COST OF CAPITAL
Prof. Dr. Mehmet Şükrü Tekbaş
COST OF CAPITAL
From a company’s point of view "the cost of using funds of owners
and creditors".
From an investor's point of view "the shareholder's required return
on a portfolio company's existing securities”.
COST OF CAPITAL
Similar terms:
• Minimum required rate of return:
• Hurdle rate
• Cut-off rate
• Opportunity cost
COST OF CAPITAL
• Explicit cost: directly borne cost, cost at the
time of source
• Implicit cost: opportunity cost, cost at the
time of use
COST OF CAPITAL
The cost of capital for firm A is 10%, which is explicit cost.
A is looking for projects having IRR above 10%.
There are several projects.
Project
IRR
X
14%
Y
12%
Z
9%
Projects X and Y are acceptable. However a new project with an IRR
above 12% will replace Y. In this case 12% is implicit rate.
COST OF CAPITAL
Where do we use cost of capital:
• Valuation of a company or equity (share),
• Evaluation of investment projects (Capital budgeting)
• Working capital decisions (sales and credit policy…)
WEIGHTED AVERAGE COST OF CAPITAL
(WACC)
ki = wd kd + we ke
• w = Weights
• k = Cost of each source of capital
WEIGHTS
Book Value or Market Value can be used as weights
• Weights by book value:
Balance sheet of Company A
Assets 100
Debt
40
Paid in capital
25
Retained earnings 35
Total assets 100
Total liabilities
100
Weights by using book value:
wd = 40/100
= 40%
we = (25 + 35)/ 100 = 60%
WEIGHTS
• Weights by market value:
Market of price of debt (bond) = 105
Price of stock = 2,50
Weights by using market value:
Market value of debt = 40 * 105/100 = 42
Market value of equity = 25 * 2,50 = 62,50
(Retained earnings are counted within the share price)
Total value of debt and equity = 42 + 62,50 = 104,50
wd = 42/ 104,50
= 40,20%
we = 62,50 / 104,50 = 59,80%
COST OF EACH SOURCE:
DEBT
• Cost of debt:
it is an after tax cost:
kd = i (1 – t)
where:
i = interest rate
t = corporate tax rate
COST OF PREFERRED STOCK
Preferred stocks are in between stocks and bonds. Technically,
they are equity securities, but they share many characteristics
with debt instruments.
Cost of preferred stock (kps) can be calculated as follows:
kps = Dps / Pps
COST OF EQUITY
Cost of equity can be found by:
•
•
CAPM
Dividend Discount Model
CAPM
Required rate of return by CAPM (Security Market Line, SML)
.
ri = rf + ( r m – rf ) bi
Where:
rf =
rm =
bi =
risk free rate
return on market portfolio
sensitivity to changes in market return, a
measure of systematic risk
( rm – rf ) = equity premium or market risk premium
( rm – rf ) bi = risk premium for the asset, or company
CAPM
ri = rf + ( rm – rf ) b i
Risk free rate, rf should be consistent with the length of the project. For
valuation purposes usually the return on the government bond with 10
years maturity,
For market return, rm the return of broad market or benchmarket index
is used.
bi , a measure of asset’s sensivity to market return.
CAPM
• Example:
rf = 6%
rm = 9%
b = 1,25
ri =6% + (9% - 5%) * 1,25 = 11%
BETA (b)
b is computed by the linear regression between company return and
market return. It is the slope of this regression line which is called
Security Characteristic Line.
ri = a + bi Rm + ei
b also be found by the formula:
bi = Covi,m / sm2 or
bi = ri,m si sm / sm2
Characteristic Line and Beta
y = 0,3585x + 0,0082
R² = 0,0188
Characteristic Line
0,08
0,06
0,04
Ri
0,02
-0,02
-0,01
0,00
0,00
0,01
0,02
-0,02
-0,04
-0,06
Rm
0,03
0,04
BETA (b)
The companies which are not publicly traded do not have betas; for them
industry betas can be used with some adjustment according to leverage, D/E.
Firms in the same industry face similar business risks and should have similar
asset betas. When the information on betas from a peer group is used, the
business risk, which is common to all firms in the industry, can be separated
from the financial risk that will be specific to each firm given its financial
leverage. This can be done by converting the equity betas (levered betas)
into asset betas (unlevered betas) through the so called Hamada equation.
BETA
Beta which is found by Characteristic Line or by the formula
bi = Covi,m / sm2
is called equity beta or levered beta, bL
There is also an asset beta or unlevered beta, bU.
LEVERING AND UNLEVERING BETAS
To find asset beta or unlevered beta the formula (Hamada equation):
bU = bL ( 1 / ( 1 + (1 – t ) D / E )
To convert the asset beta into equity beta:
bL = bU / ( 1 + (1 – t ) D / E )
t = corp. income tax rate
D = debt
E = equity
LEVERING AND UNLEVERING BETAS: EXAMPLE
We want to find the cost of capital of a non listed company.
Since the company is not trading on the stock exchange it does not have a share
price and therefore not a beta. Here we can use industry beta to find beta for
Company A.
With following information for the industry and company A:
Industry
Company A
Debt
40 %
50 %
Equity
60 %
50 %
Equity beta
1,5
?
Tax rate = 30 %
Asset beta = bU = 1,50 /( 1 + ( 1-30%) (40/60)) = 1,02
Equity beta = bL = 1,02 ( 1 + (1-30%) (50/50)) = 1,73
We can find equity beta for company A as 1,73, and we can use it finding the
cost of equity and WACC.
