WEIGHTED AVERAGE COST OF CAPITAL (WACC):Summary of Formulas

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Financial Management MGT201

Lesson 29

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

Learning Objectives:

After going through this lecture, you would be able to have an understanding of the following topics

· WACC (Weighted Average Cost of Capital)

In this lecture, we are going to talk about the very important component of capital structure which is

known as weighted average cost of capital (WACC).In previous lecture, we have introduced some of the

broad concepts of capital structure. We discuss about the company's ways to raise capital. one of two

basic ways is the equity and the other is debt .The objective of the company is to raise capital at the

lowest possible cost .just as when you go to the market you try to buy things at the lowest possible cost.

Similarly, companies go looking for money in financial markets they try to raise funds at the lowest

possible cost. This means that when the company raises money in the stock market issues that it try to

sell its shares at the price at which it can earn maximum profit .Similarly, when a company go to the

money market to take loan it tries to get the loan at the lowest possible rate of interest .

We mentioned that weighted average cost of capital concept is similar to concept of the required

rate of return which we have discussed earlier lectures. It is also known as opportunity cost and by

opportunity cost we mean "the rate of return that investors sacrifices by investing in the present

investment". So, the rate of return that he can get from the second best of investment is the opportunity

cost or ROR. We used the required rate of return in our present value formula .WACC is similar to the

required rate of return .There is only slight difference between required rate of return and

WACC.WACC only takes into account the practical aspects such as impact of taxes and transaction

costs or flotation costs. .By taxes we mean income tax or corporate tax that the company needs to pay

to the govt. at the end of the year depending upon their net income and transaction associated with the

issuing selling and marketing of the financial securities like stocks and bonds. When we talk about

WACC, we generally include three possible types of capital.

WACC = rDxD + rExE + rPxP

Weighted % Cost of Bond (Debt):

rD XD :

Where rD is the Average Rational Investors' Required ROR for investing in the Bond, XD is

the Weight or Fraction of Total Capital value raised from Bonds = Bond Value / Total Capital

Weighted % Cost of Common Equity:

rE XE :

Where rD is the Average Rational Investors' Required ROR for investing in Common Share,

XD is Weight or Fraction of Total Capital raised from Common Equity. Note that rE is Not the WACC

and Not the ROE (=NI / common stock)

Weighted % Cost of Preferred Equity

rP XP:

Where rP is the Average Rational Investors' Required ROR for investing in Preferred Share, XP

is Weight or Fraction of Total Capital raised from Preferred Equity

Weighted Cost of Debt % = rD XD

Required ROR for Debt

The first term is the rD which is the required rate of return and the cost of debt can be interpreted

as the required rate of return. You will recall that when we were talking about bond pricing that we

also spoke about the over all return on a bond and that is referred to as yield to maturity or YTM.

YTM= interest yield +capital gain yield and it is representative of over all cost of debt in the form of

bond.

Cost of Debt Capital = rD

Practically speaking, Bonds are Issued (or sold) in the Market at a Premium (above Par Value) or

Discount (below Par Value). And, the Issuance of Bonds has Transaction Costs. These transaction

costs include Legal, Accounting, and Marketing and Sales fees. Both these are factored into the Market

Price of the Bond used in PV Formula to calculate the Pre-Tax Cost of Debt Capital = rD*. So, rather

than using Market Price of Debt, use the

Net proceeds = Market Price Transaction Costs

Finally, Debt becomes less Costly because Additional Interest creates a new form of Tax Saving

or Tax Shield.

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After Tax Cost of Debt = rD = rD* (1 - TC)

Where TC is the Marginal Corporate Tax Rate on the Net Income of the Firm

Example:

Company ABC issues a 2 Year Bond of Par Value Rs 1000 and a Coupon Rate of 10% pa (and

annual coupon payments). Company ABC pays an Investment Bank Rs 50 per Bond to structure and

market the bond. They decide to sell the Bond for Rs 950 (i.e. At a Discount). At the end of the first

year, Company ABC's Income Statement shows the Coupon Interest paid to Bondholders as an expense.

Interest represents a Tax Saving or Shield. Based on the Net Income and Industry Standard, the

Marginal Corporate Tax Rate is 30% of Net Income. Assuming that the 2 Year Bond represents the

ONLY form of Capital, calculate the After-Tax Weighted Average Cost of Capital (WACC) % for

Company ABC.

Step 1:

Calculate Required ROR using Bond Pricing or PV Formula

PV = 100/ (1+r*) +100/ (1+r*) 2 +1000/ (1+r*) 2

= 100/ (1+r*) + 1100/ (1+r*) 2

= Net Proceeds = NP = Market Price -Transaction Costs

= 950 - 50 = Rs 900

Solve the Quadratic Equation for Pre-Tax Required ROR = r*

Using the Quadratic Formula: r* = 16% AND r = - 5 %

Step 2:

Calculate After Tax Cost of Debt

rD = rD* ( 1 - TC ) = 0.16 ( 1 - 0.30) = 0.16 (0.70) = 11 . 2 %

Step 3:

Calculate Weighted Cost of Capital (WACC)

WACC = rD XD. + rP XP + rE XE .

= rD XD + 0 + 0

= 11.2 (1) = 11.2 %

Weighted Cost of Preferred Equity = rP XP

Required ROR for Preferred Equity

The important thing to remember is that we calculated the price by using the Perpetuity Formula for

Perpetual Investment & Constant Div

PV = Present Price = Po= DIV1 / r.

So, r = DIV1 / Po. If you use the Actual Observed Market Price for Po then r = Required ROR.

