CHAPTER 14
COST OF CAPITAL
BY
T.M.D.SAUMYA
DIMANTHA SAMARAJEEWA
MADUSHI RATHNAYAKE
OVERVIEW OF THE LESSON
• Introduction to Cost of Capital
• Cost of Equity
• Cost of Debt and Preferred Stock
• Weighted Average Cost of Capital
• Divisional and Project Cost of Capital
• Floating Costs and the Weighted Average Cost of Capital
• Summary and Conclusion
INTRODUCTION TO COST OF
CAPITAL
Cost of capital of a project can be explained as the minimum
required return from that project.
Ex:
Project A
T0
Initial
Investment
T1
Cash Flows
T2
Cash Flows
T3
Cash Flows
DETERMINANTS OF THE COST
OF CAPITAL
• Risk Associated with the Investment
• Discount Rate
• Tax Rate
OVERALL COST OF CAPITAL OF A
FIRM
This will reflect required return on the firm’s assets as
a whole. If we consider that firm uses both debt and
equity capital, this overall cost of capital will reflect
both cost of debt and its cost of equity capital
P1
Stock
Holders
P2
Firm ABC
Creditors
P3
P4
COST OF EQUITY
Creditors
Cost of debt Capital
Firm’s a Capital
Structure
Capital Mixture
Debt/ Equity Capital
Compensate
Cost of Equity Capital
Investors
COST OF EQUITY
• The return that equity investors require on their
investment in the firm.
• It is difficult to determine Firms overall cost of capital
• WHY?
• Because there is no way of directly observing the return
that the firm’s investors require on their investments
• Need to somehow estimate the firm’s cost of capital
• Hence there are two approaches use to determine the
cost of capital such that;
• Dividend growth model approach
• Security market line approach (SML)
DIVIDEND GROWTH MODAL
APPROACH
•
Estimate cost of equity using dividend growth
model approach.
•
Estimate based on the information ;
- P0 = Price per share of the stock
- D0 = The dividend just paid
- g = Expected growth rate
•
P0 and D0 are available in publicly traded, dividendpaying company
•
Only g variable must be estimated.
DIVIDEND GROWTH MODAL
APPROACH
The equation of dividend growth model:
D1 = D0 (1+ g)
P0 = Price per share of the
stock
D0 = The dividend just paid
g = Expected growth rate
RE = Return that shareholder
requires on stock
D1 = Next period’s projected
dividend
Hence:
2
DIVIDEND GROWTH MODAL
APPROACH
Using equation
2
we can derive
RE = D1/P0 +g
RE = Return that shareholder requires on stock
P0
D1
= Price
per share of stock
= Next period’s projected dividend
g = Expected growth rate
DIVIDEND GROWTH MODAL
APPROACH
Example 1
Suppose Greater State Public Service, paid a dividend
of $4 per share last year. The stock currently sells for
$60 per share. Company estimate that the dividend
will grow steadily at 6% per year into the indefinite
future. What is the cost of equity capital to the Greater
State ?
DIVIDEND GROWTH MODAL
APPROACH
Answer:
Dividend for coming year
D1 = D0 (1+ g)
= $4 * 1.06
= $4.24
RE = D1/ P0 + g
= $4.24 / $60 +0.6
= 13.07%
DIVIDEND GROWTH MODAL
APPROACH
Estimation of growth Rate :
• Analyst’s forecast of future growth rate
• Different sources give different estimates
• Get average of multiple estimates
• Using historical growth rate
• Observe dividend for previous years
• Calculate year to year growth rate
• Take the average
ESTIMATION OF GROWTH RATE
USING HISTORICAL GROWTH RATES
Example
Year
Dividend
Dividend ($) Change ($)
Pecentage Change
1990
$1.10
1991
$1.20
0.1
9.09%
1992
$1.35
0.15
12.50%
1993
$1.40
0.05
3.70%
1994
$1.55
0.15
10.71%
Average growth rate = ( 9.09+ 12.5 + 3.7 + 10.71) / 4
= 9%
Hence expected growth rate (g) = 9% per year
DIVIDEND GROWTH MODAL
APPROACH
Advantage
Disadvantage
Simplicity – Easy to
understand and easy to use
• Applicable only for the companies
that pay dividend
• Underlying assumption of dividend
grows at a constant rate
• Estimated Cost of capital is very
sensitive to the growth rate
