FIN 614
Pricing the Capital Structure
Professor Robert B.H. Hauswald
Kogod School of Business, AU
Weighted Average
Cost of Capital
• Investors’ risk perceptions determine prices
– firms face different sources of risks
– risk varies with capital structures: endogenous
• Given capital structure: what is its price?
– pricing rule pre-requisite for capital structure design
– yields “opportunity” cost of funds for a firm, and thus
its discount rate used in NPV calculations
– solution to discount rate selection puzzle
• What is a firm’s Asset Beta & how do we lever
Asset Betas and unlever Equity Betas?
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Project Assessment
• So far, focus on cash flows: open questions
– projects differ in riskiness: pricing risk?
– choosing the “right” discount rate: dangers?
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Cost of Capital and Required
Rate of Return (RoR)
• Cost of capital - required return - appropriate
discount rate
– all denote the same opportunity cost of using capital
– compared to alternative investment in the financial
market having the same systematic risk
• Different perspectives on the same numbers
– required return: from an investor's point of view
– cost of capital: same return from the firm's point of view
– appropriate discount rate: same return yet again to be
used in a present value calculation
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Required (rate of) Return
•
From investors to corporate decision making
–
a firm’s cost of capital (discount rate) is determined by
investors’ willingness to fund firm and, ultimately, by
investors’ required rate of return (RoR): price of funds
–
•
How much can the firm afford to offer:
–
•
depends on return to investment decisions!
NPV of a project is dependent on:
1. expected cash flows
2. riskiness of cash flows
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Determinants of RoR
•
Put yourselves in investors’ shoes:
–
–
what are investors’ concerned about?
so, what should firms worry about?
1. Real or inflation-adjusted rate of interest to
compensate for the TIME VALUE OF MONEY
2. An inflation premium - equal to expected
inflation
3. A Premium for systematic risk
4. Amount of systematic risk (beta)
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Market Returns
• Rates of returns are determined in markets
–
–
on the basis of supply, demand and risk, i.e.,
Volume and risk: expected rate of return on
productive investments in the economy
demand for (financial) capital
supply of available capital to exploit investment
opportunities
risk preferences of investors
–
–
–
• These items are given in the market place
–
firms can take these as exogenously given: outside of
their control
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Financial Policy and Cost of
Capital
• Capital structure: a particular combination of debt
and equity (several instruments)
– for the moment we take it as given: choosing a capital
structure is discussed in subsequent lectures
• A firm's cost of capital will reflect the average
riskiness of all its securities: perspective?
– less risky (bonds) or more risky (common stock)
– calculated as a weighted average of the various
components
• WACC - Weighted Average Cost of Capital
– discount rate used by firm to value investment projects
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Weighted Average Cost of
Capital: WACC
•
•
•
•
•
•
•
•
E, S: the market value of the firm's equity (# shares x price per share)
re, rs = required rate of return for equity - (Expected Return).
D, B - market value of the firm's debt (# bonds x price per bond)
rd , rb = required rate of return for debt (YTM).
V = E + D combined market value of firm's equity and debt,
Capital structure weights: E/V and D/V
tc = marginal corporate tax rate (given after-tax cash flows).
WACC - the overall return the firm must earn on its assets to maintain
the value of its stock.
WACC =
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WACC
E
D
re + rd ( 1 − t c )
V
V
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Equity Capital
Firm with
excess cash
Pay cash dividend
Shareholder
invests in
financial
asset
A firm with excess cash can either pay a
dividend or make a capital investment
Invest in project
Shareholder’s
Terminal
Value
Because stockholders can reinvest the dividend in risky financial assets,
the expected return on a capital-budgeting project should be at least as
great as the expected return on a financial asset of comparable risk.
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The Cost of Equity
• From the firm’s perspective, the expected
return is the Cost of Equity Capital:
R i = RF + βi ( R M − RF )
• To estimate a firm’s cost of equity capital, we need
to know three items:
1. The risk-free rate, RF
− RF
Cov ( Ri , RM ) σ i , M
= 2
3. The company beta, βi =
Var ( RM )
σM
2. The market risk premium, R M
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IRR
Project
Estimating Risk-Adjusted Discount
Rate for Projects: the SML
30%
5%
Good
A
project
SML
B
Bad project
C
Firm’s risk (beta)
2.5
An all-equity firm should accept a project whose IRR
exceeds the cost of equity capital and reject projects
whose IRRs fall short of the cost of capital.
