ch. 12-1 ~ 12-2 geothermal's cost of capital

8/2/2019 Ch. 12-1 ~ 12-2 Geothermal's Cost of Capital

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Ch. 12 The Cost of Capital

12-1 Geothermals Cost of Capital

Geothermals market value balance sheet

Market Value Balance SheetAssets (V) $647 | Debt (D) $194 (30%)

| Equity (E) 453 (70%)

$647 $647

Geothermal is a business.

=> value of business = value of theportfolio of all firms debt and equity securities

riskof business = risk of theportfolio

invetors required rate of return on business = investors required rate of returnon theportfolio

= the company cost of capital

Example: rD = 8%, rE = 14%

=> the portfolio return = 0.38% + 0.714% = 12.2%

=> rA (the company cost of capital) = 12.2%

12-2 The Weighted-Average Cost of Capital

estimating company cost of capital as a weighted average

The company cost of capital (rA) is the weighted average of the returns demanded by

debt and equity investors:

)()( EDA rV

Er

V

Dr +=

The return is also called the weighted-average cost of capital (the WACC

).

Notes: 1) Recall the definition of the company cost of capital: the opportunity cost

of capital for the firms existing assets.

2) The WACC is a way of estimating the company cost of capital.

taxes and the WACC

Interest payments on debt securities are deducted from income before tax is

calculated. A simple Income Statement:

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Sales $100

- Costs of Goods Sold -70

Operating Income $30

- Interest Expense -10

Taxable Income $20

the after-tax cost of debt (the after-tax rD):

Geothermals cost of debt (rD) = 8%

With a corporate tax rate (TC) of 0.35, the income tax that the firm pays

is reduced by 35% of its interest expense (i.e., reduced by 35%$30 = $10.5).

=> the after-tax cost of debt = pretax cost of debt (1 corporate tax rate)= rD (1 - TC) = 8% (1 0.35) = 5.2%

=> the WACC (rA) = )(])1([ EDC rV

ErT

V

D+

= [0.3(1 0.35) 8%] + (0.714%) = 11.36% 11.4%

more sources of financing

the WACC (rA) = )()(])1([ EPDC rV

Er

V

PrT

V

D++

, where V = D + P + E,

P = preferred stock ()

example: estimating Executive Fruits WACC

the value of debt (D) = $4 million r D = 6%

the value of preferred stock (P) = $2 million rP = 12%

the value of common stock (E) = $6 million rE = 18%

the corporate tax rate (TC) = 35%

What is the Executive Fruits WACC?

We find that: V = $12 million, and D/V = 0.33, P/V = 0.17, and E/V = 0.5.

The WACC is given by [0.33(1-0.35)6%] + (0.1712%) + (0.518%) = 12.3%.

example: evaluating Geothermals proposed expansion at its WACC (rA):

The proposed expansion costs $30 million and generates a perpetual cash flow of

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$3.42 million per year. A simple cash-flow worksheet might look like this:

Revenue $8.34 million

- Operating Expenses - 3.08

Pretax Operating Cash Flow $5.26- Tax at 35% - 1.84

After-tax Cash Flow $3.42 million

With an investment of $30 million (C0 = $30 million), the internal rate of return

(IRR) on this perpetuity () is exactly 11.4%:

rate of return = 3.42/30 = 11.4%

a note: Recall the definition of the IRR in Section 11-2:

The IRR for the project is the discount rate at which NPV equals zero.

0)1(

...)1(

...)1()1(

0221 =

+++

+++

++

+= C

IRR

C

IRR

C

IRR

C

IRR

CNPV

T

T

t

t

In this perpetuity example, we see:

0)1(

01

0 = =

+

=

=

C

IRR

CC

IRR

CNPV

tt => 114.0

30

42.3

0

===

C

CIRR

Recall in Section 12-1 that Geothermals WACC is 11.4%. Since the rate of return

(the IRR) on the expansion project is exactly the same as the WACC, its NPV is

zero. To see this, we could also calculate the projects NPV:

030114.0

42.3

)1(000 = ==

+=

=tt

Cr

CC

r

CNPV

, where r = the WACC.

assumption in the example:

When we calculated Geothermals WACC, we recognized that the companys debt

ratio was 30%. (Recall in Section 12-1 that Geothermas D/V is 0.3.) When

Geothermals analysts use the WACC to evaluate the new project, they are

assuming that the $30 million additional investment would support the issue of

addition debt equal to 30% of the investment, or 0.3$30 = $9 million. The

remaining $21 million is provided by the shareholders.

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The following table shows how the cash flows would be shared between the

debtholders and shareholders:

Revenue $8.34 million

- Operating Expenses - 3.08Pretax Operating Cash Flow $5.26

- Interest Payment (0.08$9) -0.72

Pretax Cash Flow $4.54

- Tax at 35% - 1.59

After-tax Cash Flow $2.95 million

Geothermal needs to pay interest of 8% (rD = 8%) of $9 million, which comes to

$0.72 million. Shareholders are left with $2.95 million, just enough to give themthe 14% return (rE = 14%) that they need on their $21 million investment. (Note

that $2.95/$21 = 0.14).

summary in this expansion example:

If a project has zero NPV when the expected cash flows are discounted at the

WACC, then the projects cash flows are just sufficient to give debtholders and

shareholders the returns they require.

question: the effect of D or D/V

D/V => financial risk (since default risk)

=> the risk of debt => rD

=> rE

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ch. 12-1 ~ 12-2 geothermal's cost of capital

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