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^. ^. ^. ^. ^. ^. CF 1 (1 + r) 1. CF 1 (1 + r ) 1. CF 2 (1 + r) 2. CF 2 (1 + r ) 2. CF n (1 + r ) n. CF n (1 + r) n. Asset Value. Asset Value. + … +. + … +. =. =. +. +. Cost of Capital.

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Cost of Capital


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cost of capital

^

^

^

^

^

^

CF1

(1 + r)1

CF1

(1 + r)1

CF2

(1 + r)2

CF2

(1 + r)2

CFn

(1 + r)n

CFn

(1 + r)n

Asset

Value

Asset

Value

+ … +

+ … +

=

=

+

+

Cost of Capital

r = firm’s required rate of return, which represents the return investors receive for providing funds to the firm

chapter essentials the questions
Chapter Essentials—The Questions

What types of capital do firms use to finance investments?

What is the cost of capital?

How is the cost of capital used to make financial decisions?

Why do funds generated through retained earnings have a cost?

Who determines a firm’s cost of capital?

cost of capital3
Cost of Capital
  • Introduction
  • Cost of Debt, rdT
  • Cost of Equity, rps and (rs or re)
  • Marginal Cost of Capital (MCC)
  • MCC and Investment Opportunity (IOS) Schedules
basic definitions
Basic Definitions
  • Capital—refers to the long-term funds used by a firm to finance its assets.
  • Capital components—the types of capital used by a firm—long-term debt and equity
  • Cost of capital—the cost associated with the various types of capital used by the firm, which is based on the rate of return required by the investors who provide the funds to the firm.
  • Weighted average cost of capital, WACC—the average percentage cost, based on the proportion of each type of capital, of all the funds used by the firm to finance its assets.
  • Capital structure—the mix of the types of capital used by the firm to finance its assets.
  • Optimal capital structure—the mix of capital that minimizes the firm’s WACC, thus maximizes its value.
weighted average cost of capital wacc logic
Weighted Average Cost of Capital (WACC)—Logic
  • A firm generally uses different types of funds to finance its assets—that is, debt and equity.
  • Costs associated with different types of capital (funds) usually are not the same—e.g., debt generally is cheaper than equity.
  • The overall cost, or average, should be weighted based on the proportion of each type of funds used by the firm.
  • Example: A firm is financed with debt and equity with the following characteristics:

CostProportion

Debt rdebt=8%10%

Equity rstock=12%90%

The average cost of each dollar of financing is:

Weighted average = 8%(0.1) + 12%(0.9) = 11.6%

cost of capital6
Cost of Capital
  • Investors who are the participants in the financial markets determine the firm’s costs of funds.
  • The firm’s costs of funds change when
    • conditions in the financial markets change
    • investors’ general risk aversion changes
    • firm’s risk changes
cost of debt r dt
Cost of Debt, rdT

rd—the before-tax cost of debt is simply the yield to maturity (YTM) of the debt

YTM—bondholders’ required rate of return = rd

rdT—the after-tax cost of debt

T = marginal tax rate

cost of debt r dt example
Cost of Debt, rdT—Example

A firm has debt with the following characteristics:

Maturity value, M$1,000.00

Coupon rate, C8.0% (paid semiannually)

Years to maturity6 yrs

Market price$1,099.50

Marginal tax rate40.0%

Based on this information, we know that the following relationship exists:

Solving for rd gives us the YTM for this bond

cost of debt r dt example9
Cost of Debt, rdT—Example

Solve using:

  • Trial-and-error process (numerical solution)
    • approximation equation
  • Financial calculator
  • Spreadsheet
cost of debt r dt example10
Cost of Debt, rdT—Example

rd approximation

rd/2 = 2.97% per six-month period (interest payment)

rd = 2.97% x 2 = 5.94% ≈ 6%

cost of debt r dt example11
Cost of Debt, rdT—Example

Financial calculator solution:

N=12=6 years x 2

PV=-1,099.50

PMT=40= (0.08 x 1,000)/2

FV=1,000

I/Y=? = 3.0% per six-month period

rd=3.0% x 2= 6.0% per year = YTM

cost of debt r dt example12
Cost of Debt, rdT—Example

Bondholders/investors demand a 6 percent rate of return to invest in this firm’s long-term debt.

rd = YTM = 6% is the rate of return paid to bondholders.