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WACC: Water's Beginning
• Water's Beginning has
– 1 million shares of common stock outstanding: price
$12 per share
– outstanding bonds: 10 years to maturity, a total face
value of debt = $5 million, face value per bond of
$1,000, current price = $985 with a coupon rate of 10%.
– The risk-free rate is 7%, and analysts' expected return
for the market is 14%.
– Water's Beginning stock has a beta of 1.2 and is in the
34% marginal tax bracket.
• What is the ROE? What is its WACC?
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Solution
• Capital structure weights:
–
–
–
–
–
market value of equity = 1,000,000 x $12 = $12,000,000
market value of debt = $5,000,000 x .985 = $4,925,000
V = $12,000,000 + $4,925,000 = $16,925,000
D/V = $4,925,000/$16,925,000 = .29 or 29%
E/V = 1 - D/V = 1 - .29 = .71 or 71%
• Cost of equity:using the SML approach:
– E(re) = rf + β[E(rm) - rf] so,
– E(re) = 7% + 1.2x(14% - 7%) = 7% + 8.4% = 15.4%
• Cost of debt: YTM on the debt is 10.25% before taxes
• Weighted average cost of capital:
– WACC = .71 x 15.4% + .29 x 10.25% x (1 - .34) = 12.9%
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Divisional and Project WACC
• Often, corporations need to assess specific
projects: stand-alone principle
• The SML and the WACC
– WACC: appropriate discount rate only if the proposed
investment is similar to the overall existing business
– WACC for a project that is much like to the rest of the
firm is the same as that for the firm
• What happens if the project is not comparable?
– need project or division specific WACC
– where from?
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Project
IRR
WACC Problems: Firm vs. Project
The SML can tell us why:
SML
Incorrectly accepted
negative NPV projects
RF + β FIRM ( R M − RF )
Hurdle
rate
rf
βFIRM
Incorrectly rejected
positive NPV projects
Firm’s risk (beta)
A firm that uses one discount rate for all projects may
over time increase the risk of the firm while decreasing
its value: holds both for ROE and, hence, WACC
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Example: Conglomerate Co.
• Suppose the Bad Conglomerate Company has a cost of
capital, based on the CAPM, of 17%. The risk-free rate is
4%; the market risk premium is 10% and the firm’s beta is
1.3.
17% = 4% + 1.3 × [14% – 4%]
• This is a breakdown of the company’s investment projects:
1/3 Automotive retailer β = 2.0
1/3 Computer Hard Drive Mfr. β = 1.3
1/3 Electric Utility β = 0.6
average β of assets = 1.3
When evaluating a new electrical generation investment,
which cost of capital should be used?
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SML
IRR
Project
Capital Budgeting & Project Risk
24%
Investments in hard
drives or auto retailing
should have higher
discount rates.
17%
10%
Firm’s risk (beta)
0.6
1.3
2.0
r = 4% + 0.6×(14% – 4% ) = 10%
10% reflects the opportunity cost of capital on an investment in
electrical generation, given the systematic risk of each project
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Divisional Cost of Capital
• Different operating divisions with different risks
– WACC is an average of the divisional required returns.
– find cost of capital for different risks within same firm
• Portfolio: T-bills, corporate bonds, stocks
– equal amount invested in each with average return of
5%, 10%, 15% respectively
– average portfolio return will have been 10%.
• Evaluate new investments at average return of
10%??
– say T-bills offering 7% and stocks 13%
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The Pure Play Approach
• Consider a company that has a single line of
business
– find the required return on a near substitute investment
• Using the Pure-Play approach we find a similar company
– problem: that “similar” company may have different
amounts of debt: equity risk is different
– answer: adjust beta!
• Solution: lever and un-lever Betas and get “asset”
Beta
– adjust ROE calculation for differences in capital
structure
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Financial Leverage and Beta
• Operating leverage refers to the sensitivity to the
firm’s fixed costs of production.
• Financial leverage is the sensitivity of a firm’s
fixed costs of financing.
• The relationship between the betas of the firm’s
debt, equity, and assets is given by:
β Asset =
Debt
Equity
× βDebt +
× βEquity
Debt + Equity
Debt + Equity
• Financial leverage always increases the equity beta relative
to the asset beta.
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Levering and Unlevering Betas
• Notation: m is for the market, d is for debt, E is
for Equity, A is for Assets
• Focus on returns: comp-comp analysis
– use competitor’s asset beta to get divisional asset beta
– then “re-lever” at OUR target debt ratio
• Example: GE engine division and Pratt-Whitney
(PW) aircraft engines.
