1

COST OF CAPITAL

WEIGHTED AVG COST OF CAPITAL (WACC)

r = wdrd + were

wd = proportion of assets funded by debt

rd = After-tax cost of debt

we = proportion of assets funded by equity

re = cost of equity

2

COST OF CAPITAL

rd = 10% rp = 15% re = 18%

wd = 40% wp = 10% we = 50%

Proof: Firm raises $100 -- Buys an Asset

Asset earns $14.50:

Debt: $40 @ 10% = $ 4.00

Prefs: $10 @ 15% = $ 1.50

Equity: $50 @ 18% = $ 9.00

Total $14.50

WACC = 40(.10)+10(.15)+50(.18)= 4 + 1.50 + 9= 14.50%

3

COST OF CAPITAL

WEIGHTS:• BOOK VALUE

• MARKET VALUE

• TARGET

COSTS:• HISTORIC

• CURRENT (MARGINAL)

4

COST OF CAPITAL

ESTIMATING COSTS

DEBT: BANK RATE

YIELD TO MATURITY ON BONDS

Find the IRR on the bond: PV=Price

FV = 1000

Payment = Coupon/2

N = #years * 2

Return you get (irr) is a six month return

Yield to maturity = rd = 2*irr

Note: Strictly, rd = (1+irr)2 - 1

5

COST OF EQUITY

Constant Growth Model:

re = DY + CGY

DY = Dividend Yield

CGY = Capital gains Yield (Growth)

Capital Asset Pricing Model

re = rf + (Mkt Premium)

rf = Risk Free Rate

= Relative Riskiness of Firm

Mkt Prem =Risk Premium Paid on Average Company

= rmkt - rf

6

Example: Kelloggs

Weights: Book Value %Debt 2802.6 73.8Equity 997.5 26.2

-------- -------3800.1 100.0-------- -------

Mkt Value %

Debt 2802.6 14.9Equity 16029.0 85.1(411*39) --------- -------

18831.6 100.0---------- -------

7

Kellogg’s Costs

Debt: Bank Rate: 8.0%

rd = 8.0 * (1-0.34) = 5.28%

Equity: CGM: re = DY + CGY

= 0.90(1.08)/39 + .08

= .025 + .08

= 10.5%

CAPM: re = rf + (Mkt Premium)

= 6.00 + 0.73(6)

= 6.00 + 4.38

= 10.38%

8

Kellogg’s WACC

BV Weights

WACC = .738*5.28 + .262*10.38

= 3.90 + 2.72

= 6.62%

MV Weights

WACC = .149*5.28 + .851*10.38

= 0.79 + 8.83

= 9.62%

9

FINANCIAL STRUCTURE

Firm U: All equity FIRM; 400 shares at $1 each

Firm L: 50% debt at 10% 50% equity: 200 shares at $1

Economic Expansion Economic RecessionFirm U Firm L Firm U Firm L

Sales 500 500 150 150COS (300) (300) (90) (90)Gross Pft 200 200 60 60SGA (100) (100) (100) (100)EBIT 100 100 (40) (40)Interest - (20) - (20)Taxable Inc 100 80 (40) (60)Taxes (40) (32) 16 24N/Inc 60 48 (24) (36)

OROA 25% 25% -10% -10%ROA 15% 12% -6% -9%ROE 15% 24% -6% -18%EPS 0.15 0.24 -0.06 -0.18

10

LEVERAGE

Effect of Leverage

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

(150) (100) (50) 0 50 100 150 200 250 300 350 400 450 500

EBIT

EP

S

EPS-L EPS-U

11

EFFECTS OF LEVERAGE ON BETA

asset = unlevered = WE* equity

tgt = asset / WE;tgt

port = w11 + w22 + w33

12

Target Cap Structure: 25% Debt, 75% Equity

asset = unlevered = (E/V)* equity

= .851 * 0.73

= .621

tgt = (V/E)tgt* asset

= (1/.75) * .621

= 1.33 * .621

= .828

Example: Kelloggs

13

re = rf + (Mkt Premium)

= 6.00 + 0.83(6)

= 6.00 + 4.98

= 10.98%

WACC = .25(5.28) + .75(10.98)

= 1.32 + 8.24

= 9.56%

Example: Kelloggs