The firm pays $80 interest per year, which is a tax deductible expense.

rd is a before-tax amount that needs to be adjusted so as to represent the actual after-tax cost to the firm—that is, the cost of the bond to the firm isn’t really 6 percent.

cost of debt r t tax deductibility of interest
Cost of Debt, rTTax Deductibility of Interest

Example: The firm issues a new $1,000 face value bond with a 6 percent coupon rate, thus interest equal to $60 is paid each year. If the firm’s taxable income before considering the interest payment is $500 and its marginal tax rate is 40 percent, then the tax liability with and without the interest expense is:

Tax without interest = $500(0.40) = $200

Tax with interest = ($500 - $60)( 0.40) = $176

Savings = $24

= $60(0.4)

Net interest after tax savings = $60 - $24 = $36

After-tax cost of the new bond = $36/$1,000 = 3.6%

rdT = rd x (1 – T) = 6% x (1 – 0.4) = 3.6%

cost of debt r dt14
Cost of Debt, rdT

rdT= rd x (1 – T)

rdT= rd x (1 – T)

= YTM x (1 – T)

rd= before-tax cost of debt

T = marginal tax rate

cost of equity
Cost of Equity

The cost of equity is based on the rate of return required by the firm’s stockholders.

Cost of preferred stock—dividends received by preferred stockholders represent an annuity

Cost of retained earnings (internal equity)—return that common stockholders require the firm to earn on the funds that have been retained, thus reinvested in the firm, rather than paid out as dividends

Cost of new (external) equity—rate of return required by common stockholders after considering the cost associated with issuing new stock (flotation costs)

cost of equity preferred stock
Cost of Equity—Preferred Stock

Most preferred stocks pay constant dividends, thus the dividend stream represents a perpetuity.

Valuing preferred stock as a perpetuity gives:

  • Solving for the required rate of return, rps, gives:
  • Because flotation (issuing) costs have to be paid when preferred stock is issued, the cost of preferred stock is:

NP0= net proceeds from issue

F= flotation costs (percent)

cost of preferred stock r ps example
Cost of Preferred Stock, rps—Example

A firm has preferred stock with the following characteristics:

Market price, P0$75.00

Dividend, Dps$5.76

Flotation cost, F4.0%

= 0.08 = 8.0%

  • No tax adjustment, because dividends are not a tax-deductible expense.
cost of equity retained earnings r s
Cost of Equity—Retained Earnings, rs

The firm must earn a return on reinvested earnings that is sufficient to satisfy existing common stockholders’ investment demands.

If the firm does not earn a sufficient return using retained earnings, then the earnings should be paid out as dividends so that stockholders can invest the funds outside the firm to earn an appropriate rate.

cost of equity retained earnings r s19
Cost of Equity—Retained Earnings, rs

Assuming the stock market is at or near equilibrium, we know that the following relationship exists:

= next expected dividend

rRF= risk-free rate

rM= market return

bs= stock’s beta coefficient

g= constant growth rate

cost of retained earnings r s capm approach
Cost of Retained Earnings, rsCAPM Approach

Assumes the firm’s stockholders are very well diversified; if not, then beta probably is not the appropriate measure of risk for determining the firm’s cost of retained earnings.

rRF generally is associated with with Treasury securities; there are many different rates for Treasuries that have different terms to maturity.

If rRF= 4%, rM = 9%, and bs = 1.4

rs= 4% + (9% - 4%)1.4 = 11.0%

cost of retained earnings r s bond yield plus risk premium approach
Cost of Retained Earnings, rsBond-Yield-Plus-Risk-Premium Approach

Studies have shown that the return on equity for a particular firm is approximately 3 to 5 percentage points higher than the return on its debt.

As a general rule of thumb, firms often compute the YTM, or rd, for their bonds and then add 3 to 5 percent.

In the current example, rd = 6.0%. As a rough estimate, then, we might say the cost of retained earnings is

rs ≈ rd + 4% = 6% + 4% = 10.0%

cost of retained earnings r s discounted cash flow dcf approach
Cost of Retained Earnings, rsDiscounted Cash Flow (DCF) Approach

If the firm is expected to grow at a constant rate, then we have the following relationship:

  • Example: The firm, which is growing at a constant rate of 5 percent, just paid a dividend equal to $1.20; its stock currently sells for $18.

= 0.07 + 0.05 = 0.12 = 12.0%

cost of retained earnings r s
Cost of Retained Earnings, rs

The three approaches we used to determine the cost of retained earnings give three different results.

The three approaches are based on different assumptions:

CAPM approach assumes investors are extremely well diversified

DCF approach assumes the firms grows at a constant rate

Bond-yield-plus-risk-premium approach assumes that the return on equity is related to the return on the firm’s debt

Ideally all three approaches should give the same result; if not, however, we might average the results:

rs = (11% + 10% + 12%)/3 = 11%

cost of equity newly issued common stock r e
Cost of EquityNewly Issued Common Stock, re

Rate of return required by common stockholders after considering the costs associated with issuing new stock, which are called flotation costs.

