MONASH

BUSINESS
SCHOOL

BFF2140
CORPORATE FINANCE I

Joshua Shemesh
 MONASH
BUSINESS
SCHOOL

Teaching Week Ten

Cost of Capital

Readings
Chapter 13, pp. 386 – 405
 MONASH
BUSINESS
SCHOOL

Learning Objectives

 Explain the drivers of the firm’s overall cost of capital

 Measure the costs of debt and shares
 Compute a firm’s overall cost of capital
 Apply the weighted average cost of capital to value projects
 Adjust the cost of capital for the risk associated with the project
 Account for the direct costs of raising external capital
Cost of Capital: Bringing it all together!

 So far we understand the cost of capital can be employed to:

– discount cash flows;
– calculate NPV;
– compared to the IRR

 The idea is, we finance our assets through debt and equity and so in
everything we do we need to at least ensure we recover AT LEAST
the cost of financing.
Cost of Capital: Bringing it all together!

 The cost of capital (COC) is the rate of return the firm must earn to
maintain its market value and attract investors.

 projects with return > COC will improve the firm’s value

 projects with return < COC will harm the firm’s value
So today:

 How to calculate the weighted average Cost of Capital? (abbreviated WACC)

 Logically, the WACC is simply a combination of the cost of equity and cost of debt
as this is, after all, how we finance our assets!

 Therefore today involves nothing new!

 We need to: (1) estimate the capital structure of the firm; (2) estimate the cost of equity and cost of
debt; and (3) employ these to estimate the WACC!
Why Cost of Capital Is Important

 We know that the return earned on assets depends on the risk of

those assets (higher risk assets mean WACC higher too).

 The return to an investor is the same as the cost to the company

(investors will require a return AT LEAST compensating them for
the risk they take in investing)

 Cost of capital thus provides us with an indication of how the

market views the risk of the companies assets

 Knowing the cost of capital can also help us determine the required
return for capital budgeting projects – minimum return to “break
even” and at least cover our costs!
Overall Cost of Capital of the Firm

Cost of Capital is the required rate of return on the three main types
of financing:

(1) Cost of debt

(2) Cost of Preference Shares (most companies will not always have)
(3) Cost of Ordinary Equity

The overall cost of capital is a weighted average of the individual

required rates of return (costs).
The good news…

Cost of Debt (rD) = YTM on bonds

Cost of Equity (rE) = E(Ri) using CAPM; or rE from DDM

Cost of preference shares (rP) = Div / Price (a perpetuity)

Therefore nothing new, we are just combining prior knowledge!

Weighted average cost of capital

• WACC =

𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐷𝑒𝑏𝑡 𝑉𝐷
𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑜𝑟 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝐷𝑒𝑏𝑡 (𝐷%) = 𝑊𝐷 = =
𝑇𝑜𝑡𝑎𝑙 𝐹𝑖𝑟𝑚 𝑉𝑎𝑙𝑢𝑒 (𝑉) 𝑉𝐷 + 𝑉𝐸

𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦 𝑉𝐸
𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑜𝑟 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦 (𝐸%) = 𝑊𝐸 = =
𝑇𝑜𝑡𝑎𝑙 𝐹𝑖𝑟𝑚 𝑉𝑎𝑙𝑢𝑒 (𝑉) 𝑉𝐷 + 𝑉𝐸
Example 1: calculating weights
(Market values vs Book-values)
Suppose Kenai Corp. has debt with a book (face) value of $10 million, trading at
95% of par value. It also has book equity of $10 million, and 1 million ordinary
shares trading at $30 per share.
 Compute the capital structure market-value weights and book-value weights.
 Which are more relevant, book- or market-values?

Using market values:

9.5m ÷ (9.5m + 30m) x 100 = 24.05% for debt and
30m ÷ (9.5m + 30m) x 100 = 75.95% for equity
Using book values:
10 m ÷ (10m + 10m) x 100 = 50% for debt and
10m ÷ (10m + 10m) x 100 = 50% for equity

The market value weights are more relevant because they represent a more
current valuation of debt and equity
Example 2: calculating weights

Suppose 3M Corp. has debt with a book (face) value of $25 million, trading
at 110% of face value. It also has book equity of $35 million, and 3 million
ordinary shares trading at $25 per share. What weights should 3M use in
calculating its WACC?

