Chapter 14
The Cost of
Capital
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1
Chapter 14 Contents
1. The Cost of Capital: An Overview
2. Determining the Firm’s Capital Structure
Weights
3. Estimating the Costs of Individual Sources of
Capital
4. Summing Up – Calculating the Firm’s WACC
5. Estimating Project Cost of Capital
6. Floatation costs and Project NPV
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Learning Objectives
1. Understand the concepts underlying the firm’s
overall cost of capital and its calculation.
2. Evaluate firm’s capital structure, and determine
the relative importance (weight) of each source
of financing.
3. Calculate the after-tax cost of debt, preferred
stock, and common equity.
4. Calculate firm’s weighted average cost of capital
5. Understand: a)Pros and cons of using multiple,
risk-adjusted discount rates; b)divisional cost of
capital as alternative for firms with divisions.
6. Adjust NPV for the costs of issuing new securities
when analyzing new investment opportunities.
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Principles Used in Chapter 14
• Principle #1: Money Has a Time Value.
• Principle #3: Cash Flows Are the Source of Value.
– Estimates of investor’s required rate of return
extracted from observed market prices are
based on principles #1 and #3.
• Principle #2: There Is a Risk-Return Tradeoff.
– Investors who purchase a firm’s common stock
require a higher expected return than investors
who loan money.
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The Cost of Capital: An Overview
• The Firm’s Cost of capital is the value-weighted
average of the required returns of the securities
that are used to finance the firm.
– Officially refer to this as the firm’s Weighted Average
Cost of Capital, or WACC.
• Most firms raise capital with a combination of
debt, equity, and hybrid securities.
• WACC incorporates the required rates of return of
the firm’s lenders and investors and the particular
mix of financing sources that the firm uses.
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The Cost of Capital Overview (cont.)
• How does riskiness of firm affect WACC?
– Required rate of return on securities will be higher if the
firm is riskier.
– Risk will influence how the firm chooses to finance i.e.
proportion of debt and equity.
• WACC is useful in a number of settings:
–
–
–
WACC is used to value the firm.
WACC is used as a starting point for determining the
discount rate for projects the firm might undertake.
WACC is the appropriate rate to use when evaluating
performance, specifically whether or not the firm has
created value for its shareholders.
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After-Tax WACC equation (WACCAT)
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3-Step Procedure to Estimate Firm WACC
1.
Define the firm’s capital structure by determining the
weight of each source of capital. (see column 2, fig 14-2)
2.
Estimate the opportunity cost of each source of financing.
We will use the current market value of each source of
capital based on its current, not historical, costs. (see
column 3, fig 14-2)
3.
Calculate a weighted average of the costs of each source
of financing. (see column 4, fig 14-2)
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Determining Firm’s Capital Structure Weights
• The weights are based on the following sources of
capital: debt (short-term and long-term),
preferred stock and common equity.
• Liabilities such as accounts payable and accrued
expenses are not included in capital structure.
• Ideally, the weights should be based on observed
market values. However, not all market values
may be readily available.
– Hence, we generally use book values for debt and
market values for equity.
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Example 1: Calculating the WACC for
Templeton Extended Care Facilities, Inc.
In the spring of 2010, Templeton was considering the acquisition of a
chain of extended care facilities and wanted to estimate its own
WACC as a guide to the cost of capital for the acquisition.
Templeton’s capital structure consists of the following:
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Example 1 Continued (Info)
Templeton contacted the firm’s investment banker to get estimates
of the firm’s current cost of financing and was told that if the firm
were to borrow the same amount of money today, it would have to
pay lenders 8%. However, given the firm’s 25% tax rate, the aftertax cost of borrowing would only be 6% = 8%(1-.25).
Preferred stockholders currently demand a 10% rate of return.
Common stockholders demand 15% returns.
Templeton’s CFO knew that the WACC would be somewhere between
6% and 15% since the firm’s capital structure is a blend of the three
sources of capital whose costs are bounded by this range. (Think
about the GOOD logic and intuition.)
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Computing the Weights - Finally
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Example 1 – Solution to WACCAT
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Example 2 – Impact of Capital Structure
Change on WACC
• After completing her estimate of Templeton’s WACC, the CFO
decided to explore the possibility of adding more low-cost
debt to the capital structure.
• With the help of the firm’s investment banker, the CFO
learned that Templeton could probably push its use of debt
to 37.5% of the firm’s capital structure by issuing more debt
and retiring (purchasing) the firm’s preferred shares.
• Assume this could be done without increasing the firm’s
costs of borrowing or the required rate of return demanded
by the firm’s common stockholders.
• What is your estimate of the WACC for Templeton under this
new capital structure proposal?
