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Calculating the Cost of Capital

Three steps to calculate it:

1. Find the required rate of return on each kind of security the firm has issued

2. Find the fraction of the firm’s value financed by each type of security

3. Use the weights in (2) to average the rates of return in (1)

• Note: We use market values of the equity and bonds to determine the weights, not book values.

• Use the rates of return investors are currently demanding.• This is the way investors are currently valuing the firm’s debt

and equity (and therefore, the whole firm.)

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Weighted Average Cost of Capital (WACC)

• Definition: the company’s weighted-average after-tax cost of funds using the current capital structure.

• where– D is the market value of outstanding debt– P is the market value of outstanding preferred shares– E is the market value of outstanding equity– V = D + P + E = the market value of the firm– R is the required market rate of return of each asset– TC is the marginal corporate tax rate

PCDE RV

PTR

V

DR

V

EWACC *))1(*(**

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Solving for WACC

• Problems involving WACC may seem tricky, but become much simpler if you remember a few basic rules.

Solve in Steps!1. What is the value of each kind of finance?

need to find the weights, based on market values.

2. What is the cost of each kind of finance? need to find net cost to the firm (i.e. after taxes)

• Remember all your lessons from the first half on time value of money.• You have to remember how to value bonds, stocks, perpetuities, etc.• You have to know how to solve for the missing information.

• Know how to use CAPM to calculate ’s and required rates of return.• E.g. r for project vs. r for equity; for projects with different degrees of

risk.

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Example: ABC Company

ABC Company Inc.’s balance sheet shows the following (in millions of dollars):

Long Term LiabilitiesLong Term Bank Loan $100Debentures $200

Total Long Term Liabilities $300

Shareholders’ EquityPreferred Shares $150Common Stock $300Retained Earnings $100

Total Shareholder’s Equity $550

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The Gory Details

• The long term bank loan bears interest at prime plus 2%. Prime is currently 5%.

• The debentures have coupon rate of 12%, paid on a semi-annual basis. They will mature in 15 years. The current annual percentage rate on similar financial instruments is 10%.

• There are 1,500,000 preferred shares issued and outstanding with a par value of $100/share. These shares receive a 15% cumulative dividend and are currently trading on the market for $108/share.

• There are 10,000,000 common shares issued and outstanding that are currently trading at $45/share. The last dividend paid was $6.75/share. The company expects that dividends and share prices should grow at a constant 4% rate.

• ABC Company Inc. is a well-established public company with a tax rate of 35%.

Calculate ABC Company Inc.’s weighted average cost of capital.

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Step 1: Find the market values

Bank Loan:• They still owe $100 M. The loan is floating rate.• The market value must be $100 M!

Debentures:• 12%, semi-annual coupon, 15 yr. term, 10% discount rate, $200M

face value.• Coupon payments are $12 M, 30 payments, 5% periodic rate• PV of coupon stream is $184.47 M• Market value of debentures is $230.74 M.

Preferred Shares:• 1.5 M shares outstanding trading at $108/share = $162 M.

Common Shares:• 10 M shares outstanding trading at $45/share = $450 M.

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Find the Weights

• Note that we don’t count retained earnings!• Price of common shares already reflects payout rate.• We assume that the firm keeps doing what its doing.

Total Market Value of the Firm:$100 M + $230.74 M + $162 M + $450 M = $942.74 M

Weights for each source of funds:

• Bank loan = 100 / 942.74 = 10.6%• Debentures = 230.74 / 942.74 = 24.5%• Preferred shares = 162 / 942.74 = 17.2%• Common shares = 451 / 942.74 = 47.7%

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Step 2: Find the cost of each source of funds

Bank Loan:

• cost is prime (5%) plus 2%

• tax rate is 35%

• net cost must be (1 - 0.35) x 7% = 4.55%

Debentures:

• current rate on similar instruments is 10%

• tax rate is 35%

• net cost must be (1 - 0.35) x 10% = 6.5%

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Cost of Funds (cont)

Preferred Shares:

• Market price of $108/share, par value of $100/share, 15% dividend.

• perpetuity formula is PV = C / r , so r = C / PV

• 15 / 108 = 13.89%

• pre-tax cost = after-tax cost.

Common Stock:• market price is $45/share, last dividend $6.75/share, constant

4% growth.• Gordon model is PV = D1 / ( RE - g ), so RE = g + D1 / PV.• 4% + 6.75*1.04 / 45 = 19.60%

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Step 3: Put it all Together

WACC for ABC Company Inc.

Bank Deben- Pref. Commonloan tures Shares Shares Total

Weight 10.6% 24.5% 17.20% 47.7% 100%

Net Cost 4.55% 6.50% 13.89% 19.60%

WACC 0.48% + 1.59% + 2.39% + 9.36% = 13.82%

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Interpreting WACC

How will this help increase the value of the firm?• If NPV@WACC > 0 then the value of the project’s returns to the

market is greater than the value of the securities used to finance it The project increases the firms value

• If NPV@WACC < 0 then the project decreases the firm’s value, because the marginal value of liabilities used to finance it is greater than the marginal value of the assets that it generates.

WACC is not the only way of determining r.• Another way (not taught in this course) is to use the r based on equity

but replace project cash flows with cash flows to shareholders • Scale by debt/equity ratio and payout ratio• This alternative approach typically gives the same answer.• See Annex A to Chapter 14 for details.