• Does not explicitly consider the risk
(No allowance for the degree of
uncertainty of certainty)
SECURITY MARKET LINE (SML)
APPROACH
• Cost of equity will be calculated based on market risk
premium and beta coefficient β
• Expected return on a risky investment depends on 3
attributes;
• Rf = Risk free rate
• E(RM) – Rf = The market risk premium
• β = Systematic risk of the asset relative to average, which is
called beta coefficient
Expected return on the company’s equity, E(RE) can be
written as;
E(RE) = Rf + βE × [ E(RM) – Rf ]
SECURITY MARKET LINE (SML)
APPROACH
• Since SML approach use for equity capital we can
denote the equation as;
RE = Rf + βE × [ (RM– Rf )]
• Rf
= Risk free rate
• RM – Rf = The market risk premium
• β
= An estimate of relevant beta factor
SECURITY MARKET LINE (SML)
APPROACH
Example 2
Company C is an active player of the market ,assuming that
the estimate of market risk premium of the market (Based on
large common stock) is 8.6%. Treasury bills are paying
about 5.4% and the estimated beta coefficient of the
company C, is 0.9. Estimate the cost of equity of company C
RC = Rf + βC × [ (RM– Rf )]
= 5.4% + 0.9 × (8.6%)
= 13.4%
SECURITY MARKET LINE (SML)
APPROACH
Advantage
Disadvantage
• Explicitly adjust for risk
• Two elements should be estimated
to calculate the problem. (Risk
premium and β )
• Steady dividend growth is • Poor estimation can result
irrelevant for the
inaccurate output
estimation
COST OF EQUITY CAPITAL
Example 3
Suppose stock in Alpha Air Freight has a beta of
1.2. The market risk premium is 8% , and the risk
free rate is 6%. Alpha’s last dividend was $2 per
share, and the dividend expected to grow at 8%
indefinitely. The stock currently sells for $30. What
is Alpha’s cost of equity Capital?
Answer :
• Using SML approach
Expected return on the common stock of Alpha Air Freight is;
RE = Rf + βE × [ (RM– Rf )]
= 6% + 1.2 × 8%
= 15.6%
• Using Dividend growth model
The projected dividend for next year
D1 = D0 × (1+ g)
= $2 × (1.08)
= $2.16
Expected return
RE = D1 /P0 + g
=$2.16 / 30
= 15.2%
COST OF DEBT
• Cost of Debt is the return that lenders require on
the firm’s debt.
• Cost of debt can be easily identified as the
interest rates that we have to pay creditors.
• If company has outstanding bonds, cost of
bonds
•
can be directly identified as the yield to
maturity.
COST OF DEBT…
Cost of Bonds
t
Bond Value=C*[1-1/(1+r)]/r + F/(1+r)t
C= Coupon paid each period
R= Yield to maturity
T=Number of periods
F=Bonds face value
COST OF DEBT…
Cost of Bonds…
Ex:
Suppose the ABC company issued a 30 year , 7 percent
bond eight years ago .The bond is currently selling 96% of
its face value,(960).What is the ABC’s cost of debt?
(Hint- The bond is selling at a discount ,so the yield to maturity is
greater than 7%.But the discount is 40 ,so the increase of
percentage also shouldn’t be that much higher from 7%.Use Trial
and Error Method)
COST OF DEBT…
Bond Value=C*[1-1/(1+r) ]/r + F/(1+r)
Trial 1(Considering YTM is 7.4%)
Bond Value = 70*(1-1
t
(1+0.074 22 ))/0.074
t
+ 1000/(1 + 0.07422 )
=749.261+207.925
=957.185
But it is lesser than 960(actual value),so the rate should be reduced further…
Trial 2(Considering YTM is 7.3%)
Bond Value = 70*(1-1
(1+0.07322 ))/0.073+
1000/(1 + 0.07322 )
=755.369+212.23
=967.598
But it is greater than 960(actual value),so the YTM should be in between
Through further calculations.. YTM=7.37%
Cost of Bond= 7.37%
COST OF DEBT…
Cost of Preferred Stock
Cost of Preferred Stock is simply equal to dividend yield of
that preferred stock.
Dividend Yield= D
P0
D -Fixed Dividend
P0- Current Price per Share
COST OF DEBT…
Ex:
ABC company has issued preferred stock which is paying
$7.72 of annual dividend and it is currently sold for $102 per
share. What is ABC’s cost of preferred stock?
