Principles of Managerial Finance 9th Edition Chapter 11 The Cost of Capital.

Principles of Managerial Finance

9th Edition

Chapter 11

The Cost of Capital

Learning Objectives• Understand the basic cost of capital concept and the

specific sources of capital it includes.

• Determine the cost of long-term debt and the cost of

preferred stock.

• Calculate the cost of common equity and convert it

into the cost of retained earnings and the cost of new

issues of common stock.

• Find the weighted average cost of capital (WACC) and

discuss the alternative weighting schemes.

Learning Objectives• Describe the rationale for and procedures used to

determine breaking points and the weighted marginal

cost of capital (WMCC).

• Explain how the weighted marginal cost of capital

(WMCC) can be used with the investment

opportunities schedule (IOS) to make the firm’s

financing/investment decisions.

The Firm’s Capital Structure

Current Assets

Fixed Assets

Current Liabilities

Long-TermDebt

Equity

The Firm’s

Capital Structure

& Cost of Capital

定義：Cost of Capital: focus on long-term financing because it is permanent rate of return that a firm must earn on its project investment to maintain its market value. COC is required by the Suppliers of capital to attract their funds to the firm,

COC 與 NPVCOC 與 IRR

(1)common stock(2)retained earnings(3)preferred stock

• 不管是何種 long-term financing ，其資金成本 ke=rf +business risk

premium+financial risk premium

– (1) time-series 比較 rf

– (2) cross-sectional 比較 bp 和 fp

• 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.

• COC 乃指 today ，而非 historical

Some Basic Assumptions

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.

• 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

• 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).

The Basic Concept

∴ 須要知道 firm’s long-run target capital structure

Capital Structure Theory• According to finance theory, all firms possess a target

capital structure that will minimize its cost of capital.

Source of Capital Capital CapitalCapital Structure 1 Structure 2 Structure 3

Debt 25% 40% 70%

Equity 75% 60% 30%

WACC 10% 8% 13%

Expected Future

Annual Cash Flows 20$ 20$ 20$

Firm Value 200$ 250$ 160$

Cost of Capital & Firm Value for Alternative Capital StructuresNote that

Firm Value is equal tothe Firm’s

Annual CashFlow divided

by the WACC:

V1 = $200 .10

= $200

Graphically

Kd (1-t)

Ke

WACC (ka)

Cost (%)

TD/TA (%)0 Target

Capital Structure

Ke

Kd (1-t)

Capital Structure Theory

GraphicallyFirmValue ($)

TD/TA (%)0 Target

Capital Structure

V($)

Capital Structure Theory

Required Return and the Cost of Capital

For example, suppose a company wishes to spend

$1,000,000 on a particular investment project and

plan to finance it with $600,000 of 9% debt and

$400,000 of 15% equity.

Investors will only invest money if they expect to earn enough to compensate them for:

(a) the risk they are taking by making the investment,

(b) current capital market conditions such as inflation.




Given the data, the annual cost to the firm and the return demanded by investors may be calculated as:

9%($600,000) + 15%($400,000) = $114,000

Therefore, the minimum annual cash flow necessary from the investment must be $114,000 or 11.4%.


This simple example demonstrates that the minimum

required rate of return demanded by investors is

equal to the cost of raising capital to the company

and it is a weighted average cost of all sources of

capital being utilized by the firm.





The After-Tax Cost of Debt (kd)

• The pretax cost of debt is equal to the the yield-to-maturity on the firm’s debt adjusted for flotation costs.

• Recall from Chapter 8 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 Specific Sources of Capital包括 costs of underwriting 及administrative

Par Value (1,000.00)$

Flotation Costs (% of Par) 2.00%

Flotation Costs ($) (20.00)$

Issue Price 980.00$

Net Proceeds Price 960.00$

Coupon Interest (%) 9.00%

Coupon Interest ($) (90.00)$

Time to maturity 20

Before-tax cost of debt 9.45%

Finding the Cost of Debt

The Cost of Specific Sources of Capital

Suppose a company could issue 9% coupon, 20 year debt with a face value of $1,000 for $980. Suppose further that flotation costs will amount to 2% of par value. Find the

before-tax cost of debt.

EXCEL Formula for

computing the

cost of debt

=RATE(B10,B9,B7,B3)


B3

B7

B9B10

Suppose a company could issue 9% coupon, 20 year debt with a face value of $1,000 for $980. Suppose further that flotation costs will amount to 2% of par value. Find the

before-tax cost of debt.

