cost of capital with examples -weighted average

Cost of Capital: A Critical Element
in Business Decisions
• Used to decide whether to make an
investment in capital projects:Most important business decisions require
capital, including decisions to develop new products, build factories and distribution centres, install information technology, expand
internationally, and acquire other companies. For each of these decisions, a company must estimate the total investment required and
decide whether the expected rate of return exceeds the cost of the capital.
• Used in compensation plans:The cost of capital is also used in many
compensation plans, with bonuses dependent on whether the company’s return on invested capital exceeds the cost of capital
• Used in choosing the mixture of debt and
equity to finance the firm: The cost of capital is also a key factor in choosing the
mixture of debt and equity used to finance the firm and in decisions to lease rather than buy assets.
• As these examples illustrate, the cost of capital is a critical element in business decisions

9-1 The Weighted Average Cost of
Capital
• Long-term sources of financing
• Firms use three major long-term capital to
support growth:
– Long-term debt
– Preferred stock
– Common equity
• These are capital components coming from
investors.
9-4

Long-Term Sources of Financing

Capital Components
• The returns on these capital components required by
investors are costs to a firm – (capital) component
costs.
• Accounts payable, accruals, and deferred taxes are
not sources of funding that come from investors, so
they are not included in the calculation of the cost of
capital.
• We do adjust for these items when calculating the
cash flows of a project but not when calculating the
cost of capital.

Defining WACC
• The cost of capital used to analyze capital
budgeting decisions should be a weighted
average of the various components’ costs,
called the weighted average cost of capital
(WACC).
• WACC is also used to discount a firm’s
expected free cash flows to arrive at its value.

9-2 After-Tax Cost of Debt, rd(1 – T)
• Before-tax vs. after-tax capital costs
• Historical (embedded) costs vs. new
(marginal) costs
• Estimating cost of debt
• Component cost of debt, rd(1 – T)

Before-Tax vs. After-Tax Capital Costs
• Tax effects associated with financing can be
incorporated either in capital budgeting cash
flows or in cost of capital.
• Most firms incorporate tax effects in the cost
of capital. Therefore, focus on after-tax costs.
• Only cost of debt is affected.

Historical (Embedded) Costs vs.
New (Marginal) Costs
• The cost of capital is used primarily to make
decisions that involve raising and investing
new capital. So we should focus on new, or
marginal, costs.
• The cost of previously issued capital, the
historical or embedded cost, is important for
decisions such as setting rates for profit
regulation, not for investment.

Estimating Cost of Debt
• Method 1: Ask an investment banker what the
coupon rate would be on new debt.
• Method 2: Find the bond rating for the
company and use the yield on other bonds
with a similar rating.
• Method 3: Find the yield (to maturity or to
call) on the company’s debt, if it has any.

A 22-Year, 7% Semiannual Bond Sells for $897.26. What’s the Pre-Tax
Cost of Debt rd?
35 35 + 1,000
35
0 1 2 44
i =
?
–897.26
...
44 –897.26 35 1,000
4.0%×2 = rd = 8%
N I/YR PV FV
PMT
INPUTS
OUTPUT
Cost of Debt

Component Cost of Debt
• Interest is tax-deductible, so the after-tax (AT)
cost of debt is:
– rd AT = rd (1 – T)
– rd AT = 8%(1 – 0.30) = 5.6%
• Use nominal rates.
• flotation costs .
(9-1)

Flotation Costs and the Cost of Debt
• Alternative 1: Find the pre-tax yield based on
pre-tax cash flows and then adjust it to
reflect taxes and flotation costs
• Alternative 2: Find the after-tax cost of debt
incorporating flotation costs based on after-
tax cash flows using this formula:

 







N
1
t
N
d
t
d )]
T
1
(
r
[1
M
T)]
1
(
r
1
[
T)
INT(1
F)
M(1 (9-2)

Example1 cost of debt
• Suppose a company will issue new 10-year debt with a par value of
$1,000 and a coupon rate of 7.5%, paid annually. The tax rate is 30%. If
the flotation cost is 2% of the issue proceeds, what is the after-tax cost
of debt?

