2. 4.1 CONCEPT OF COST OF CAPITAL
Cost of capital refers to the minimum rate of return a
firm must earn on its investment, so that the market
value of the company's equity shares does not fall.
“The rate of return, the firm requires from investment
in order to increase the value of the firm in the market
place”. – Hampton,
John. J.
It is not a cost as such. It is really the rate of return that
a firm requires to earn from its project.
3. 4.2 COMPONENTS OF COST OF CAPITAL
Return to zero risk level: This refers to the
expected rate of return when a project involves no
risk.
Premium for business risk: Business risk refers
to the variability in operating profit due to changes
in sales.
Premium for financial risk: Financial risk refers
to the risk on account of higher debt content in
capital structure.
4. 4.3 SIGNIFICANCE OF COST OF CAPITAL
1. Capital Budgeting Decision
Cost of capital is used as the measuring rod for
selecting an investment proposal, out of various
proposals pending before management.
According to discounted cash flow methods of capital
budgeting, if the present value of expected return from
investment is greater than or equal to the cost of
investment, the project may be accepted; otherwise the
project may be rejected. Hence, the concept of cost of
capital is very useful in capital budgeting decision.
5. 2. Designing the Capital Structure
While designing an optimal capital structure, a proper
mix of debt and equity capital, the management has to
keep in mind the objective of maximizing the value of
the firm and minimizing the cost of capital.
3. Decision about the Method of Financing
An efficient financial executive must analyze the rate
of interest on loans and normal dividend rates in the
market form time to time. Then, he may have a better
choice of the source of finance which bears the
minimum cost of capital, whenever the company
requires additional finance.
6. 4. Evaluation of Performance of Top Management
The actual profitability of the project is compared
with projected overall cost of capital and actual cost
of capital of funds raised to finance the project. If the
actual profitability of the project is higher than the
projected, the performance is satisfactory.
5. Other Areas of Decision Making
It is also used in making other financial decisions such
as dividend decisions, working capital management
policies, capital expenditure control, capitalization of
profits and making the right issues.
7. 4.4 DIFFERENT TYPES OF COSTS
1. Explicit Cost and Implicit Cost
The explicit cost is the discount rate that equates the
present value of the cash inflows with that of cash
outflow. In other words, it is the internal rate of return.
The implicit cost is also known as opportunity cost or
cost of retained earnings. It is the rate of return
associated with the best investment opportunity of its
shareholders, that will be foregone if the project
presently under consideration by the firm were
accepted.
8. 2. Specific Cost and Composite Cost
Specific cost refers to the cost of a specific source of capital.
Example: Interest is the specific cost of Bond and Dividend
is the specific cost of Preferred Capital. Composite cost is
the combined cost of various sources of capital. (i.e., the
total of equity shares, preference shares, bonds, loans
etc.,) It is also called overall cost of capital.
3. Historical cost and Future cost
Historical cost is the cost which is calculated on the basis
of existing capital structure.
9. Future cost refers to expected cost of funds to finance
the expected project.
4. Average cost and Marginal cost
Average cost is the weighted average cost of the
various sources of finance.
Marginal cost refers to average cost of capital which
has to be incurred to obtain additional funds required
by a firm.
10. 4.5 DETERMINANT OF COMPONENTS COST OF
CAPITAL
1. Cost of Debt
According to Weston and Brigham, the cost of debt is defined
as “the rate of return that must be earned on debt-finance
investment in order to keep unchanged the earnings available to
equity share holders”. Thus it is required rate of return that the
debt investment yield to protect the shareholders interest.
Computing Cost of Debt:
i) Debt issued at Par: Cost of debt is the rate of interest payable
on debt.
Kdb = I / P
Where, Kdb – Cost of debt before tax; P – Par value of
debentures; I – Interest;
11. ii) Debt issued at Premium or Discount: If the bonds are
issued at premium or discount, the cost debt will not be
equal to the coupon rate of interest as adjusted by the
company’s rate of tax. Hence it should be calculated on
the basis of net proceeds realized on account of such
issues.
Kdb = I / NP
Where, Kdb – Cost of debt before tax; NP – Net proceeds
of debentures; I – Interest;
Kda = Kdb(1-T) = (I / NP) * (1-T)
Where, Kda – Cost of debt after tax; Kdb – Cost of debt
before tax; NP – Net proceeds of debentures; I – Interest;
12. iii) Cost of Debt Redeemable at Par: If the bonds are redeemable after
the expiry of fixed period the effective cost of debt after tax can be
calculated.
Kda = {[I + (P-NP)/n] / [(P+NP)/2]}*(1-T)
Where, Kda – Cost of debt after tax; NP – Net proceeds; P = Par value
of debentures; I – Interest; T – Tax; n = Number of years to maturity;
iv) Cost of Debt Redeemable at Premium: If the bonds are
redeemable at premium after the expiry of fixed period the effective
cost of debt after tax can be calculated.
Kda = [I + (RV-NP)/n] / [(RV+NP)/2]
Where, Kda – Cost of debt after tax; NP – Net proceeds; RV -
Redeemable value of debentures; I – Interest; n = Number of years to
maturity;
13. Example:1
A company issues 10% irredeemable debentures of
Br 100,000. The company is in the 55% tax bracket.
