (D1 / Po) + g
where Re = required rate of return
D1 = dividends expected next period on the index
Po = current market value of the equity market index
g = expected growth rates of the dividends
- D1/Po = dividend yield
- the ERP is the expected return on equity market minus the risk free rate
- Survey approach
- based on estimates provided by a panel of finance experts
Dividend discount Model
Re = (D1 / Po) + g
where Re = required rate of return
D1 = dividends expected next period on the index
Po = current market value of the equity market index
g = expected growth rates of the dividends
g = (1 - D/EPS) ROE
also known as sustainable growth rate
D/EPS = stable dividend payout ration or DPR
ROE = historical return on equity
1-D/EPS = company’s earnings retention rate
Bond Yield Risk premium method
- cost of capital of riskier cash flows is higher than that of less risk cash flows
Re = Rd + risk premium
where Rd is the before tax cost of debt
Estimating Beta and determining a project beta
Multiple ways to estimate beta
- Using a market model regression of the company’s stock returns against market returns over T periods
Beta estimates are sensitive to the method of estimation because:
a) estimation period - sensitive to the length of estimation period, with beta commonly estimated using data over 2-9 years
b) periodicity of the return interval (daily, weekly, monthly) - more accurate using smaller return intervals
c) Selection of appropriate market index
d) Using of a smoothing technique
e) Adjustments for small capitalisation stocks - small caps stocks generally have greater risks and greater returns than large cap stocks over long run
Companies are affected by business risks (risks related to uncertainty of revenues) such as sales risk and operating risks and financial risks (uncertainty of net income and net cash flows attributed to the use of financing that has a fixed cost such as debt and leases) IE company that relies heavily on debt financing instead of equity financing is assuming a great deal of financial risk
- Pure play method - using a comparable publicly traded company’s beta and adjusting it for financial leverage differences
- comparable company = company with same business risks
- analysts must make adjustments to accounts for differing degrees of financial leverage through a process of unlevering and levering the beta
- beta of comparable first unlevered by removing effects of financial leverage. unlevered beta is often referred to as asset beta
Bequity = Basset (1+ ((1-t)D/e)
Bleverageproject = Bunleveragecomparable [1+((1-tproject) d/e)]
- asset risk does not change with higher debt to equity ratio. equity risk rises with higher debt