Example2,3 cost of debt
• 2 Duchess Corporation, a major hardware manufacturer, is contemplating selling
$10 million worth of 20-year, 9% coupon (stated annual interest rate) bonds,
each with a par value of $1,000. Because bonds with similar risk earn returns
greater than 9%, the firm must sell the bonds for a 2% discount to compensate
for the lower coupon interest rate. The flotation costs are 2%. (rd 9.45%)
• 3 Currently, Warren Industries can sell 15-year, $1,000-par-value bonds paying
annual interest at a 12% coupon rate. As a result of current interest rates, the
bonds can be sold for $1,010 each; flotation costs of $30 per bond will be
incurred in this process. The firm is in the 40% tax bracket

Cost of Preferred Stock
•rps=Div/p
• Or rps=Div/p(1-F) F=floatation cost

9-3 Cost of Preferred Stock, rps=div/P0
PPS = $25, DPS = $1.75, Par = $25, F = 2.5%
No maturity dates. DPS is the annual
preferred dividend.
rps =
Pps (1 – F)
Dps
=
$1.75
$25(1 – 0.025)
=
$1.75
$24.37
= 0.072 = 7.2%
(9.3)

Component Cost of Preferred Stock
• Flotation costs for preferred are significant, so
are reflected. Use net price, i.e., PPS(1 – F).
• Preferred dividends are not deductible, so no
tax adjustment, just rps.
• Nominal rps is used.

Is Preferred Stock More or Less Risky to
Investors Than Debt?
• More risky; the company is not required to
pay the preferred dividend.
• However, firms want to pay the preferred
dividend. Otherwise, (1) they cannot pay the
common dividend, (2) it is difficult to raise
additional funds, and (3) preferred
stockholders may gain control of firm.

Cost of pref.stock ex:
• Long Haul Trucking can issue perpetual preferred stock at a price of $25 a share. The issue is
expected to pay a constant annual dividend of $1.75 a share. Ignoring flotation costs, what is
the company’s cost of preferred stock, rps?
• Burnwood Tech plans to issue some $25 par preferred stock with a 6% dividend. The stock is
selling on the market for $27.00, and Burnwood must pay flotation costs of 4% of the market
price. What is the cost of the preferred stock?

9-4 Cost of Common Stock, rs
• Two ways of raising common equity
• Rationale behind assigning a cost to retained
earnings
• Three methods of estimating cost of equity

Two Ways of Raising Common Equity
• Directly, by issuing new shares of common
stock
• Indirectly, by reinvesting earnings that are not
paid out as cash dividends—retaining earnings

Rationale behind Assigning a Cost to
Retained Earnings
• Earnings can be either retained and reinvested
or paid out as dividends.
• Investors could use the cash paid out by the
firm to buy other securities and earn a return.
• Thus, an opportunity cost is incurred if earnings
are retained and reinvested.
• Retained earnings are not free sources of
capital.

Cost for Reinvested Earnings
• Opportunity cost: The return stockholders could
earn on alternative investments of equal risk.
• They could buy similar stocks and earn rs, or the
company could repurchase its own stock and
earn rs. So, rs is the cost of reinvested earnings
and it is the cost of equity.

Three Methods of Estimating the Cost of
Equity, rS
1. CAPM: rs = rRF + (rM – rRF)b
= rRF + (RPM)b
2. DCF: rs = (D1/P0)+ g
3. Bond-Yield-Plus-Risk Premium:
rs = rd + Bond RP
(9-4)
(9-6)
(9-8)

9-5 The CAPM Approach
Four-step process:
1. Estimate the risk-free rate, rRF.
2. Estimate the current expected market risk
premium, RPM.
3. Estimate the stock’s beta coefficient, b.
4. Apply the CAPM equation
E(r)=rfr + beta*(Rm-Rfr)

Estimating the Risk-Free Rate, rRF
Many analysts use the yield on a long-term (10
to 20 years) government bond as a proxy for
rRF, because:
1. Most shareholders invest on a long-term
basis.
2. Yields on T-bills are more volatile than those
on long-term ones and rs.
3. Many projects have long lives.

Estimating RPM = rM – rRF
1. Historical data: Difference between the
historical realized return on stocks and the
return for long-term federal government
bonds
2. Forward-looking data: The expected market
return being the sum of the current dividend
yield (on some market index) and the
expected growth rate in dividends
rM = D1/P0 + g = D0(1 + g)/P0 + g

Expected Dividend Growth Rate, g
1. The historical dividend growth rate
2. Analysts’ forecasts for earnings growth rates
There are problems with both methods; e.g.,
there is no reason to expect future growth to
be exactly like past growth, and growth rates
in earnings and in dividends are not always
identical.