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Before
Debt
Preferred
Common
MV
100
50
250
Weight
0.250
0.125
0.625
Total
400
1.000
After
Debt
Preferred
Common
MV
150
0
250
Weight
0.375
0.000
0.625
Total
400
1.000
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AT Rate
6%
10%
15%
WACC
AT Rate
6%
10%
15%
WACC
W*R
1.500%
1.250%
9.375%
12.125%
W*R
2.250%
0.000%
9.375%
11.625%
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14.3 Estimating
the Cost of
Individual
Sources of Capital
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The Cost of Debt
• The cost of debt is the rate of return the firm’s
lenders demand when they loan money to firm.
• The rate of return is not the same as coupon rate,
which is rate contractually set at the time of issue.
• Can estimate the market’s required rate of return
by examining the yield to maturity on firm’s debt.
• After-tax cost of debt = Yield (1-tax rate)
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Example 2: The Cost of Debt Estimate
• What will be the yield to maturity on a debt that
has par value of $1,000, a coupon interest rate
of 5%, time to maturity of 10 years and is
currently trading at $900?
• What will be the cost of debt if tax rate is 30%?
• Enter:
– N = 10; PV = -900; PMT = 50; FV =1000
– I/Y = 6.38%
– After-tax cost of Debt = Yield (1-tax rate)
= 6.38 (1-.3)
= 4.47%
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The Cost of Debt – Other Approaches
• It is not easy to find the market price of a specific
bond as most bonds do not trade in the public
market.
• Because of this, it is a standard practice to
estimate the cost of debt using yield to maturity
on a portfolio of bonds with similar credit rating
and maturity as the firm’s outstanding debt.
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Cost of Preferred Equity Estimates
• The cost of preferred equity is the rate of
return investors require of the firm when they
purchase its preferred stock.
• The cost is not adjusted for taxes since
dividends are paid to preferred stockholders
out of after-tax income.
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Example: Estimate Cost of Preferred Equity
• Consider the preferred shares of Relay Company
that are trading at $25 per share. What will be
the cost of preferred equity if these stocks have a
par value of $35 and pay annual dividend of 4%?
• kps = $1.40 ÷ $25 = .056 or 5.6%
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Cost of Common Equity Estimates
• The cost of common equity is the rate of return
investors expect to receive from investing in
firm’s stock. This return comes in the form of
cash distributions of dividends and cash proceeds
from the sale of the stock.
• Cost of common equity is harder to estimate since
common stockholders do not have a contractually
defined return (unlike bonds or preferred stock).
• There are two approaches to estimating the cost
of common equity:
– Dividend growth model (chapter 10)
– CAPM (chapter 8)
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The Dividend Growth Model – Discounted
Cash Flow Approach
• Using this approach, estimate the expected
stream of dividends as the source of future
estimated cash flows.
• Use the estimated dividends and current stock
price to calculate the internal rate of return on the
stock investment. This return is used as an
estimate of cost of equity.
• Essentially, cost of equity is the I/Y that supports
current stock price and our dividend forecast
assumptions
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Step 1: Picture the Problem
• We are given the following:
– Price of common stock (Pcs ) = $10.09
– Growth rate of dividends (g) = 5% and 7.81%
– Dividend (D0) = $0.47 per share
– Cost of equity is given by dividend yield +
growth rate.
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Step 1: Picture the Problem (cont.)
Dividend Yield
=D1 ÷ P0
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Growth
Rate (g)
Cost of
Equity (kcs )
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Step 3: Solve
• At growth rate of 5%
• kcs = {$0.47(1.05)/$10.09} + .05
= .0989 or 9.89%
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Step 3: Solve (cont.)
• At growth rate of 7.81%
• kcs = {$0.47(1.0781)/$10.09} + .0781
= .1283 or 12.83 %
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Estimating the Rate of Growth, g
• The growth rate can be obtained from various
websites that post analysts forecasts of growth
rates.
• We can also estimate the growth rate using the
historical data and computing the arithmetic
average or geometric average.
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Estimating the Rate of Growth, g (cont.)
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Pros and Cons of the Dividend
Growth Model Approach
• While dividend growth model is easy to
use, it is severely dependent upon the
quality of growth rate estimates.
– When you look at real dividend policies, you
will see that dividends don’t grow smoothly but
are a “stair-stepped” function.
– This means using smooth g-function
systematically over and under estimates any
given future dividend
• Furthermore, not all firms pay dividends.
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The Capital Asset Pricing Model
• CAPM was used to determine the expected or
required rate of return for risky investments.
• Previous Equation illustrates that the expected return on
common stock is determined by three key ingredients:
– The risk-free rate of interest,
– The beta or systematic risk of the common stock returns,
– The market risk premium.
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Advantages of the CAPM approach
1. The model is simple to understand and use.
2. The model does not depend on dividends or
growth rate so it can be applied to companies
that do not currently pay dividends or are not
expected to experience a constant rate of growth
in dividends.
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Disadvantages of the CAPM Approach
1. CAPM does not offer any guidance on the
appropriate choice for the risk-free rate. Risk-free
rate may vary widely depending on the Treasury
security chosen.
2. Estimates of beta can vary widely depending upon
the market index and time period chosen.