Cost of Preferred Equity Capital = rP

Practically speaking, the process of Legally Structuring, Printing, and Marketing Preferred Share

Certificates costs money in the form of Flotation Costs (including Brokerage and Underwriting Fees).

These Costs are factored directly into the PV or Observed Market Price.

PV = Net Proceeds = Market Price - Flotation Costs

Preferred Stock Dividends are paid out from Net Income After taxes. So they are not Tax Deductible

(unlike Bond Interest Payments).

Example:

Company ABC wants to issue a Preferred Stock of Face Value Rs 10. The Board of Directors has

agreed to fix the Annual Dividend at Rs 2 per share. The Lawyer's fee and Stock Brokers'

Commissions will cost Rs 1 per share. The Preferred Share is floated at Face Value. What is the Cost of

Capital to Company ABC for raising money through Preferred Stocks?

Use Perpetuity Formula to Compute the Required ROR

r = DIV1/ Po = Rs 2 / Rs 10 = 20%

Minor Change in Perpetuity Formula to Compute the Cost of Preferred Equity Capital

Net Proceeds = NP =Price-Flotation Costs =10-1= Rs 9

r = DIV1/ NP = Rs 2 / Rs 9 = 22%

Flotation Costs ADD TO COST of Company Issuing the Preferred Equity Capital

Weighted Cost of Common Equity = rE XE.

Required ROR for Common Equity (or Shares): 2 Approaches

Dividend Growth Model: Gordon Formula (simplified PV Formula) for Perpetual Investment &

Constant Growth in Dividends

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r = DIV1 / Po + g. If you use the Actual Observed Market Price for Po then r =

Required ROR. Now 2 Approaches for proceeding to calculate Cost of Capital:

CAPM (SML Equation) Assuming Efficient Markets

r = rRF + Beta (rM - rRF). Advantage: does not rely on Dividend Forecast

Cost of Common Equity Capital = rE

Most complex cost of capital to calculate

Required ROR on Common Equity NEITHER observable NOR certain unlike Bond Coupon Interest &

Preferred Dividends both of which are fixed

Equity Capital can be raised in 2 Ways and Required ROR and Costs are different for each: (1)

Retained Earnings and (2) Issue of New Common Stock. You can use rE for New Stock or Retained

Earnings (which is lower).

Common Stock Dividends are paid out from Net Income AFTER TAXES. So they are NOT Tax

Deductible (unlike Bond Interest Payments).

Example:

Company ABC wants to issue more Common Stock of Face Value Rs 10. Next Year the

Dividend is expected to be Rs 2 per share assuming a Dividend Growth Rate of 10% pa. The Lawyer's

fee and Stock Brokers' Commissions will cost Rs 1 per share. Investors are confident about Company

ABC so the Common Share is floated at a Market Price of Rs 16 (i.e. Premium of Rs 6).

If the Capital Structure of Company ABC is entirely Common Equity, then what is the

Company's WACC? Use 2 Approaches and Compare the Results

Example - Cost of Common Equity Capital

Dividend Growth Model

Step 1: Calculate Required ROR for Common Stock using Gordon's Formula (Perpetual Investment

and Constant Growing Dividend):

Approach I: Retained Earnings Approach (use Market Price)

r = (DIV1/Po) + g = 2/16 + 0.10 =0.125 +0.1 =0.225 = 22.5%

Approach II: New Stock Issuance Approach

Net Proceeds = Flotation Price - Flotation Costs = 16 - 1 = 15

r =(DIV1/NP) + g = 2/15 + 0.10 = 0.133 + 0.1 =0.233 = 23.3%

Cheaper for Company ABC to Raise Equity Capital through Retained Earnings than to incur costs of

issuing New Equity

Problem: Which Cost to Pick?

Example - Cost of Common Equity Capital

CAPM Model (SML) Efficient Market

Given some additional data: T-Bill ROR = 10% pa. Market ROR = 20%. Beta for ABC Common

Stock = 1.25

r = rRF + Beta (rM - rRF) = 10% + 1.25 (20%-10%)

= 10% + 12.5% = 22.5%

Same answer as Retained Earnings Approach in Dividends Growth Model. Advantage: Don't need to

forecast dividends in CAPM Approach.

CAPM matches Dividends Model if No Flotation / Transaction Costs and Market is Efficient

Required ROR (or Opportunity Cost) %

CAPM Theory (SML for Efficient Markets) & NPV

Minimum ROR required to attract investor into buying a Security (i.e. Stock or Bond ...)

Opportunity Cost: Investor Sacrifices the ROR available from the 2nd best investment.

Cost of Capital %

Weighted Average Cost of Capital (WACC)

Combined costs of all sources of financing used by Firm (i.e. Debt and Equity)

Similar to Required ROR BUT Takes into account some Practical Factors:

TAXES:

Interest Payments are P/L Expenses and NOT Taxed.

TRANSACTION COSTS:

Brokerage, Underwriting, Legal, and Flotation Costs incurred when a Firm

issues Stocks or Bond Securities

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Financial Management MGT201

Summary of Formulas

Total risk= market risk

+ company specific risk

σ 2 + β 2σ 2 + σ 2

NPV Bond Pricing Equation:

Bond Price = PV = C1/ (1+rD) + C2 (1+rD) 2 + C3 / (1+rD) 3 +..... + PAR / (1+rD) 3

Gordon's Formula for Share Pricing:

rCE = (DIV 1 / Po) + g = Dividend Yield + Capital Gains Yield

SML Equation (CAPM Theory)

r = rRF + Beta (rM - rRF)

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