MGT 423: Sourcing and Managing Funds
Session 8
Cost of Capital
© Duguay, Rouwenhorst & Thomas
Today’s class
• Define the cost of capital
• Estimate the cost of capital for IBM
• Does leverage affect the cost of capital?
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Cost of Capital for a Company
• Return that the firm needs to offer to its investors
• Separate from (one time) fees paid to investment banks when raising capital
• Different investors (debt, equity) in the company bear different amounts of risk, and
will require (expect) different returns
• Weighted average cost of capital is the return required by the “average investor”
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How are Debt and Equity Different?
• Interest versus dividends
• Priority of claims
• Taxes
• Risk
4
Legend: V = firm (enterprise) value; FCF = free cash flow ; D = market value debt; E = market value equity; NPV = Net Present Value;
Thought Question
Because the equity of IBM is riskier than its debt, the CFO of IBM estimates that the company
cost of equity capital exceeds the cost of debt. Can IBM lower its weighted average cost of
capital by increasing the proportion of “cheap” debt in its capital structure?
5
How do CFOs Measure the Cost of Equity?
6
Cost of Equity
Cost of equity:
• Return that investors require to invest in the equity of the firm
Investor Class:
• Investors require (expect) a return that compensates for the risk of the investment
• Capital Asset Pricing Model: risk = systematic risk or “beta”
• Cost of equity
rE = rF + βE × rP
• rF = risk free rate
• rP = market risk premium
Legend: rE = cost of equity; rD = cost of debt; FCF = free cash flow; rF = risk free rate; rP = market risk premium; V = firm (enterprise) value; FCF = free cash flow
; D = market value debt; E = market value equity
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Cost of Debt
Berk DeMarzo
Chapter 12.4
Return that investors require / expect to invest in the debt of the firm (i.e. lend to the firm).
Several approaches:
•
The interest rate on loans or coupon on bonds that a firm has outstanding
•
The yield to maturity on the debt
•
Use a model to estimate the expected return on the debt, like the CAPM
Legend: rE = cost of equity; rD = cost of debt; FCF = free cash flow; rF = risk free rate; rP = market risk premium; V = firm (enterprise) value; FCF = free cash flow
; D = market value debt; E = market value equity
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Debt Betas are Small for Relatively Safe Debt
See also Modules on Canvas
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Weighted Average Cost of Capital
• Firms use a mix of different capital sources debt and equity to finance their
operations
• The average return required by investors:
r=
E
r
V E
+
D
r
V D
1−t
= WACC
• D, E and V = D+E are market values
Legend: V = firm (enterprise) value; FCF = free cash flow ; D = market value debt; E = market value equity; r = discount rate; rE = cost of equity; rD = cost of
debt; rP = market risk premium; t=marginal corporate tax rate; EBIT = earnings before interest and tax; WACC = weighted average cost of capital
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Weighted Average Cost of Capital – More Details
E
V
D
V
WACC = rE + rD 1 − t
• Discount rate for FCF to all investors combined (i.e. FCFD+E)
• Interest on corporate debt is tax deductible: rD × (1–t)
• Firm maintains a constant proportional capital structure
Legend: V = firm (enterprise) value; FCF = free cash flow ; D = market value debt; E = market value equity; r = discount rate; rE = cost of equity; rD = cost of
debt; rP = market risk premium; t=marginal corporate tax rate; EBIT = earnings before interest and tax; WACC = weighted average cost of capital
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Example: WACC for IBM
IBM’s data
E
D
WACC = rE + rD 1 − t
V
V
E/V = 72.7%
rE = 9.17%
D/V = 27.3%
rD = 3.64%
t = 25%
Calculate IBM’s WACC.
Legend: Vt = firm (enterprise) value in year t; FCF = free cash flow ; A = market value assets; D = market value debt; E = market value equity; r = discount
rate; E[.] = expectation; r = cost of equity; r = cost of debt; t=marginal corporate tax rate
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Calculating the Cost of Capital for IBM: What Data do we Need?
