Ch11 - The Cost of Capital

Chapter 11
The Cost of
Capital

Copyright © 2009 Pearson Prentice Hall. All rights reserved.

Learning Goals

1. Understand the key assumptions, the basic concept,
and the specific sources of capital associated with the
cost of capital.
2. Determine the cost of long-term debt and the cost of
preferred stock.
3. Calculate the cost of common stock equity and
convert it into the cost of retained earnings and the
cost of new issues of commons stock.

Copyright © 2009 Pearson Prentice Hall. All rights reserved. 11-2

Learning Goals (cont.)

4. Calculate the weighted average cost of capital
(WACC) and discuss alternative weighting schemes.
5. Describe the procedures used to determine break
points and the weighted marginal cost of capital
(WMCC).
6. Explain the weighted marginal cost of capital
(WMCC) and its use with the investment
opportunities schedule (IOS) to make financing and
investment decisions.


An Overview of the Cost of Capital

• The cost of capital acts as a link between the firm’s
long-term investment decisions and the wealth of the
owners as determined by investors in the marketplace.
• It is the “magic number” that is used to decide whether
a proposed investment will increase or decrease the
firm’s stock price.
• Formally, the cost of capital is the rate of return that a
firm must earn on the projects in which it invests to
maintain the market value of its stock.


The Firm’s Capital Structure


Some Key Assumptions

• Business Risk—the risk to the firm of being unable to cover
operating costs—is assumed to be unchanged. This means that
the acceptance of a given project does not affect the firm’s
ability to meet operating costs.
• Financial Risk—the risk to the firm of being unable to cover
required financial obligations—is assumed to be unchanged.
This means that the projects are financed in such a way that the
firm’s ability to meet financing costs is unchanged.
• After-tax costs are considered relevant—the cost of capital is
measured on an after-tax basis.


The Basic Concept

• Why do we need to determine a company’s overall
“weighted average cost of capital?”
Assume the ABC company has the following investment
opportunity:
- Initial Investment = $100,000
- Useful Life = 20 years
- IRR = 7%
- Least cost source of financing, Debt = 6%
Given the above information, a firm’s financial manger
would be inclined to accept and undertake the investment.

The Basic Concept (cont.)

• Why do we need to determine a company’s overall
“weighted average cost of capital?”
Imagine now that only one week later, the firm has another
available investment opportunity
- Initial Investment = $100,000
- Useful Life = 20 years
- IRR = 12%
- Least cost source of financing, Equity = 14%
Given the above information, the firm would reject this
second, yet clearly more desirable investment opportunity.

The Basic Concept (cont.)

• Why do we need to determine a company’s overall “weighted
average cost of capital?”
• As the above simple example clearly illustrates, using this
piecemeal approach to evaluate investment opportunities is
clearly not in the best interest of the firm’s shareholders.
• Over the long haul, the firm must undertake investments that
maximize firm value.
• This can only be achieved if it undertakes projects that provide
returns in excess of the firm’s overall weighted average cost of
financing (or WACC).


Specific Sources of Capital:
The Cost of Long-Term Debt

• The pretax cost of debt is equal to the the yield-to-maturity on
the firm’s debt adjusted for flotation costs.
• Recall that a bond’s yield-to-maturity depends upon a number
of factors including the bond’s coupon rate, maturity date, par
value, current market conditions, and selling price.
• After obtaining the bond’s yield, a simple adjustment must be
made to account for the fact that interest is a tax-deductible
expense.
• This will have the effect of reducing the cost of debt.


The Cost of Long-Term Debt (cont.)

Net Proceeds

Duchess Corporation, a major hardware manufacturer, is
contemplating selling $10 million worth of 20-year, 9% coupon
bonds with a par value of $1,000. Because current market
interest rates are greater than 9%, the firm must sell the bonds
at $980. Flotation costs are 2% or $20. The net proceeds to
the firm for each bond is therefore $960 ($980 - $20).



• Before-Tax Cost of Debt
• The before-tax cost of debt can be calculated in
any one of three ways:
– Using cost quotations
– Calculating the cost
– Approximating the cost



– Using Cost Quotations
– When the net proceeds from the sale of a bond equal
its par value, the before-tax cost equals the coupon
interest rate.
– A second quotation that is sometimes used is the
yield-to-maturity (YTM) on a similar risk bond.