Estimating Beta
Beta is estimated as the slope efficient in a
regression of a company’s stock returns
against market return.
The historical beta is subject to problems such
as:
1. No theoretical guidance as to the correct
holding period and
2. Statistical imprecision
Choosing beta involves judgment.

An Illustration of CAPM
Given: rRF = 5%, RPM = 5.5%, bi = 1.3
= 5.0% + (5.5%)1.3 = 12.2%
rS = rRF + RPM ×bi

Issues in Using CAPM
• It is difficult to estimate the market risk premium.
Most analysts use a rate of 3% to 6% for the
market risk premium (RPM).
• Estimates of beta vary, and estimates are “noisy”
(they have a wide confidence interval).

9-6 Dividend-Yield-Plus-Growth-Rate,
or Discounted Cash Flow (DCF), Approach
• Assuming that dividends are expected to grow
at a constant rate and
• That markets are at equilibrium
(9-6)

Estimating the Growth Rate
• Use the historical growth rate if you believe
the future will be like the past.
• Apply the retention growth model.
• Obtain analysts’ estimates from sources such
as the Bank of Canada website or the National
Post.
• Uncertainty in the growth estimate induces
uncertainty in the DCF cost estimate.

Retention Growth Model
Assumptions:
1. The payout rate and the retention rate are
expected to be constant.
2. ROE is expected to remain constant.
3. No new common stock is to be issued or
new stock is to be sold at book value.
4. Future projects are to be of the same
degree of risk as existing assets.

Retention Growth Model (cont’d)
NCC has had an average ROE = 14.5% over the
past 15 years. The ROE has been relatively
steady. NCC’s dividend payout rate has
averaged 52% over the same time period.
The expected future growth rate:
g = (Retention rate)(ROE)
g = (1 – payout rate)(ROE)
g = (1 – 0.52)(14.5%) = 7%
(9-7)

Illustration of DCF Approach
rs =
D1
P0
+ g
= $2.40
$32
+ 0.05
= 0.075 + 0.05
= 12.5%
Given: D1 = $2.40; P0 = $32; g = 5%

Could DCF Methodology Be Applied
If g is Not Constant?
• YES; nonconstant g stocks are expected to
have constant g at some point, generally in 5
to 10 years.
• But calculations get complicated.

9-7 Bond-Yield-Plus-Risk-Premium
Approach
• rs = rd + RP
• Given rd = 8%, RP = 3.7%, rs = 8% + 3.7% =
11.7%
• This RP  RPM (CAPM). It is a subjective value
between 3% to 5%.
• Produces ballpark estimate of rs, giving a
useful check.
(9-8)

9-8 Comparison of the CAPM, DCF, and
Bond-Yield-Plus-Risk-Premium Methods
Method Estimate
CAPM 12.2%
DCF 12.5%
rd + RP 11.7%
Average 12.1%

Costs of Issuing New Common Stock
(External Equity)
• When a company issues new common stock it
also has to pay flotation costs to the
underwriter.
• Issuing new common stock may send a
negative signal to the capital markets, which
may depress stock price; this is another type
of issuing cost.

9-9 Adjusting the Cost of Stock for
Flotation Costs
• The cost of new common equity (re) is higher than
the cost of internal equity (rS) due to the flotation
costs.
• Flotation costs depend on the risk of the firm and
the amount being raised.
• Flotation costs are highest for common equity.
While firms issue equity infrequently, the per-
project cost is fairly small.
• We usually ignore flotation costs when calculating
the WACC.

Cost of New Common Equity:
P0 = $32, D1 = $2.40, g = 5%,
and F = 12.5%
re =
D1
P0(1 – F)
+ g
=
$2.40
$32(1 – 0.125)
+ 5.0%
= $2.40
$28.00
+ 5.0% = 13.6%
(9-9)

Cost of Equity Including Flotation Costs
• Ignoring flotation costs, NCC’s shareholders
require a return of 12.5% according to DCF
model.
• NCC has to earn a return of 13.6% on newly
issued equity capital.
• Flotation costs add 13.6% – 12.5% = 1.1% to
its cost of equity.
• 1.1% may be added to the cost of equity
numbers by using other models.