3. Estimates of market risk premium will also vary
depending on the time period and security
chosen.
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Example: Estimating Cost of Common
Equity using the CAPM
At the end of March 2009, the 10-year U.S. Treasury Bond
yield that we will use to measure the risk-free rate was 2.81%
Estimated market risk premium at the time is 6.5%, and the
beta for Pearson’s common stock is 1.20
Determine Pearson’s cost of common equity using the CAPM, as
of March 2009.
Ke =
Rf + Beta * MRP
=
2.81% + 1.2*6.5%
=
2.81% + 7.8%
=
10.61%
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14.5 Estimating
Project Cost of
Capital
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Estimating Project Cost of Capital
• Should the firm-wide (overall) WACC be used to
evaluate all new investments?
– Appropriate only if the risk of the new project
is equal to the overall risk of the firm.
– When not be the case, need a unique cost of
capital for each project.
• Recent survey found that more than 50% of the
firms tend to use single, company-wide discount
rate to evaluate all of their investment proposals.
• There are advantages and costs associated with
estimating a unique discount rate for each
project.
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Rationale for Multiple Discount Rates
• Multiple discount rates is consistent with finance
theory that suggests that unique discount rate
will reflect the unique risk of the investment.
• Figure 14-6 illustrates the problems that arise
when a single discount rate is used to evaluate
investment projects with different levels of risk.
• A conglomerate would have a menu of risk
profiles for various elements of the economy in
which they operate.
– This would lead to considering divisional WACC’s
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Why Firms Don’t Use Project Cost of Capital
1. It may be difficult to trace the source of
financing for individual project since most firms
raise money in bulk for all the projects.
2. It adds to the time and cost in getting approval
for new projects.
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Estimating Divisional WACCs
• If firm undertakes investment with very different
risks, it will try to estimate divisional WACCs.
• Divisions are generally defined by geographical
regions (e.g., Asian region versus European
region) or industry.
• Advantages of a divisional WACC:
– The discount rate reflects the risk of projects evaluated
by different divisions.
– Requires estimating only one cost of capital estimate for
entire division (rather than one for each project).
– Limits managerial latitude and attendant influence costs.
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Using Pure Play Firms to Estimate
Divisional WACCs
• Here a firm with multiple divisions may
identify a comparable firm with only one
division (called a pure play firm).
• The estimate of pure play firm’s cost of
capital can then be used as a proxy for
that particular division’s cost of capital.
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Divisional WACC – Issues and Limitations
1. The sample of firms in a given industry may
include firms that are not good matches for
the firm or one of its divisions.
2. The division being analyzed may not have a
capital structure that is similar to the sample
of firms in the industry data.
3. The firms in the chosen industry that are
used to proxy for divisional risk may not be
good reflections of project risk.
4. Good comparison firms for a particular
division may be difficult to find.
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WACC, Floatation Costs and Project NPV
• Floatation costs are costs incurred by a firm
when it raises money to finance new investments
by selling bonds and stocks.
– Costs may include fees paid to an investment
banker, and costs incurred when securities are
sold at a discount to the current market price.
• Because of floatation costs, the firm will have to
raise more than the amount it needs.
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Floatation Costs Example
• Firm needs $100 million to finance its new project
and the floatation cost is expected to be 5.5%.
– How much should the firm raise by selling securities?
$105.82 million = $100 million ÷ (1-.055)
• Thus the firm will raise $105.82 million, which
includes floatation cost of $5.82 million.
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Comprehensive Floatation Cost Example 1
Flotation Cost Impact on NPV
The Tricon is considering a $100 million investment that would allow
it to develop fiber optic high-speed Internet connectivity.
Investment will be financed using the firm’s desired mix of debt and
equity with 40% debt financing and 60% common equity financing.
Firm’s investment banker advised the CFO the issue costs associated
with debt would be 2% while the equity issue costs would be 10%.
Tricon uses a 10% cost of capital to evaluate its telecom investments
and has estimated that the new fiber optic project will yield future
cash flows with present value of $115 million.
Account for the effect of the costs of raising the financing for the
project or flotation costs. Should the firm go forward with the
investment in light of the flotation costs?
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Checkpoint 14.4
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Example 2 – Change Float Costs
• Stock market conditions changed such that new
stock became more expensive to issue. Tricon’s
floatation costs rose to 15% of new equity
issued and the cost of debt rose to 3%.
– Is the project still viable (assume the present value of
future cash flows remain unchanged at $115)?
NPV
= PV(inflows) – Initial outlay – Floatation costs
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Solution Strategy Steps
• First, estimate the average floatation costs that
Tricon will incur when raising the funds.
= .40 × .03 + .60 × .15 = .102 or 10.2%
• Next, estimate the “grossed up” initial outlay for
$100 million project:
$111.36 million = $100 million ÷ (1- 0.102)
• Thus, floatation costs is equal to $11.36 million
and NPV = 115-111.36 = 3.64 and accept.
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