WACC = (E/V) × rE
Market Values of
E & V=D+E
+
(D/V)
× rD
Market Values of
D & V=D+E
× (1 – t)
Corporate tax
rate = 25%
Assume the CAPM
Assume the CAPM
Cost of Equity: rE = rF + βE × rP
Cost of Debt: rD = rF + βD × rP
• βE
• rP : market risk premium ≈ 6.5%
• rF : risk free rate
• βD : for highly rated debt ≈ 0
• rP : market risk premium ≈ 6.5%
• rF : risk free rate
Legend: V = firm (enterprise) value; D = market value debt; E = market value equity; rE = cost of equity; rD = cost of debt; t=marginal corporate tax rate; WACC =
weighted average cost of capital; rp = risk premium on the market portfolio; CAPM = Capital Asset Pricing Model; β = risk according to CAPM
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Collecting Data for IBM’s WACC – 1 (Yahoo Finance 2/9/2023)
Calculations:
• E = 120.519
• D = 54.013 – 8.738 = 45.275
• V = 120.519 + 45.275 = 165.794
• E/V = 120.519/165.794 = 0.727
• D/V = 45.275/165.794 = 0.273
• βE = 0.85
Total Debt
Cash
54,013,000
8,738,000
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The Risk-free Rate (2/9/2023)
• Common assumption: yield to maturity on US government securities
• Use short-term risk-free rate for short-term decisions / long-term rate for long-horizon decisions
• Match risk-free rate to the decision horizon
• Alternative: yield to maturity on highly rated corporate debt
• Yield on safe corporate debt is higher because less liquid
Berk and DeMarzo
Chapter 12.2
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Calculating the Cost of Capital for IBM
WACC =
(E/V) × rE
E/V = 0.727
+
(D/V) ×
rD
D/V = 0.273
× (1 – t)
Corporate tax
rate = 25%
Assume the CAPM
Assume the CAPM
Cost of Equity: rE = rF + βE × rP
Cost of Debt: rD = rF + βD × rP
• βE =
• rP : market risk premium ≈ 6.5%
• rF :
• βD : for highly rated debt ≈ 0
• rP : market risk premium ≈ 6.5%
• rF :
V = firm (enterprise) value; D = market value debt; E = market value equity; rF = risk free rate; rE = cost of equity; rD = cost of debt; t= marginal corporate tax
rate; WACC = weighted average cost of capital; rp = risk premium on the market portfolio; CAPM = Capital Asset Pricing Model; β = risk according to CAPM
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Quiz: Company Risk and Leverage
Suppose IBM increases its leverage (issue more debt
and use the proceeds from the debt issue to buy
back stock).
How will this affect:
1. IBM overall: do its operations become riskier?
2. The risk to investors:
o
o
o
Poll
Equity?
Debt?
All investors combined?
17
18
Capital Structure Changes and
the Risk and Return to Debt and Equity (Combined)
If IBM changes its capital structure to have more debt and less equity:
• Does the overall business risk of IBM change?
• Does the risk to equity investors change?
• Does the risk to debt holders change?
• Does the risk to all investors combined change?
Legend: V, D, & E are market value of firm (enterprise), Debt, & Equity; β = risk according to CAPM (subscripts E, D, & A refer to Equity, Debt, &Assets)
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Asset Beta and the Risk to Debt and Equity Combined
• Overall firm-wide risk: asset beta βA
• Firm-wide risk is shared by investors:
βA = wD βD+ wE βE = (D/V) βD + (E/V) βE
Berk and DeMarzo
Chapter 14.3
• Asset beta = weighted average of the betas of debt and equity
• Firm can change its capital structure (D/V and E/V), but βD and βE will adjust in a way
that keeps βA the same
Legend: V, D, & E are market value of firm (enterprise), Debt, & Equity; β = risk according to CAPM (subscripts E, D, & A refer to Equity, Debt, &Assets)
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The Asset Beta for IBM
• Yahoo publishes IBM’s equity beta, but not its asset beta
• Assuming the IBM’s debt is relatively safe (βD = 0) we can calculate it:
βA = (D/V) βD+ (E/V) βE
= 0.273 × 0 + 0.727 × 0.85 = 0.62
• The asset beta is sometimes called the “unlevered equity beta” βU, because it would be
the equity beta of IBM if it had no debt (financed with 100% equity).
