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Reading 33: Cost of Capital (Weight Average Cost of Capital (WACC)…
Reading 33: Cost of Capital
Weight Average Cost of Capital (WACC)
\(WACC = W_{d}\times k_{d}\times (1-t)+W_{p}\times k_{p}+W_{e}\times k_{e}\)
Calculating Cost of Debt \(k_{d}\)
The Yield-to-maturity approach: \(k_{d}\) is the YTM on the firm's existing publicly-traded debt.
The Debt-rating approach: using market yield for debt with same rating and average maturity as the firm's existing debt. (for non-publicly-traded companies)
If interest is not tax-deductible, after-tax cost of debt = before-tax cost of debt = \(k_{d}\)
If tax deduction for interest is capped, use pretax cost for a project if it will require the firm's interest costs to exceed the maximum
For firms that use floating-rate debt (not having a fixed rate of interest over the life of the debt), estimate cost of the firm's debt using the yield curve and firm's debt rating
Calculating Cost of Preferred Stocks \(k_{p}\)
\( k_{p} =\frac{Dividend_{ps}}{Price_{ps}}\)
Calculating Cost of Equity Capital \(k_{e}\)
\(k_{e}\) is the required return rate on the firm common stock.
Estimating approaches (3)
(1) Capital Asset Pricing Model (CAPM) Approach
: \(k_{e}=R_{f}+\beta \times [E(R_{mkt})-R_{f}]\)
Calculate beta \(\beta\)
Pure-play method
When a project risk differs from that of the firm's average projects
Step 1: Estimate the beta for a comparable (pure play) company
Step 2: Un-lever the beta to get the asset beta, using the marginal tax rate and debt-to-equity ratio OF the comparable company:
\(\beta_{asset}= \beta_{pure.play}\times \frac{1}{1+(1-t_{pure.play})\times \frac{D_{pure.play}}{E_{pure.play}}}\)
Step 3: Re-leverage the beta using marginal tax rate and debt-to-equity ratio OF the firm considering the project:
\( \beta_{project}=\beta_{asset}\times \left [ 1+(1-t_{project})\times \frac{D_{project}}{E_{project}} \right ]\)
(2)Dividend Discount Model (DDM) Approach
: \( k_{e} =\frac{Dividend}{Price_{e}} + g\)
g: firm's expected constant growth rate = ROE x (retention rate)
(3) Bond-yield-risk-plus-premium approach
Add a risk premium to the market yield on the firm's long-term debt.
\(k_{ce}\) = bond market yield + risk premium
It assumes that investors require a higher return on a firm's equity than on its debt
based on judgement → imprecise
Target Capital Structure
Target Capital Structure: is the proportions (based on market values) of debt, preferred stock, and equity that the firm expected to achieve over time
How do analysts determine target weights?
Can use stated targets of firm management.
Can use existing capital structure weights
Can adjust existing weights for firm trends
Can use industry average weights
Definition: The overall opportunity cost of the firm's capital is a weighted average of the opportunity costs of capital from debt, preferred equity, and common equity
Project should be undertaken only if the return of invested capital (IRR) is greater than its opportunity cost
terminology
\(k_{d}\): Yield-to-maturity on existing/ new debt; This is the before-tax cost of debt
\(k_{d}(1-t)\): After-tax cost of debt, where
t
is the marginal tax rate; only interest on debt is paid pre-tax
\(k_{ps}\): Cost of preferred stock
\(k_{ce}\): Cost of common equity
Role of WACC
WACC is the appropriate discount for projects that have the same level of risk as the firm's existing projects
For a project with greater-than-average risk, use a discount rate greater than the firm's existing WACC
For a project with below-average risk, use a discount rate less than the firm's WACC
Marginal Cost of Capital & Investment Opportunity Schedule
Marginal Cost of Capital (MCC)
MCC curve is UPWARD SLOPING: the larger amount of capital needed, the higher the Marginal Cost of Capital (more costly to raise more money)
should be used as discount rate when calculating project NPV for capital budgeting decisions.
Adjustment to the cost of capital is necessary if the project differ in risk from the average risk of existing project.
MCC is the cost of an additional dollar of capital, the WACC for raising an additional dollar of capital
Investment opportunity schedule
shows the expected return (vertical axis), and the initial investment amounts for a firm's potential project (horizontal axis)
IOS is DOWNWARD SLOPING: the larger amount of capital needed the lesser the expected return would be.
Optimal Capital Budget
Is the intersection between the Marginal Cost of Capital and the Investment Opportunity Schedule (optimal capital budget and optimal rate of return)
Usually MCC and Investment Opportunity is stair-shape
the breakpoint shows the amount of new capital investment at which WACC increases because one of its component cost of capital increases
Breakpoint= \(\frac{Amount.Of.Capital.At.Which.The.Component's.Cost.Of.Capital.Changes}{Weight.Of.The.Component.In.The.Capital.Structure}\)
Break point for debt = \( \frac{Cost.Of.Debt.Increased}{W_{debt}}\)
Break point for equity = \( \frac{Cost.Of.Equity.Increased}{W_{equity}}\)
Raising capital above the breakpoint (whether for debt or for equity) will cause the cost of component to increase, causing WACC to jump up
Country risk premium (CRP)
Should be added to the market risk premium in the CAPM to reflect the added risk associated with investing in a developing market.
CRP = Sovereign Yield Spread x \( \frac{Annualized.Standard.Deviation.Of.Equity.Index}{Annualized.Standard.Deviation.Of. Sovereign.Bond.Market.In.Term.Of.Developed.Market.Currency}\)
Country must have sovereign bonds denominated in developed market currency
Flotation Cost
Correct way: To increase a project initial cash outflow to include flotation costs when computing NPV
Flotation cost is the cost to issue new equity, charged by investment bank
Incorrect way: Increase the cost of equity
To include flotation cost to NPV
Step 1: Find WACC
Step 2: Find Flotation cost (to raise such amount of equity)
Include such flotation cost into NPV calculation