– Calculating the Cost
– This approach finds the before-tax cost of debt by
calculating the internal rate of return (IRR).
– As discussed in earlier in the text, YTM can be
calculated using: (a) trial and error, (b) a financial
calculator, or (c) a spreadsheet.



– Approximating the Cost



Find the after-tax cost of debt for Duchess
assuming it has a 40% tax rate:
ri = 9.4% (1-.40) = 5.6%

This suggests that the after-tax cost of raising
debt capital for Duchess is 5.6%.


The Cost of Preferred Stock

Duchess Corporation is contemplating the issuance of a
10% preferred stock that is expected to sell for its $87-per
share value. The cost of issuing and selling the stock is
expected to be $5 per share. The dividend is $8.70 (10%
x $87). The net proceeds price (Np) is $82 ($87 - $5).

rP = DP/Np = $8.70/$82 = 10.6%


The Cost of Common Stock

• There are two forms of common stock financing: retained
earnings and new issues of common stock.
• In addition, there are two different ways to estimate the cost of
common equity: any form of the dividend valuation model, and
the capital asset pricing model (CAPM).
• The dividend valuation models are based on the premise that the
value of a share of stock is based on the present value of all
future dividends.


The Cost of Common Stock (cont.)

Using the constant growth model, we

rS = (D1/P0) + g

• We can also estimate the cost of common equity
using the CAPM:

rE = rF + b(rM - rF).



• The CAPM differs from dividend valuation
models in that it explicitly considers the firm’s
risk as reflected in beta.
• On the other hand, the dividend valuation model
does not explicitly consider risk.
• Dividend valuation models use the market price
(P0) as a reflection of the expected risk-return
preference of investors in the marketplace.



• Although both are theoretically equivalent, dividend
valuation models are often preferred because the data
required are more readily available.
• The two methods also differ in that the dividend
valuation models (unlike the CAPM) can easily be
adjusted for flotation costs when estimating the cost of
new equity.
• This will be demonstrated in the examples that follow.



• Cost of Retained Earnings (rE)
– Constant Dividend Growth Model
rs = D1/P0 + g

For example, assume a firm has just paid a dividend of
$2.50 per share, expects dividends to grow at 10%
indefinitely, and is currently selling for $50.00 per share.

First, D1 = $2.50(1+.10) = $2.75, and

rS = ($2.75/$50.00) + .10 = 15.5%.


– Security Market Line Approach

rs = rF + b(rM - rF).

For example, if the 3-month T-bill rate is currently 5.0%,
the market risk premium is 9%, and the firm’s beta is
1.20, the firm’s cost of retained earnings will be:

rs = 5.0% + 1.2 (9.0%) = 15.8%.




The previous example indicates that our estimate of the cost
of retained earnings is somewhere between 15.5% and
15.8%. At this point, we could either choose one or the
other estimate or average the two.

Using some managerial judgment and preferring to err on
the high side, we will use 15.8% as our final estimate of the
cost of retained earnings.



• Cost of New Equity (rn)
– Constant Dividend Growth Model

rn = = D1/Nn - g

Continuing with the previous example, how much would it
cost the firm to raise new equity if flotation costs amount
to $4.00 per share?

rn = [$2.75/($50.00 - $4.00)] + .10 = 15.97% or 16%.

The Weighted Average Cost of Capital

WACC = ra = wiri + wprp + wsrr or n
• Capital Structure Weights

The weights in the above equation are intended to
represent a specific financing mix (where wi = % of debt, wp
= % of preferred, and ws= % of common).

Specifically, these weights are the target percentages of
debt and equity that will minimize the firm’s overall cost of
raising funds.



One method uses book values from the firm’s balance
sheet. For example, to estimate the weight for debt, simply
divide the book value of the firm’s long-term debt by the
book value of its total assets.

To estimate the weight for equity, simply divide the total
book value of equity by the book value of total assets.


A second method uses the market values of the firm’s debt and
equity. To find the market value proportion of debt, simply
multiply the price of the firm’s bonds by the number
outstanding. This is equal to the total market value of the
firm’s debt.

Next, perform the same computation for the firm’s equity by
multiplying the price per share by the total number of shares
outstanding.



Finally, add together the total market value of the firm’s
equity to the total market value of the firm’s debt. This yields
the total market value of the firm’s assets.