Because the firm has to provide the same gross return to new stockholders as existing stockholders, when the flotation costs associated with a common stock issue are considered, the cost of new common stock always must be greater than the cost of existing stock—that is, the cost of retained earnings.

Modify the DCF approach for computing the cost of retained earnings to include flotation costs

cost of newly issued common stock external equity r e
Cost of Newly Issued Common Stock (External Equity), re

NP0 = net proceeds from the sale of the stock

If flotation costs equal 6 percent, then re in our example is

cost of newly issued common stock r e rationale
Cost of Newly Issued Common Stock, reRationale

Assume a firm (different than in our example) has:

total assets equal to $50,000

is financed with common stock only (5,000 shares)

pays all earnings as dividends, thus g = 0

cost of retained earnings, rs = 10% = ROE

cost of newly issued common stock r e rationale27
The firm sells new common stock:

800 shares, so that 5,800 shares are outstanding after the sale

market price, P0 = $10.00

net proceeds received by the firm, NP0 = $9.50

total amount received by the firm = $9.50 x 800 = $7,600

total assets after stock sale = $50,000 + $7,600 = $57,600

Cost of new equity, re

Cost of Newly Issued Common Stock, reRationale
cost of newly issued common stock re rationale29
Total assets after stock sale = $57,600

If the firm earns re = 10.53% on new investments

Cost of Newly Issued Common Stock, reRationale
  • Stock price would remain at $10, because investors require a 10 percent return; but, the firm must earn 10.53 on new investments to generate 10 percent to investor (due to flotation costs)
weighted average cost of capital wacc
Weighted Average Cost of Capital, WACC

To make decisions about capital budgeting projects, we need to combine the various costs of capital—debt, preferred stock, and common stock—into a single required rate of return.

Weighted average cost of capital, or WACC—the weighted average of the component costs of capital using as the weights the proportion each type of financing makes up of the total financing of the firm.

weighted average cost of capital wacc31
Weighted Average Cost of Capital, WACC

Suppose our illustrative firm has the following capital structure:

Percent

Type of Financingof total

PercentAfter-Tax

Type of Financingof total Cost, r

Debt, d40.0

Preferred stock, ps10.0

Common equity, s 50.0

100.0

3.6%

8.0

11.0 or 12.45

  • If the firm can use retained earnings to finance new projects

WACC = 0.4(3.6%) + 0.1(8.0%) + 0.5(11.0%) = 7.74%

  • If the firm has to issue new common stock to finance new projects

WACC = 0.4(3.6%) + 0.1(8.0%) + 0.5(12.45%) = 8.47%

marginal cost of capital mcc
Marginal Cost of Capital, MCC

Weighted average cost of raising additional funds.

Generally, MCC often is greater than the existing WACC—that is, the cost of new funding increases—because the

firm’s risk increases, which causes investors to require a higher rate of return

costs of issuing new funds increase

MCC schedule—a graph that shows the average cost of funds at various levels of new financing

mcc schedule
MCC Schedule

If the firm expects to retain $200,000 this year

New WACC =

MCC (%)

8.5

Total of New

Funds Raised ($)

0

WACC2

WACC1

7.7

Break

Point

400,000

CE = 400,000 x 0.5 = 200,000

mcc schedule break points
MCC Schedule—Break Points

Break points occur when WACC increases, which is caused by an increase in any of the component costs of capital

debt—when rd1 < rd2 < … < rdn

preferred stock—when rps1 < rps2 < … < rpsn

common equity—retained earnings or new common stock

There is a break point when retained earnings generated in the current period is exhausted.

Once the current addition to retained earnings is exhausted, then the firm must issue new common stock to satisfy additional common equity financing requirements.

Costs of funds often increase as the firm uses significantly higher amounts—risk increases.

mcc schedule break points example
MCC Schedule Break Points—Example

Assume the firm faces the following situation this year:

Debt (40%):

Amount of Funds Cost of Debt, rdT

$ 0 -$100,0006.0%

100,001-200,0006.5

200,001-7.0

Preferred Stock (10%): rps = 8.0%, no matter the amount needed

Common Equity (50%):

Retained earnings generated during the year = $200,000

Cost of retained earnings (internal equity), rs = 11.0%

Cost of new common stock (external equity), re = 12.4%, no matter how much is needed

mcc schedule break points example37
MCC Schedule Break Points—Example

Debt (40%):

Amount of Funds Cost of Debt, rdT

$ 0 -$100,0006.0%

100,001-200,0007.0

200,001-7.5

If the firm needs total funds equal to $250,000, 40%, or $100,000 would be debt.