– assume they have the same asset beta (reasonable?)
β AGE engines = β APW
– what is the Asset Beta βA for PW? let’s find out…
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Finding Asset Beta
• Use asset beta of “comparable firm:” PW
• However, all we know is the equity beta of PW
– solve for the relationship between asset and equity beta
β APW
E
 D

Cov  rd + re , rm 
Cov(r A ,rm )
V
V


= ASSET BETA =
=
Var(rm )
Var ( rm )
=
D
E
E PW
β d + βe =
βe
V
V
V
– using βd = 0 in last step: riskless debt assumption
– since we can derive the equity Beta for Pratt- Whitney using stock
market data BACK OUT the Asset Beta βA for Pratt Whitney
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Divisional Equity Beta
• Assume equal asset betas for GE and Pratt-Whitney: i.e.,
βAGE engines = βAPW
• Final step to get GE’s divisional equity beta: lever the asset
beta at GE’s target capital structure
β eGE =
V GE
 D
β A ⇒ β eGE = 1 +  β APW
E
 E
• To include taxes simply add a (1- corporate tax rate) = (1-tc)
D
to the formula:
β GE
= (1 + ( )(1 − t c )) β GE
e
A
E
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Levering and Unlevering Betas
1. Find comparator company: Pratt&Whitney
2. Calculate comparator’s asset beta:
β APW =
D
E
E PW
β d + βe =
βe
V
V
V
3. Calculate GEE’s divisional beta (reverse of
second step): β AGE engines = β APW
4. Assume equal asset betas for GE and PrattV
 D
Whitney:
β eGE = β AGE ⇒ β eGE = 1 +  β AGE
E
 asset
5. To find divisional beta,Esubstitute in PW’s
V
 D
beta:
β eGE = β AGE ⇒ β eGE = 1 +  β APW
E
 E
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WACC and Capital Budgeting
• WACC represents the appropriate discount rates for
projects that:
– are similar systematic risk to the whole firm
– but: carbon copies are not likely in most cases
• In addition, differential project maturities and risks
– require: differential rates
• Remember WACC is the rate that must be earned
on investments to repay providers of capital
– how do we know? risk adjustments
– opportunity cost of capital
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The Subjective Approach
• What happens when no “pure play” exists?
– art and science: combine assessment and CAPM
• Use the SML and a subjective approach
– assign investments to "risk" categories that have higher
and higher systematic risk
– market concerned with systematic/undiversifiable risk
– assigning an investment's total risk to a risk category,
the risk categories may not line up with the SML
• Pitfalls of discount rate selection: be careful!
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Art and Science in WACC
– Consider a firm with high systematic risk in its
usual business
– The firm is considering adding a new product
line with low systematic risk
– A conventional subjective scheme might assign
a higher discount rate to the new product line
and a lower one to any expansion of existing
business, just the opposite of the financial
market's evaluation
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Summary
• Risk attitudes vary between firms (management)
and investors (debt- and share-holders)
– an individual firm’s risky investment might not be what
the financial market considers a risky investment
• When a firm has different operating divisions with
different risks, its WACC is an average of the
divisional required returns
– to find the NPV of individual projects use a discount
rate appropriate for that projects level of risk - not the
whole company discount rate
• Art and science of discount rate selection
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Appendix:
The Cost of Capital with Debt
• The Weighted Average Cost of Capital
is given by:
rWACC =
Equity
Debt
× rEquity +
× rDebt ×(1 – TC)
Equity + Debt
Equity + Debt
rWACC =
S
B
× rS +
× rB ×(1 – TC)
S+B
S+B
• It is because interest expense is tax-deductible that
we multiply the last term by (1 – TC)
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International Paper’s Cost of
Equity Capital
• The industry average beta is 0.82; the
risk free rate is 8% and the market risk
premium is 9.2%.
• Hence, the cost of equity capital is
re = RF + βi ( R M − RF )
= 8% + 0.82 × 9.2%
= 15.54%
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IP’s Cost of Capital
• The yield on the company’s debt is 8% and the
firm is in the 37% marginal tax rate.
• The debt to value ratio is 32%
 S 
 B 
rWACC = 
 × rS + 
 × rB × (1 − TC )
S+B
S +B
= 0.68 × 15.54% + 0.32 × 8% × (1 − .37)
= 12.18%
12.18 percent is International’s cost of capital. It should be
used to discount any project where one believes that the
project’s risk is equal to the risk of the firm as a whole, and the
project has the same leverage as the firm as a whole.
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