或用財務計算機N PV PMT FV CPT i%20 -960 90 1000

2021 )1(

100090......

)1(

90

)1(

90960

rrr

求 r, 也就是 IRR ，可用 EXCEL 算 IRR 或 RATE 的函數此 IRR 就 bondholder 投資人的角度看就是 YTM此 IRR 從 issuer 發行公司的角度看就是 cost of debt

Kd = YTM (1-t)

Find the after-tax cost of debt assuming the company in the previous example is in the 40% tax bracket:

kd = 9.45% (1-.40) = 5.67%

This suggests that the after-tax cost of raising debt capital is 5.67%.



The Cost of Preferred Stock (kp)

KP = DP/(PP - F)

In the above equation, “F” represents flotation costs

(in $). As was the case for debt, the cost of raising

new preferred stock will be more than the yield on the

firm’s existing preferred stock since the firm must pay

investment bankers to sell (or float) the issue.


若現在發行 preferred stock ，一般的市價

For example, if a company could issue preferred

stock that pays a $5 annual dividend, sell it for $55

per share, and have to pay $3 per share to sell it,

the cost of preferred stock would be:

kP = $5/($55 - $3) = 9.62%

The Cost of Preferred Stock (kp)

KP = DP/(PP - F)


不須作稅的調整， why? 因為特別股股息，是公司稅後淨利裡發放出來的，不會節稅

The Cost of Common Equity


• 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.



• Using the constant growth model, we have:

kS = (D1/P0) + g.

• We can also estimate the cost of common equity using

the CAPM:

kS = rF + b(kM - 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, dividend valuation models do not

explicitly consider risk.

• These 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.


Security Market Line Approach

kS = rF + b(kM - 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:

kS = 5.0% + 1.2(9)% = 15.8%.


企業若決定以普通股資金來融資其投資案，則有 2 種方式：(1) 發行新股，仍續支付股利(2) 不發行新股，少發股利，改以保留盈餘作為資金來源第二種方法不會降低 EPS 也不會稀釋控制權

Constant Dividend Growth Model

kR = (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 per share.

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

kR = (2.75/50) + .10 = 15.5%.


Cost of Retained Earnings (kR)


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 earn on the high side, we will use 15.8% as our final

estimate of the cost of retained earnings.


Cost of Retained Earnings (KR)


Constant Dividend Growth Model

Cost of New Equity (Kn)

Kn = [D1/(P0 - F)] + 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?

Kn = [2.75/(50 - 4)] + .10 = 15.97% or 16%.



包括 flotation cost 及 underpricing ∵(1) additional supply (2) bad signal (3)dilution of ownership

Capital Structure Weights

WACC = wiki + wpkp + wsks

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.

The Weighted Average Cost of Capital

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 .




結論 : 用 market value weight, 不用 book value weight

用 target weight, 不用 historical weight

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 = .4(5.67%) + .1(9.62%) + .5 (15.8%)

= 11.13%

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




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 earnings and is forced to raise new, more expensive equity capital.

The WMCC & Investment DecisionsThe Weighted Marginal Cost of Capital (WMCC)

不管是 common equity, preferred stock, or bond

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.


Finding Break Points

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

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:



BPequity = $2,000,000/.5 = $4,000,000

BPdebt = $1,000,000/.4 = $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:

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%

WACC for Ranges of Total New Financing

The WMCC & Investment Decisions注意：第一個轉折點發生在 2.5million時， why?

注意：不管資金需求在那個區間 (range) ，假設這公司都要維持一個固定的 target capital structure

The WMCC & Investment Decisions

$2.5 $4.0 Total New Financing (millions)

11.75%

11.25%

11.50%

WMCC11.76%

11.66%

11.13%

The WMCC & Investment DecisionsInvestment 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$

Combining the WMCC with the IOS yields the following:

The WMCC & Investment Decisions

$2.5 $4.0 Total Financing (millions)

WMCC

11.66%

11.13%

$1.0

13.0%A

B

$2.0 $3.0

C

D

11.5%

11.0%

12.0%

This indicates that the firm can

accept only Projects A & B.

Principles of Managerial Finance 9th Edition Chapter 11 The Cost of Capital.

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Transcript of Principles of Managerial Finance 9th Edition Chapter 11 The Cost of Capital.