Legend: V, D, & E are market value of firm (enterprise), Debt, & Equity; β = risk according to CAPM (subscripts E, D, & A refer to Equity, Debt, &Assets)
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Recalculating WACC when Leverage Changes
Prior example:
• WACC = 7.41%
• E/V = 72.7%
• D/V = 27.3%
• βA = 0.62
• βD = 0
• rF = 3.64%
• rP = 6.5%
New Example:
• E/V = 60%
• D/V = 40%
• βD = 0
Formula:
• βA = (D/V) βD + (E/V) βE
• WACC = (E/V) × rE + (D/V) × rD × (1 – t)
• t=25%
•
•
rE = rF + βE × rP
rD = rF + βD × rP
Hint:
• Under both scenarios, βA should be the same
→ Calculate IBM’s new WACC
V = firm (enterprise) value; D = market value debt; E = market value equity; rF = risk free rate; rE = cost of equity; rD = cost of debt; t= marginal corporate tax22
rate; WACC = weighted average cost of capital; rp = risk premium on the market portfolio; CAPM = Capital Asset Pricing Model; β = risk according to CAPM
The Equity Beta for IBM at New Leverage
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The Cost of Equity and WACC for IBM at New Leverage
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Summary of IBM’s Cost of Capital
Leverage and WACC of IBM
D/V
E/V
Beta A
Beta D
Beta E
rE
rD
WACC
D/V * t * r D
0.0%
100.0%
0.618
0
0.618
7.66%
3.64%
7.66%
0
10.0%
90.0%
0.618
0
0.687
8.10%
3.64%
7.57%
0.09%
20.0%
80.0%
0.618
0
0.772
8.66%
3.64%
7.47%
0.18%
27.3%
72.7%
0.618
0
0.850
9.17%
3.64%
7.41%
0.25%
40.0%
60.0%
0.618
0
1.030
10.33%
3.64%
7.29%
0.36%
If it were not for taxes, the WACC would not have changed
Tax
advantage
of debt
Legend: V = firm (enterprise) value; D = market value debt; E = market value equity; rE = cost of equity; rD = cost of debt; t=corporate tax rate; WACC =
weighted average cost of capital; Beta = risk according to CAPM
26
Thought Question:
Can CFO Lower Overall Capital Cost by Using More Lower Cost Debt?
• When leverage increases total risk stays the same:
• Asset beta remains the same (risk of the combined FCF to D+E is constant)
• Debt beta remains small (reasonable assumption for safe debt)
• Equity beta goes up (systematic risk borne by smaller shareholder base)
• WACC falls
• Not because “debt is cheap” in the sense of rD < rE
• Because debt has tax advantage, WACC falls by amount of tax subsidy: (D/V) × t × rD
• If it were not for taxes, WACC would have stayed the same
Legend: V = firm (enterprise) value; D = market value debt; E = market value equity; rE = cost of equity; rD = cost of debt; t=corporate tax rate; WACC =
weighted average cost of capital; Beta = risk according to CAPM
27
Leverage, WACC and the Value of IBM
• Effects of increasing leverage for IBM:
• WACC falls
• FCFs can be discounted at a lower rate
→ IBM’s firm value increases
• Value of IBM increases by the (present)
value of the tax shields
Legend: WACC = weighted average cost of capital; FCF = free cash flows
• Preview of next sessions:
• Why is IBM not financed with 100% debt?
• What are the limits to debt financing?
28
Estimating the WACC for a Non-traded Company
Focus of the
THI case
For a company that is not publicly traded:
•
•
the cost of debt can be estimated from interest rates on borrowings
risk (Beta) needed to calculate the cost of equity is unavailable
Solution: Use peer companies that are publicly traded as comparable for risk
-
Think back to the lecture on multiples where we used valuation ratios of peers
How would peers be comparable in terms of equity risk?
•
Equity beta = average equity beta from peers
-
-
works when the peers have similar underlying business risk and leverage as the non-traded entity
Asset beta = average asset beta from peers
-
works when the underlying business risk is comparable to peers
need to adjust for company-specific leverage to calculate the equity beta
Berk and DeMarzo
Chapter 12.6
Legend: V = firm (enterprise) value; D = market value debt; E = market value equity; rE = cost of equity; rD = cost of debt; rP = market risk premium; WACC =
weighted average cost of capital; FCF = free cash flows; PV = present value
29
Review
• WACC is the discount rate used to calculate present value of FCF to all investors
• The risk of the FCF to all investors is determined by the risk of its projects (assets). The amount of risk
is measured by the asset beta: βA
• The capital structure determines how that risk is distributed among different investors. The weighted
average of the risk of debt and equity adds up to the asset beta: βA = (D/V) βD+ (E/V) βE
• In perfect capital markets (no taxes, etc.), a firm cannot change its cost of capital by choosing a
different mix of debt and equity (Modigliani-Miller)
•
Using more “lower cost” debt increases the cost of equity, with offsetting effects on WACC
• The corporate tax code creates a benefit for debt financing.
•
•
“Debt is cheap”, not because interest rates are lower than the cost of equity, but because debt is tax
advantaged.
Increasing leverage lowers the WACC (reduces tax payments) and increases firm value
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Next Session
THI case (cost of capital for a division / private company)
31