Cost of Capital
Wacc
• Assumptions - Optimal Capital Structure
capital structure is not changing overtime
𝐹𝐶𝐹𝑡
NPV = -𝐼0 + Σ𝑡
(1 + 𝑤𝑎𝑐𝑐𝑡 )
ValueFirm = Σ𝑡
𝐹𝐶𝐹𝑡
(1 + 𝑤𝑎𝑐𝑐𝑡 )
Free Cash Flows to Firm
• FCF
These are the cash flows to be paid to all capital suppliers
ignoring interest rate payments
(i.e., as if the project(firm) were 100% equity financed).
FCF = EBIT(1-tc) +D -Δnoncash NWC - CAPEX
Cost of Capital
“The cost of capital of an asset depends primarily on the risk of
that asset
The cost of capital is asset-specific
Formula
𝑊𝑎𝑐𝑐 = 𝐾𝐷 (1 −
𝐷𝑒𝑏𝑡
tc)
𝐷𝑒𝑏𝑡+𝐸𝑞𝑢 𝑖𝑡𝑦
+
𝐸𝑞𝑢𝑖𝑡𝑦
𝐾𝐸
𝐷𝑒𝑏𝑡+𝐸𝑞𝑢 𝑖𝑡𝑦
𝑊𝑎𝑐𝑐 = 𝐾𝐷 (1 − 𝑡𝑐) 𝑊𝐷 + 𝐾𝐸 𝑊𝐷
Optimal Capital Structure Weights
Cost of Debt
Before Tax Cost of Debt :
𝐾𝐷
→It reflects the return that debt-holders require on their
investment (YTM)
or
the risk-free rate plus a default spread given actual debt rating
→ The cost of debt is mainly determined by two factors
- Current level of interest rates
- Rating of the company (if available)
Cost of Debt (cont’d)
If you do not have ratings for the debt. There are alternatives:
→ Use the rate at which it can borrow from local banks
→ Estimate the YTM on a portfolio of bonds with similar credit
ratings and maturity.
Cost of Debt (cont’d)
Marginal Tax Rate :
tc
→It’s the marginal tax rate of the firm
Cost of Common Equity
• Cost of Common Equity Capital : 𝐾𝐸
The cost of equity is the return that equity investors require on
their investment.
The main approach to estimate the cost of equity is to use a
risk model (CAPM, APT, Gordon…)
We will focus on the CAPM:
𝐾𝐸 = Rf + β ( E(RM ) − Rf )
Risk free rate
• Use short term government rate
• Use long term government rate
• What if the government is not a default-free entity or does not
issue long term bonds?
find the rate at which the largest and safest corporations can
borrow long-term and
reduce the rate by a small default premium (i.e., 0.3%).
Market Risk Premium (MRP)
• The MRP in the CAPM is the difference between
the return of the market portfolio and the risk-free rate
• In general, the MRP
→is greater than zero (risk aversion)
→increases with the risk aversion of the investors
• The risk premium may change over time
Risk Premium (cont’d)
Estimating the Market Risk Premium
Methods:
• Estimate the implied premium in today’s asset prices
• Estimate the market risk premium using historical data
Risk Premium (cont’d)
HISTORICAL Market RISK PREMIUMS FOR THE US MARKET
Arithm.
1928-2017
1968-2017
2008-2017
[Mkt - T.Bill ]
8.09
6.58
9.85
[Mkt - T.Bonds]
6.1
4.24
5.98
Beta
Two approaches to estimate the Beta:
1. Beta estimate based on βS of comparable firms
2. Estimation based on Historical Market data
Return on Stock vs Mkt (like SP500)
Beta?
• If βi > 1
more risky than the market
If βi = 2
Stock i fluctuates twice as much as the market
• If βi < 1
less risky than the market
If βi=.5
• If βi =1
Capital Structure Weights
𝐷𝑒𝑏𝑡
Leverage Ratio
𝐷𝑒𝑏𝑡+𝐸𝑞𝑢 𝑖𝑡𝑦
𝐷𝑒𝑏𝑡
should be the target capital structure (in MV)
𝐷𝑒𝑏𝑡+𝐸𝑞𝑢 𝑖𝑡𝑦
for the particular asset under consideration
• Market Value of Debt is more difficult to estimate
because few firms have only publicly traded debt
There are solutions:
→Assume book value of debt is equal to market value
→Estimate the market value of debt from the book value
Capital Structure Weights (cont’d)
𝐸𝑞𝑢𝑖𝑡𝑦
Equity Ratio
𝐷𝑒𝑏𝑡+𝐸𝑞𝑢 𝑖𝑡𝑦
• Market Value of Equity
→Share price * Shares outstanding
• Assume book value of equity is equal to market value
If firm(project/division) is not publicly traded debt
Capital Structure Weights (cont’d)
Common mistakes
→ Use 100% debt if Asset is all debt financed
→ Use 100% Equity if Asset is all equity financed
𝐷𝑒𝑏𝑡
→ Using
of the firm undertaking the
𝐷𝑒𝑏𝑡+𝐸𝑞𝑢 𝑖𝑡𝑦
project(division) when the risk is different
Example
General Electric’s
businesses:
→Power systems
→Aircraft engines
→Industrial
→Engineered plastics
→Technical products
→Appliances
→Broadcasting
Multidivisional firms
should calculate a
different WACC
for each division
𝐾𝐷
𝐾𝐸 ?
Vive la difference
• If the risk of the project(division) # risk of the firm,
use cost of capital of the project (division)
use comparable firms (Pure Play) to estimate cost of equity
Pure Play
- Find similar risk firms (N firms) that are publicly traded
- Get Beta (βL) for each firm and plug it in
βL(i)= βU(i) (1+(1-tc) D/E(i))
- N firms [βU (1) , ,
…., βU (N) ]
- Compute The average βUnlevered
βU = Σi βU(i) /N i =1,2….N
Hamada Model
Pure Play (cont’d)
- Compute βSL of the project(division) using its own leverage ratio
βL = βU (1+ (1-tc) D/E)
- Compute 𝐾𝐸 of the project
𝐾𝐸 = Rf + β L MRP
Note
Preferred stock
Using the preferred dividend and observed price of preferred stock,
𝐷𝑖𝑣
𝐾𝑃 =
𝑃
𝐷𝑒𝑏𝑡
𝐸𝑞𝑢𝑖𝑡𝑦
𝑃𝑟𝑒𝑓𝑒𝑟𝑟𝑟𝑒𝑑
𝑊𝑎𝑐𝑐 = 𝐾𝐷 (1 − tc) 𝐷𝑒𝑏𝑡+𝐸𝑞𝑢 𝑖𝑡𝑦+𝑃𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑 + 𝐷𝑒𝑏𝑡+𝐸𝑞𝑢 𝑖𝑡𝑦+𝑃𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑+𝐾𝑃 𝐷𝑒𝑏𝑡+𝐸𝑞𝑢 𝑖𝑡𝑦+𝑃𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