BETA
Factors Affecting Beta:
• Leverage
• Liquidity
• Asset growth rate
• Size
• Dividend payout ratio
• Volatility in earnings
• Accounting Beta
BETA
Beta of a company is not stable over time. It changes because of:
- Change in product line,
- Change in technology,
- Deregulation,
- Change in financial leverage
DIVIDEND DISCOUNT MODEL
ki = (D1 / P0) + g
where:
D1 = dividend for the coming year
P0 = current share price
g = growth rate in EPS, or dividend
Assumptions:
Stable growth rate
P0 = D1 / (k-g)
WAAC AND OPTIMAL CAPITAL STRUCTURE
The cost of debt is cheaper than cost of equity. Debt is less risky than
equity, as the payment of interest is often a fixed amount and
compulsory in nature, and it is paid in priority to the payment of
dividends. Also in the event of a liquidation, debt holders would receive
their capital repayment before shareholders as they are higher in the
creditor hierarchy as shareholders are paid out last. As debt is less risky
than equity, the required return needed to compensate the debt
investors is less than the required return needed to compensate the
equity investors.
WAAC AND OPTIMAL CAPITAL STRUCTURE
There are two counterbalancing forces in capital structure. Initially,
using debt can lower the firm’s cost of capital by taking advantage of
the lower-cost characteristics of debt financing (relative to equity).
However, too much debt, on the other side increases the risk of the
firm and causes the cost of equity and the cost of debt to rise.
Therefore, the optimal mix of debt and equity is the level at which the
cost of capital is minimized. At this level the value of the firm will be
maximized. This level varies from industry to industry.
OPTIMAL CAPITAL STRUCTURE
Optimal capital structure is the best mix of debt and equity
financing that maximizes a company’s market value while
minimizing its weighted average cost of capital.
OPTIMAL CAPITAL STRUCTURE
MARGINAL COST OF CAPITAL
Marginal cost of capital is the weighted average cost of the last dollar
of new capital raised by a company.
Companies can raise new capital from:
• retained earnings,
• issuing new stock,
• issuing new debt
Retained earnings are the only source of financing to maintain the
target capital structure without issuing new stock. Therefore, the
marginal cost of capital remains the same if new capital is raised
through retained earnings. Raising new funds by issuing new stocks
will be more costly.
MARGINAL COST OF CAPITAL
Firm A has 1000 TL assets, they are financed by debt=400 TL, and equity=600
TL. Paid in capital is 300 TL and retained earnings are 300 TL.
The share price of A is 2 TL, market return is expected as 10%, risk free rate is
6% and Beta of firm A is 1,25. Tax rate is 30%. The interest rate for debt is 9%.
The expected market return is 10%.
Firm A is expecting a level of 150 TL as retained earnings for next year’s
investment.
- What is level of optimal level of investments (optimal investment budget) for
next year without issuing new stock?
- What is the marginal cost of capital for an investment budget 400 TL?
MARGINAL COST OF CAPITAL
The WACC for firm A:
kd = 9% * (1-30%) = 6,30 %
ke = 6% + (10% - 6%) * 1,25 = 11 %
WACC = k = 6,3% * 0,4 + 9% * 0,6 = 9,12%
The optimal investment budget without issuing new stock is 250 TL
(with wd = 40% and we= 60%).
With an investment budget above 250 TL new share issue is required.
The cost of new share issue will push MCC above 9,12%
MARGINAL COST OF CAPITAL
For a level of investment budget at 400 TL, the source of funds and
MCC will be:
- 40% of 400 TL will come from new borrowing, 160 TL.
- 60% of 400 TL will come from equity, 240 TL.
150 TL of equity portion will come from retained earnings and for 90 TL
new shares will be issued.
FLOTATION COST
Flotation costs are the costs incurried by a company when issuing new
securities. The costs can be various expenses including, underwriting,
legal, registration, audit, etc. fees. Flotation expenses are expressed as
a percentage of the issue price.
Flotation costs increase the cost of capital.
FLOTATION COST
Because of floatation costs, the firm will have to raise more than the
amount it needs.
Flotation cost adjusted initial outlay =
𝐹𝑖𝑛𝑎𝑛𝑐𝑖𝑛𝑔 𝑛𝑒𝑒𝑑𝑒𝑒𝑑
(1−𝐹𝑙𝑜𝑡𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡 𝑖𝑛 %)
= P/(1-f)
WACC and FLOTATION COST
Example If a firm needs $100 million to finance its new project and the
floatation cost is expected to be 5%, how much should the firm raise by
selling securities?
Flotation cost adjusted initial outlay = $100 million ÷ (1-0,05)
= $105,26 million
MARGINAL COST OF CAPITAL
WACC and PROJECT RISK
Suppose a Company has a cost of capital, based on the CAPM, of 13,4%.
The risk-free rate is 5%;
the market return is 12%, and
the firm’s beta is 1,2
Required rate of return for the company = 5% + [12% – 5%] * 1,2 = 13,4%
The breakdown of the company’s investment projects:
1/3 Automotive retailer, b = 1.7
1/3 Computer Mfr. , b = 1.3
1/3 Energy, b = 0.6
average b of assets = 1.2
When evaluating a new investment in automobile division, which cost of capital should be
used?
WACC and PROJECT RISK
The required rate of return for the projects related to three divisions
will be different.
Automobile retailer: 5% + (12% - 5%) * 1,7 = 16,9 %
Computer:
5% + (12% - 5%) * 1,3 = 14,1 %
Energy:
5% + (12% - 5%) * 0,6 = 9,2 %
WACC and PROJECT RISK