Value of Debt = 27.5m (110% of Face Value)

Value of Equity = 75m (3000000 shares @ $25.00/share)

The weights are:

27.5 ÷ 102.5 = 26.8% for debt
75 ÷ 102.5 = 73.2% for equity
Cost of Debt (kd)

 The cost of debt is the required return on our company’s debt

 We usually focus on the cost of long-term debt or bonds

 Recall that current liabilities are already included in Working Capital
cashflows

 The required return is best estimated by computing the yield-to-

maturity on the existing debt

 The cost of debt is NOT the coupon rate

Taxes and the Cost of Debt

 We are concerned with after-tax cash flows, so we need to

consider the effect of taxes on the various costs of capital

 Why? Interest expense reduces the tax liability

 This reduction in taxes reduces the effective cost of debt
 After-tax cost of debt, ri = rd(1-T)

 Dividends are not tax deductible, so there is no tax impact on the

cost of equity
 Note that our analysis ignores personal tax considerations, such as
dividend imputation and capital gains tax discounts
Example 3: Cost of Debt

Suppose there is a bond issue currently outstanding that has 25

years left to maturity. The coupon rate is 9% and coupons are paid
semiannually. The bond is currently selling for $908.72 per $1,000
bond. Corporate rate of tax = 30%. What is the cost of debt?

– n = 25yrs x 2 = 50
– Coupon = $1,000 x (0.09/2) = $45
– M = $1,000
– Pb = $908.72
Example 3: Cost of Debt continued

1. Find the YTM (recall from teaching week 3)

CPN  1  FV
P0  1  
y  1  y n  1  y n


$45  1  $1,000
$908.72  1  
kd  (1  k )  (1  k )50
50
 d  d
hence; YTM = rd = 5% semi-annual
or Annual Percentage Yield (APY) of 10% nominally
2. Convert to Effective Annual Yield (EAY) which is the
annual cost of debt: rd = (1+0.05)2 – 1 = 10.25%
3. Find the after-tax cost of debt: ri(1 – T) = 10.25(1 – 0.3) = 7.18%
Example 3: Cost of Bonds (debt)
– Continued (using HP10II+ calculator )
Cost of Preference Share Capital

 Reminders
 Preference shares generally pay a constant dividend every period
 Dividends are expected to be paid every period forever

 Preference shares are a perpetuity, so we take the perpetuity

formula, rearrange and solve for kP

• rP = D1 (from teaching week 2) or rP= DP

P NP

Where DP = the annual preference share dividend

NP = the net proceeds from sale of preference share
Example 4: Cost of Preference Shares

A company has preference shares that have an annual dividend of

$3. If the current price is $25, what is the cost of the preference
share?

rP = 3 / 25 = 12.00%
Cost of Equity

 The cost of equity is the return required by equity investors

given the risk of the cash flows from the firm

 There are two major methods for determining the cost of

equity

 Dividend growth model (covered in week 3)

 SML or CAPM (covered in week 9)
The Dividend Growth Model Approach

Start with the dividend growth model formula and rearrange to

solve for rE

Dt 1
P0 
rE  g

Dt 1
rE   g
P0

Where rE is the cost of equity

Example 5: Dividend Growth Model

Suppose that a company is expected to pay a dividend of $1.50

per share next year. There has been a steady growth in dividends
of 5.1% per year for this company and the market expects this to
continue. The current price is $25. What is the cost of equity
using the DGM?

Dt 1
recall, rE  g
P0

$1.50
rE   0.051  0.111 or 11.10%
$25
Illustration:
Estimating the Dividend Growth Rate

One method for estimating the growth rate is to

use the historical average
– Year Dividend Percent Change (Week 8)
– 2014 1.23
– 2015 1.30 (1.30 – 1.23) / 1.23 = 5.69%
– 2016 1.36 (1.36 – 1.30) / 1.30 = 4.62%
– 2017 1.43 (1.43 – 1.36) / 1.36 = 5.15%
– 2018 1.50 (1.50 – 1.43) / 1.43 = 4.90%

Average = (5.69 + 4.62 + 5.15 + 4.90) / 4 = 5.09%

Advantages and Disadvantages of the
Dividend Growth Model

 Advantage

 easy to understand and use

 Disadvantages

 Only applicable to companies currently paying dividends

 Not applicable if dividends are not growing at a reasonably
constant rate
 Extremely sensitive to the estimated growth rate – an increase
in g of 1% increases the cost of equity by 1%
 Does not explicitly consider risk
The CAPM (or SML Approach)

Use the following information to compute our cost of

equity

 Risk-free rate, RRF

 Market risk premium, E( RM )  RRF
 Systematic risk of asset, 

E ( Ri )  RRF   i E ( RM )  RRF 
Example 6: CAPM

Suppose the same company introduced in Example 5 has an

equity beta of 0.58. Additionally assume the current risk-free rate
is 6.1% and the expected market risk premium is 8.6%. What is
the cost of equity capital for this company using the CAPM?

rE = 6.1 + 0.58(8.6) = 11.09%

Since we came up with similar numbers using both the Dividend
growth model and the SML approach, we should feel pretty good
about our estimate (Refer to Example 5)
Advantages and Disadvantages
of SML