If the firm needs total funds equal to $500,000, 40%, or $200,000 would be debt.

mcc schedule break points example38
MCC Schedule Break Points—Example

Preferred Stock (10%): rps = 8.0%, no matter the amount needed

Constant cost—no break due to preferred stock

Common Equity (50%):

Retained earnings generated during the year = $200,000

Cost of retained earnings (internal equity), rs = 11.0%

Cost of new common stock (external equity), re = 12.4%, no matter how much is needed

If the firm needs total funds equal to $400,000, 50%, or $200,000 would be RE.

mcc schedule example
MCC Schedule—Example

Funds = $0 - $250,000

Amount atAfter-Tax

$250,000Weightx Cost, k=WACC

Debt

Preferred Stock

Common Equity

Funds = $250,001 - $400,000

Amount atAfter-Tax

$400,000Weightx Cost, r=WACC

Debt

Preferred Stock

Common Equity

Funds = $0 - $250,000

Amount atAfter-Tax

$250,000Weightx Cost, r=WACC

Debt

Preferred Stock

Common Equity

$100,000

25,000

125,000

250,000

0.4

0.1

0.5

1.0

6.0

8.0

11.0

2.4

0.8

5.5

8.7%

= WACC1

$160,000

40,000

200,000

400,000

0.4

0.1

0.5

1.0

7.0

8.0

11.0

2.8

0.8

5.5

9.1%

= WACC2

mcc schedule example40
Funds = $400,001 - $500,000

Amount atAfter-Tax

$500,000Weightx Cost, k=WACC

Debt

Preferred Stock

Common Equity

Funds = above $500,000

Amount atAfter-Tax

$600,000Weightx Cost, r=WACC

Debt

Preferred Stock

Common Equity

MCC Schedule—Example

Funds = $400,001 - $500,000

Amount atAfter-Tax

$500,000Weightx Cost, r=WACC

Debt

Preferred Stock

Common Equity

$200,000

50,000

250,000

500,000

0.4

0.1

0.5

1.0

7.0

8.0

12.4

2.8

0.8

6.2

9.8%

= WACC3

0.4

0.1

0.5

1.0

3.0

0.8

6.2

10.0%

$240,000

60,000

300,000

600,000

7.5

8.0

12.4

= WACC4

mcc schedule41
MCC Schedule

MCC (%)

11.0

10.0

9.0

8.0

Total Funds

Raised ($000)

0

100

200

300

400

500

WACC4 = 10.0

WACC3 = 9.8

WACC2 = 9.1

WACC1 = 8.7

BP1 = 250

BP2

BP3

mcc schedule and investment opportunity ios schedule
MCC Schedule and Investment Opportunity (IOS) Schedule

The firm’s capital budgeting analysis results are:

Project Cost IRR

A$150,00011.0%

B200,00010.5

C200,00010.1

D100,0009.5

ios schedule
IOS Schedule

IRR (%)

11.0

10.0

9.0

8.0

0

100

200

300

400

500

600

700

Total Funds Raised ($000)

IRRA = 11.0

IRRB = 10.5

IRRC = 10.1

IRRD = 9.5

mcc schedule44
MCC Schedule

MCC (%)

11.0

WACC4 = 10.0

WACC3 = 9.8

10.0

WACC2 = 9.1

9.0

WACC1 = 8.7

8.0

Total Funds

Raised ($000)

0

100

200

300

400

500

mcc ios schedules
MCC & IOS Schedules

11.0

IRRA = 11.0

IRRB = 10.5

WACC4 = 10.0

10.0

IRRC = 10.1

WACC3 = 9.8

IRR/MCC (%)

IRRD = 9.5

WACC2 = 9.1

9.0

WACC1 = 8.7

8.0

0

100

200

300

400

500

600

700

Total Funds Raised ($000)

Optimal Capital

Budget = 550

chapter essentials the answers
What types of capital do firms use to finance investments?

Either debt (bond issues) or equity (preferred stock and common equity)

What is the cost of capital?

The average price a firm pays for the funds it uses to purchase assets

How is the cost of capital used to make financial decisions?

A firm should invest in projects that are expected to provide returns greater than its WACC

Chapter Essentials—The Answers
chapter essentials the answers47
Why do funds generated through retained earnings have a cost?

Firms may retain earnings only as long as it can reinvest the earnings at a higher rate than stockholders can earn elsewhere

Who determines a firm’s cost of capital?

Investors

Chapter Essentials—The Answers