To estimate the market value weights, simply dividend the
market value of either debt or equity by the market value of
the firm’s assets .



For example, assume the market value of the firm’s debt is $40
million, the market value of the firm’s preferred stock is $10
million, and the market value of the firm’s equity is $50 million.

Dividing each component by the total of $100 million gives us
market value weights of 40% debt, 10% preferred, and 50%
common.



Using the costs previously calculated along with the market
value weights, we may calculate the weighted average cost of
capital as follows:

WACC = .40(5.67%) + .10(9.62%) + .50(15.8%)

= 11.13%

This assumes the firm has sufficient retained earnings to fund
any anticipated investment projects.

The Marginal Cost
& Investment Decisions

• The Weighted Marginal Cost of Capital (WMCC)
– The WACC typically increases as the volume of new capital
raised within a given period increases.
– This is true because companies need to raise the return to
investors in order to entice them to invest to compensate them
for the increased risk introduced by larger volumes of capital
raised.
– In addition, the cost will eventually increase when the firm
runs out of cheaper retained equity and is forced to raise new,
more expensive equity capital.


The Marginal Cost
& Investment Decisions (cont.)

– Finding Break Points

Finding the break points in the WMCC schedule will allow us to
determine at what level of new financing the WACC will increase
due to the factors listed above.

BPj = AFj/wj

where:
BPj = breaking point form financing source j
AFj = amount of funds available at a given cost
wj = target capital structure weight for source j

The Marginal Cost


Assume that in the example we have been using that the firm has
$2 million of retained earnings available. When it is exhausted,
the firm must issue new (more expensive) equity. Furthermore,
the company believes it can raise $1 million of cheap debt after
which it will cost 7% (after-tax) to raise additional debt.

Given this information, the firm can determine its break points as
follows:


The Marginal Cost


BPequity = $2,000,000/.50 = $4,000,000

BPdebt = $1,000,000/.40 = $2,500,000

This implies that the firm can fund up to $4 million of new investment
before it is forced to issue new equity and $2.5 million of new investment
before it is forced to raise more expensive debt.
Given this information, we may calculate the WMCC as follows:


The Marginal Cost

WACC for Ranges of Total New Financing
Range of total Source of Weighted
New Financing Capital Weight Cost Cost
$0 to $2.5 million Debt 40% 5.67% 2.268%
Preferred 10% 9.62% 0.962%
Common 50% 15.80% 7.900%
WACC 11.130%

$2.5 to $4.0 million Debt 40% 7.00% 2.800%
Preferred 10% 9.62% 0.962%
Common 50% 15.80% 7.900%
WACC 11.662%

over $4.0 million Debt 40% 7.00% 2.800%
Preferred 10% 9.62% 0.962%
Common 50% 16.00% 8.000%
WACC 11.762%

The Marginal Cost

11.76% WMCC

11.75%
11.66%

11.50%

11.25%
11.13%

$2.5 $4.0 Total Financing
(millions)

The Marginal Cost

• Investment Opportunities Schedule (IOS)
• Now assume the firm has the following investment
opportunities available:
Initial Cumulative
Project IRR Ivestment Investment
A 13.0% $ 1,000,000 $ 1,000,000
B 12.0% $ 1,000,000 $ 2,000,000
C 11.5% $ 1,000,000 $ 3,000,000
D 11.0% $ 1,000,000 $ 4,000,000
E 10.0% $ 1,000,000 $ 5,000,000

The Marginal Cost

13.0% A WMCC
12.0% B

11.66%
This indicates
11.5%
C that the firm can
accept only
Projects A & B.

11.13% D
11.0%

$1.0 $2.0 $2.5 $3.0 $4.0 Total Financing
(millions)

Table 11.4 Summary of Key Definitions
and Formulas for Cost of Capital (cont.)


Table 11.4 Summary of Key Definitions
and Formulas for Cost of Capital


Table 11.1 Calculation of the Weighted
Average Cost of Capital for Duchess
Corporation


Table 11.2 Weighted Average Cost of Capital
for Ranges of Total New Financing for
Duchess Corporation


Figure 11.1 WMCC Schedule


Table 11.3 Investment Opportunities
Schedule (IOS) for Duchess Corporation


Figure 11.2 IOS and WMCC
Schedules


Ch11 - The Cost of Capital

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