 Advantages
 Explicitly adjusts for systematic risk
 Applicable to all companies, as long as we can compute beta

 Disadvantages
 Have to estimate the expected market risk premium, which
does vary over time
 Have to estimate beta, which also varies over time
 We are relying on the past to predict the future, which is not
always reliable (i.e. beta)
Example 7: Cost of Equity

Suppose a company has a beta of 1.5. The market

risk premium is expected to be 9% and the current
risk-free rate is 6%. Analysts’ estimates have been
used to determine that the market believes the
dividends will grow at 6% per year. The last dividend
was $2. The stock is currently selling for $15.65.
What is the cost of equity?
Example 7: Cost of Equity

 Using SML:
rE = 6% + 1.5(9%) = 19.50%

 Using DGM:

Dt 1
recall, rE  g
P0

rE = [2(1.06) / 15.65] + 0.06 = 19.55%

Weighted Average Cost of Capital

We can use the individual (component) costs of

capital that we have computed to get our “average”
cost of capital for the firm.

This “average” is the required return on the assets,

based on the market’s perception of the risk of those
assets.

The weights are determined by how much of each

type of financing is used.
After Tax WACC

If there is no preference shares, the formula reduces to

WACC  WE rE  WD rD  1T 
After Tax WACC for
Unlevered (Equity only) firm

 If the firm is an all equity firm and has no debt, then the WACC
formula collapses to:

WACC  wE rE

 Since the firm is equity only, E/V = 1. Hence,

WACC  rE

 That is, the WACC for an all equity firm is just the cost of
equity capital
Example 8: Comprehensive Problem

Packages R US (PRUS) Ltd. want to determine their WACC. Their 11% semi-annual
bonds (par value $1,000) are selling for $942.65 with 10 years remaining until maturity.
PRUS has 10,000 bonds currently on issue. The preference shares issued at $2.00 per
share, pay $0.20 dividends and are currently selling in the market for $1.60. There are 5
million preference shares outstanding. The firm also has 5 million ordinary shares on issue
which have a current market price of $5.00 each. Assume that the current risk-free rate is
7% and the return on market portfolio is 12%. PRUS has a beta which has been recently
estimated at 1.2. The tax rate is 30%.

Calculate PRUS’s weighted average cost of capital.

Example 8: Comprehensive Problem
Step one: calculate cost of capital components. Let’s start with debt.

C  1  Fn
PB  1  
rd  1  rd n  1  rd n

55  1  1000
942.65  1  
rd  1  r 20  1  rd 20
 d
 rd  0.06 or 6.00%

recall this is the cost of debt before tax

Example 8: Comprehensive Problem

The cost of bonds, rD = 6% per six months, so 12.36% compounding

annually

rD = (1+0.06)2 – 1 = 12.36%

Therefore, the after-tax cost of debt,

rd = 0.1236(1 – 0.3) = 0.08652, or 8.65%

Example 8: Comprehensive Problem

The cost of preference shares,

DP 0.20
rp =   0.125 or 12.50%
N P 1.60

The cost of ordinary equity, using CAPM

rE = RRF + i [E(Rm) – RRF)]

= 0.07 + (0.12 – 0.07)1.2 = 0.13, or 13.0%

Example 8: Comprehensive Problem

Step two: calculate weights of capital components

Value of bonds = 10,000 x $942.65

= $9.4265 m

Value of preference shares = 5m x $1.60

= $8.00 m

Value of ordinary shares = 5m x $5.00

= $25.00 m

Total value of firm = $42.4265m

Example 8: Comprehensive Problem

Source Cost % Value Weight Weighted

(ri) (wi) Cost
(wiri)
Bonds 8.65 9,426,500 0.222 1.920

Pref Shares 12.5 8,000,000 0.189 2.363

Equity 13.0 25,000,000 0.589 7.657

42,426,500 1.000 11.940

WACC  wD rD (1  t )  w p r  w E rE =11.94%
P
WACC for real ASX companies
Using the WACC to value a project

• WACC acts as the discount rate.

• Levered value:
FCF1 FCF2 FCF3
V0L     ...
1  rWACC 1  rWACC  1  rWACC 
2 3
Example 9

Suppose Coca-Cola Amatil is considering introducing a new ultra-

light soft drink with zero calories to be called NoGut. The firm
believes that a nougat flavour and appeal to calorie conscious
drinkers will make it a success. The cost of bringing the beverage to
market is $200 million, but Coca-Cola Amatil expects first-year
incremental free cash flows from NoGut to be $100 million and to
grow at 3% per year thereafter. Should Coca-Cola Amatil go ahead
with the project? Assume its WACC is 5.7%.
Using WACC to value a project

Key assumptions
 Average risk:
 We assume initially that the market risk of the project is equivalent to the
average market risk of the firm’s investments.