9-10 Weighted Average Cost of Capital,
WACC
• WACC = wdrd(1 – T) + wpsrps + wce rs (or re)
• WACC is the cost incurred to raise each new, or
marginal, dollar of capital—not the average cost
of dollars raised in the past.
• The weights, wd, wps, and wce, should be based
on target capital structure, not on the particular
sources of financing in any single year.
• The target weights should be on market values.
(9-10)

WACC Calculation
WACC = wdrd(1 – T) + wpsrps + wcers
Recall: rd = 8%, rPS = 7.2%, rS = 12.1%
WACC = 0.3(8%)(0.7) + 0.1(7.2%) + 0.6(12.1%)
= 1.68% + 0.72% + 7.26%
= 9.7%

9-11 Factors That Affect the Weighted
Average Cost of Capital
• Market conditions, especially interest rates,
market risk premium, and tax rates, are beyond
the firm’s control.
• The firm’s capital structure, dividend policy, and
investment policy can be controlled by a firm.
• Firms with riskier projects generally have a higher
WACC.

9-12 Adjusting the Cost of Capital for
Risk
• The divisional cost of capital
• Techniques for measuring divisional betas
• Estimating the cost of capital for individual
projects

The Divisional Cost of Capital
• The cost of capital reflects the average risk
and overall capital structure of the entire firm.
• For a firm with multiple divisions with
different degrees of risk, it does not make
sense for the firm to use its overall cost of
capital (WACC) to evaluate all projects
regardless of risk involved.

Is the Firm’s WACC Correct for Each of
Its Divisions?
• NO! The composite WACC reflects the
risk of an average project undertaken
by the firm.
• Different divisions may have different risks.
The division’s WACC should be adjusted to
reflect the division’s risk and capital structure.

The Risk-adjusted Divisional Cost of Capital
• Estimate the cost of capital that the division
would have if it were a stand-alone firm.
• This requires estimating the division’s beta,
cost of debt, and capital structure.

Pure Play Method for Estimating Beta for
a Division or a Project
• Find several publicly traded companies
exclusively in the project’s business.
• Use the average of their betas as proxy for the
project’s beta.
• It is hard to find such companies.

Estimating the Cost of Capital for
Individual Projects
• Riskier projects have a higher cost of capital.
• It is difficult to estimate project risk.
• Three separate and distinct types of risk:
– Stand-alone risk
– Corporate, or within-firm, risk
– Market, or beta, risk

How Is Each Type of Risk Used?
• Stand-alone risk is easiest to calculate.
• Market risk is theoretically best in most
situations.
• However, creditors, customers, suppliers, and
employees are more affected by corporate
risk.
• Therefore, corporate risk is also relevant.

A Project-specific,
Risk-adjusted Cost of Capital
• Start by calculating a divisional cost of capital.
• Use judgment to scale up or down the cost of
capital for an individual project relative to the
divisional cost of capital.

9-13 Four Mistakes to Avoid
• Current vs. historical cost of debt
• Mixing current and historical measures to
estimate the market risk premium
• Book weights vs. market weights
• Incorrect cost of capital components

Current vs. Historical Cost of Debt
• When estimating the cost of debt, don’t use
the coupon rate on existing debt (historical
cost of debt).
• Use the current interest rate on new debt.

Estimating the Market Risk Premium
• When estimating the risk premium for the CAPM
approach, don’t subtract the current long-term
T-bond rate from the historical average return on
common stocks.
• For example, if the historical rM has been about
12.2% and inflation drives the current rRF up to 10%,
the current market risk premium is not 12.2% – 10%
= 2.2%

Estimating Weights
• Use the target capital structure to determine the
weights.
• If you don’t know the target weights, then use the
current market value of equity, and never the book
value of equity.
• If you don’t know the market value of debt, then the
book value of debt often is a reasonable
approximation, especially for short-term debt.

Capital Components Are Sources of
Funding That Come from Investors
• Accounts payable, accruals, and deferred taxes
are not sources of funding that come from
investors, so they are not included in the
calculation of the WACC.
• We adjust for these items when calculating
the cash flows of the project but not when
calculating the WACC.

cost of capital with examples -weighted average

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