Download Methods to estimate the value of a levered firm

Asset beta – risk of assets, or risk relative to the market if funded 100% with equity (100% equity beta, unlevered beta)
Stock beta – risk of equity, or risk of stock to the market (levered beta, equity beta)
Methods to estimate the value of a levered firm – different ways to account for the value of the tax shield of debt
Estimation
Cash flows used in valuation
Discount rate
Other adjustments
method
used in valuation
Weighted average
Weighted average
100% equity cash flows
cost of capital
cost of capital
(WACC)
100% equity
Add the value of the tax shield
Adjusted present
discount rate,
100% equity cash flows
of debt (which is: present value
value
CAPM using
of interest payments * tax rate)
asset beta
Levered equity
Adjust each cash flow for
Flow to equity
discount rate,
interest payment, tax shield of
method
CAPM using
interest, and principal payments
stock beta
To calculate the WACC, you need
Weights for financing components
Cost to the firm for each financing component
Weight of component 1* required return on component 1 + weight of component 2 * required return on component 2 + etc.
Weight = dollar value of funds raised from that source/total initial investment
Cost of debt financing
Required return on debt adjusted for taxes
Yield to maturity
◦Bond – 10 years, 8% coupon, $10 million face value, $10 million
Yield to maturity is 8% (when bond trades at par, required return equals coupon rate)
◦Amortized loan – 20 year loan, $10 million borrowed, $700,000 per year payment
Present value of an annuity problem
Yield to maturity is interest rate, y, for which PV=PMT*PVIFAy%,t periods
10 million/700k = PVIFAy%,20 years
y ≈ 3½%
◦Zero coupon loan – face value 100 million, receive 45 million, 5 years
Present value of a single payment problem
Yield to maturity is interest rate for which PV=FV*PVIFy%,t periods
45 million/100 million = PVIFAy%,5 years
y ≈ 17.3%
Cost of debt = kd*(1-tax rate), where kd is the yield to maturity
If tax rate is 35%
◦Bond cost is 8%(1-.35) = 5.2%
◦Amortized loan cost is 3½%(1-.35) = 2.275%
◦Zero coupon loan cost is 17.3%(1-.35) = 11.245%
Cost of preferred stock
Required return for preferred stock
kp = Dividend/price
5000 face value, 8% coupon, 4650 price
k = .08*5000/4650 = 8.6%
Cost of retained earnings
Growing perpetuity model (P=D1/(k-g))
ks = D1/P + g = D0(1+g)/P + g
CAPM
ks = kRF + beta*(kmarket –kRF), beta is levered equity or the stock beta
Debt + risk premium
ks = kd + risk premium, no theory to guide choice of risk premium
possibly use: return on market – return on corporate bonds
Cost of new equity
Only the growing perpetuity method works
ks = D1/[P(1-f)] + g, where f is the percentage floatation costs
expected dividend $1.50, price per share $18, floatation costs are 10%, growth rate 5%
k= 1.50/[18*(1-.10)] + 5% = .1426
new project costs $100 million
$30 million from debt
$70 million from retained earnings
yield to maturity on debt 8%
CAPM required return is 15%
Tax rate 35%
Weight for debt = 30%
Weight for equity =70%
Required return on debt = kd(1-t) = .08*(1-.35) = .052
ks= .15
WACC = .30 * .052 + .70 * .15 = 12.06%
Floatation costs
Signaling