 Constant debt-equity ratio:

 We assume that the firm adjusts its leverage continuously to maintain a
constant ratio of the market value of debt to the market value of equity

 Limited leverage effects:

 We assume initially that the main effect of leverage on valuation follows
from the interest tax deduction and that any other factors are not
significant at the level of debt chosen.
Example: WACC application

An all-equity (unlevered) mining company considers extending the

life of one of its facilities for 4 years.
• Up front legal/license (non-depreciable) expense of $6.67m
• Equipment & setup cost $24m (depreciated straight-line to 0)
• Expects annual sales of $60 million per year from this
facility.
• Material costs and operating expenses are expected to total
$25 million and $9 million, respectively, per year.
• Expects no net working capital requirements for the project,
and it pays a tax rate of 30%.
• WACC = 9.11%
• NPV=?
Calculate Free Cash Flows
Using WACC

• NPV = $64.64 million - $28.67 million = $35.97 million

Summary of the WACC method

1. Determine the incremental free cash flow of the investment.

2. Compute the weighted average cost of capital using WACC

formula

3. Compute the value of the investment, including the tax benefit of

leverage, by discounting the incremental free cash flow of the
investment using the WACC.
WACC for individual projects

Limitations of WACC as a discount rate for evaluating projects

 the WACC is going to be the appropriate discount rate for

evaluating a project only when the project has cash flows with
systematic risks that are exactly the same as those for the
company as a whole.

 When a single rate, such as the WACC, is used to discount cash

flows for projects with varying levels of risk, the discount rate
will be too low in some cases and too high in others.
Using Firm’s WACC for individual projects

Potential errors when the firm uses its overall WACC to evaluate
individual projects
Example 10

Amalgamated Products is a well diversified industrial company (financed by equity only). The
risk-free rate is 5%, the expected return on market risk is 15%, and this firm’s beta is 1.3. The
firm has three divisions. They are United Foods, General Electronics and Associated Chemicals.
The company is planning to invest $10 million in each of its three divisions. The finance
manager has estimated the equity beta and cost of capital for each of its divisions by identifying
similar businesses in the market. The cost of capital for the company, Associated Products is
18%. The equity beta, cost of capital and IRR for the proposed new investments in each division
are given below.

DIVISION BETA WACC IRR

United Food 0.8 13% 15%
General Electronics 1.7 22% 21%
Associated Chemicals 1.2 17% 20%

a) Identify the projects that will be accepted using divisional cost of capital.
b) Identify the projects that will be incorrectly accepted or rejected if the firm’s overall cost of
capital is used as a hurdle rate.
Example 10: Solution

Accept United Foods (15% IRR > 13% Divisional CoC)

Accept Associated Chemicals (20% IRR > 17% Divisional CoC)

Reject General Electronics (21% IRR < 22% Divisional CoC)

Explanation:
when IRR > divisional cost of capital project will be accepted.
when IRR < divisional cost of capital project will be rejected.
Example 10: Solution
Example 10: Solution

Divisional Cost of Capital

0.25 S M L

Electronics
0.2

0.15 General Electronics will be accepted incorrectly.

Why? Plots below the SML and hence is
Return

overpriced as an investor is obtaining insufficient

0.1 return relative to the systematic risk faced

R F
0.05

0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Beta
Example 10

Divisional Cost of Capital

0.25

S M L

0.2 United Foods will be rejected

incorrectly.

0.15 Food Why? Plots above the SML

and hence is underpriced.
Return

Only rejected because plots

0.1 below overall cost of capital.

R F
0.05

0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Beta
WACC for individual projects

A company’s WACC should be used to evaluate a project only if :

Condition 1: the level of systematic risk for that project is the

same as that for the portfolio of projects that currently comprise
the company.

Condition 2: that project uses the same financing mix—the same

proportions of debt, preference shares, and ordinary shares—used
to finance the company as a whole.
Raising External Capital

 So far, we have assumed that issuing external capital does not

incur costs.
 In reality, issuing new bonds or stocks is costly
 Exchange, prospectus and advertisement fees
 Investment banking and underwriting fees (~5-7%)
 Investors’ reaction (~1.5% drop in value at the announcement of SEOs)
 Valuation needs to account for issuing costs, treated as cash
outflows that are necessary to the project
 How?
Example: costly external financing

• Suppose Woolworths plans to offer $450 million as the

purchase price for Billabong, and it will need to issue
additional debt and equity to finance the acquisition.
• The issuance costs will be $15 million and will be paid as
soon as the transaction closes.
• You estimate the incremental free cash flows from the
acquisition will be $29 million in the first year and will
grow at 4% per year thereafter.
• WACC = 10.50%
• What is the NPV of the proposed acquisition?

56
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