Risk, Return and Capital Budgeting
The Hurdle Rate – The minimum rate of return that must be met for a company to undertake a
The Weighted Average Cost of Capital (WACC)
-The hurdle rate for capital budgeting decisions
-Return on the project must EXCEED return required by provides of capital
rb= before tax cost of debt
ri= rb(1 – Tc) = after tax cost of debt
rps after tax cost of preferred shares
rs– return required by shareholders
w j proportion of debt, equity and preferred shares in the firm, based on market values of
capital structure after financing has been raised
k = rWACC= ri debt rps +ps
Capital rsW equity Structure Weights
W equity_S_ W debt _B_ W ps_P_
V V V
S = market value of equity (Market
price x number of shares)
P = market value of preferred shares
B = market value of debt
V = value of the firm
Value of the firm (V) = S + B+ +
WACC = r b (1−Tc)( ) + rps
-Need efficient markets
-If project risk = firm overall risk, use firm WACC to evaluate the project
-If project risk ≠ firm overall risk, DO NOT use the firm WACC. We should use a discount rate
that matches the risk of the project
-WACC is a discount rate that matches firm overall risk
Ex. A firm issued bonds 10 years ago at a cost of debt = 12%. The firm currently can issue bonds at a
cost of debt = 10%. Which cost of debt should be used to calculate WACC?
a. 10% *Should be looking forward, NOT back
Ex. A project costs $10M. The firm borrows $10M to fund this project at a before tax cost of debt, rb =
10%. Assume no tax. Assume project risk = firm risk. Firm WACC = 14%. Which discount rate do we use
to evaluate this project?
b. 14% *How a project is funded does not matter in discount rate
What are Efficient Markets?
-A market is efficient if prices quickly reflect all available information about the firm Ex. a) Reactive industries has the following capital structure. Its corporate tax rate is 35%. What is its
Security Market Value Return
Debt $20 M 8%
Preferred stock $10 M 10%
Equity $50 M 15%
b) Passive footwear has a WACC of 12%. Its debt sells at a yield to maturity of 9%, and its tax rate is
40%. Its cost of equity is 15%. If the firm is financed by debt and common equity only,
what fraction of the firrs= Div i g is financed by equity?
P = F x C rb +
The Cost of Equity
-The return that investors require on a stock, s
Capital Asset Pricing Model (CAPM) Valuation
R – R + β (r –
s f m
Determinants of Beta R)f
-Firms whose revenues are highly cyclical have higher β
-Firms that have a high degree of operating leverage have higher β
-Firms with a higher degree of financial leverage have higher β s
β = Covariance
Ex. The Marketretention,firmretention Bedrock Corporation’s common stock
has a beta of 1.4. IfVariable(marketretention) and the market risk premium is 9%, what is Bedrock’s cost of
YTM = coupon +
Dividend ¿of coupon payments Valuation
¿ ( ) -To solve for r s the firm’s cost of equity:
-Growth rate is usually unknown; estimate it from past growth or use analysts’ forecasts of future
Ex. The Chilton Oil Co. just issued a dividend of $3 per share on its common stock. The company is
expected to maintain a constant 5% growth rate in its dividends If the stock sells for $60 a share, what is
Chilton’s cost of equity?
Ex. Stock in Eddy Industries has a beta of 1.2. The market risk premium is 7.5% and T-bills are currently
yielding 6%. Eddy’s most recent dividend was $3.15 per share and dividends are expected to grow at a
3% annual rate indefinitely. If the stock sells for $27.50 per share, what is your best estimate of Eddy’s
cost of equity?
Cost of Debt
-The interest is tax deductible – we call it the “interest tax shield”
-Tax shield = tax savings
-The interest tax shield reduces the cost of debt
-ri= rb(1 – T )cis the after tax cost of new debt
Ex. Consider a firm that borrows $1 million at 9%. The corporate tax rate is 40%. What is the cost of debt
to this firm?
F = face value of the bond (typically $1,000)
n = number of years until the bond matures C = annual coupon rates
rb= the NOMINAL return required by investors. Also the YTM
P = the market price of the bond
*To get the semi-annual, divide r by b and
multiple n by 2
Bonds & Yield to Maturity
-The yield to maturity is the market interest rate that equates a bond’s present value of interest
payments and principal repayment with its price
YTM = C P = F Trade at par
YTM > C P < F Trade at discount
YTM < C P > F Trade at premium
Ex. An investor is considering an investment in one of two bonds which have the same yield to maturity of
9%. Both bonds pay semi-annual coupons.
Bond 1 has a coupon rate of 10% and 15 years to maturity. [premium]
Bond 2 has a coupon rate of 8% and 25 years to maturity. [discount]
Without undertaking any calculation, which bond will trade at premium? Which bond will trade at
Price both bonds.
Suppose there exists a 3 bond, bond 3. If bond 3 trades at par, what is its coupon rate?
Yield to Maturity Approximation
Ex. In the mid 1990’s Union Gas had an annual bond outstanding with 27 years to maturity and a coupon
rate of 8.65%. The bond was currently selling for 134.58% of its face value. Union Gas’ tax rate is 35%.
What is Union Gas’ (approximation) cost of debt?
Ex. Armstrong Inc. is planning to issue new debt. Armstrong can currently issue debt that has an annual
coupon rate of 10%, pays interest semi-annually