Dividend Yield= D
P0
Dividend Yield=$7.72/$102 = 7.57%
So, Cost of Preferred Stock=7.57%
THE WEIGHTED AVERAGE COST
OF CAPITAL
THE WEIGHTED AVERAGE COST
OF CAPITAL
• Firms capital structure is a specific mix
• Firm’s Total capitalization, which is the sum of its
long term debt and equity
• Total capitalization does not always imply the total
value of the company ; but the weighted average
approach is applicable in either case.
• In this process short term liabilities are often ignored
CAPITAL STRUCTURE WEIGHT
• Market value of firm’s equity (E)
• Number of share outstanding is multiplied by Price per share
• Market value of firm’s debt (D)
• Multiply the market price of a single bond by the number of
bonds outstanding
• If multiple bond issues, then repeat the calculation and add up
the result
• Privately held debt – observe yields on publicly traded debt and
them estimate the market value of firm’s debt
• Total market value of debt and equity (V)
V= E + D
• By dividing both sides by V;
100%= E/V + D/V
CAPITAL STRUCTURE WEIGHT
• The percentage of debt and equity is called the Capital
structure weight
• Example :
If the total market value of a company’s stock were calculated as
$200 million and the total market value of the company’s debt were
calculated as $50 million,
Then combined market value of the company (V)= E+D
=$200 + $50 = $250
Weight of equity = E/V = 200/250 = 80%
Weight of debt = 100% - 80% = 20%
TAXES AND THE WEIGHTED
AVERAGE COST OF CAPITAL
• Discount rate need to be expressed on an after tax basis
• Usually interest paid by a corporation is deductible for tax
purposes.
•
It is need to find after tax rate as ;
•
= R D (1 - T C )
TAXES AND THE WEIGHTED
AVERAGE COST OF CAPITAL
Example:
Suppose a firm borrows $1 million at 9 percent interest. The corporate
tax rate is 34 percent. What is the after tax interest rate on this loan?
total interest rate per year = $100,000 × 9% = $90,000
Tax deductible on loan
= $90,000 × 34% = $30,600
Hence the after tax interest bill = $90,000 - $30,600
= $59,400
Thus, after tax interest rate is = ($59,400/ $100,000) × 100%
= 5.94%.
Aftertax rate can be written as R D (1 - T C )
TAXES AND THE WEIGHTED
AVERAGE COST OF CAPITAL
WACC = (E/V) × RE + (D/V) × RD × (1- Tc)
• WACC = weighted average cost of capital
• RE = cost of equity
• Tc = Corporate tax rate
• RD = Pre tax interest rate
SOLVING (THE WAREHOUSE PROBLEM )
SIMILAR CAPITAL BUDGETING PROBLEMS
• Before rush to discount the cash flows at the WACC to estimate NPV,
firm need to make sure that they are doing the right thing.
• The WACC for a firm reflects the risk and the target capital structure of
the firm’s existing assets as a whole
• WACC is the appropriate discount rate only if the proposed investment
is a replica of the firm’s existing operating activities
• The project depends on whether the warehouse project is in the same
risk class as the firm
• Projects like the warehouse renovation that are intimately related to
the firm’s existing operations are often viewed as being in the same
risk class as the overall firm.
SOLVING (THE WAREHOUSE PROBLEM )
SIMILAR CAPITAL BUDGETING PROBLEMS
Example
Suppose the firm has a target debt/equity ratio of 1/3. We know
that a debt/equity ratio of D/E = 1/3 implies that E/V is 0.75 and
D/V is .25. The cost of debt is 10 percent, and the cost of equity is
20 percent.
Assuming a 34 percent tax rate, the WACC will be:
WACC = (E/V) × R E × (D/V) × R D ×(1 - T C )
= 0 .75 × 0.20 × .25 × 0.1 × (1 - 0 .34)
= 16.65%
• The warehouse project had a cost of $50 million and expected
after tax cash flows (the cost savings) of $12 million per year for
six years. The NPV (in millions) is thus:
• r = WACC
• WACC= 16.65% (From part 1)
NPV= −$𝟓𝟎 +
$𝟏𝟐
(𝟏+𝑾𝑨𝑪𝑪 )𝟏
= -$50 + $43.47
= -$ 6.53 million
+
$𝟏𝟐
(𝟏+𝑾𝑨𝑪𝑪 )𝟐
+ …. +
$𝟏𝟐
(𝟏+𝑾𝑨𝑪𝑪 )𝟔