Calculate the cost of debt before tax if the debentures
are issued at i) par ii) 10% discount iii) 10%
premium.
Solution:
i) Issued at Par
Kdb = I / NP = 10,000 / 100,000 = 0.1 or 10%
I = 100,000 * 10% = 10,000
ii) Issued at discount (10%)
I = 100,000 * 10% = 10,000
NP = 100,000 – (100,000*10%) = 90,000
Kdb = I / NP = 10,000 / 90,000 = 0.111 or 11.1%
14. iii) Issued at premium (10%)
I = 100,000 * 10% = 10,000
NP = 100,000 + (100,000*10%) = 110,000
Kdb = I / NP = 10,000 / 110,000 = 0.0909 or 9.09%
Example:2
A ltd. Issues Br 50,000 8% debentures. The tax rate
applicable to the company is 50%. Compute the cost of
debt capital if the debentures are issued at i) par ii) 5%
discount iii) 10% premium.
Solution:
i) Issued at Par
NP = 50,000; I = 50,000* 8% = 4000; Tax = 50% or .50;
Kda = (I / NP) * (1-T) = (4000 / 50000) * (1-0.50) = 0.04 or 4%
15. ii) Issued at discount (5%)
NP = 50,000 – (50,000*5%) = 47,500;
I = 50,000* 8% = 4000; Tax = 50% or .50;
Kda = (I / NP) * (1-T) = (4000 / 47,500) * (1-0.50)
= 0.0421 or 4.21%
iii) Issued at premium (10%)
NP = 50,000 + (50,000*10%) = 55,000;
I = 50,000* 8% = 4000; Tax = 50% or .50;
Kda = (4000 / 55,000) * (1-0.50) = 0.0363 or 3.63%
16. Example:3
D Ltd. Issues Br 100,000 9% debentures at a
premium of 10%. The costs of floatation are 2%. The
tax rate applicable is 60%. Compute cost of debt
capital.
Solution:
NP = 100,000 + (100,000*10%) = 110,000;
NP with cost floatation = 110,000 – (110,000 * 2%)
= 107,800
Tax = 0.60; I = 100,000 * 9% = 9000
Kda = (I / NP) * (1-T) = (9000 / 107,800) * (1-0.60)
= 0.0334 or 3.34%
17. Example:4
A company issues Br 1,000,000, 10% redeemable
debentures at a discount of 5%. The costs of
floatation amount to Br. 30,000. The debentures are
redeemable after 5 years. Calculate before-tax and
after-tax cost of debt assuming a tax rate of 50%.
Solution:
Kdb = [I + (P-NP)/n] / [(P+NP)/2]
I = 1,000,000 * 10% = 100,000; P= 1,000,000;
NP = 1,000,000 – (1,000,000 *5%) – 30,000 = 920,000;
Kdb= [100,000 + (1,000,000 – 920,000)/5]
(1,000,000+920,000)/2
= 116,000 / 960,000 = 0.1208 or 12.08%
Kda = Kdb(1-T) = 12.08(1-0.50) = 6.04%
18. 2. Cost of Preference Capital
A fixed rate of dividend is payable on preference
shares. The rate of dividend is fixed at the time of
issue. The cost of preference capital is a function of
dividend expected by its investors.
i) Cost of preference capital issued at par
Kp = Dp/ P
Where, Kp – Cost of preference capital;
P – Par value of preference capital;
Dp – Annual preference dividend;
19. ii) Cost of preference capital issued at premium or discount
Kp = Dp / NP
Where, Kp – Cost of preference capital; NP – Net proceeds of
preference capital; Dp – Annual preference dividend;
iii) Cost of redeemable preference shares
Kpr = [Dp + (MV-NP)/n] / [(MV+NP)/2]
Where, Kpr – Cost of redeemable preference shares;
NP – Net proceeds; MV - Maturity value of preference shares;
Dp – Annual preference dividend;
n = Number of years in which preference shares to be
redeemed;
20. Example:5
A company raises the capital of Br 100,000 by issuing
10000 preference share of Br 10 each. The dividend rate
on the preference share is 10%. Calculate the cost of
preference share when 1. Preference share are issued at
par 2. Preference shares are issued at 10% premium 3.
Preference share are issued at 10% discount.
Solution:
i) Issued at par
Dp= 100,000 * 10% = 10,000;P = 100,000
Kp = Dp/ P = 10,000 / 100,000 = 0.1 or 10%
ii) Issued at 10% premium
NP = 100,000 + (100,000*10%) = 110,000;
Dp= 100,000 * 10% = 10,000
Kp = Dp/ NP = 10,000 / 110,000 = 0.09 or 9%
21. ii) Issued at 10% discount
NP = 100,000 - (100,000*10%) = 90,000;
Dp= 100,000 * 10% = 10,000
Kp = Dp/ NP = 10,000 / 90,000 = 0.111 or 11.1%
Example:6
A firm has issued preference share of Br 100 each
generating a proceed of Br 100,000. The dividend rate is
14%.The Preference shares will be redeemed after 10
years. Floatation cost is about 5%.Determine the cost of
preference share.
Solution:
Dp= 100,000 * 14% = 14,000; MV = 100,000;
NP = 100,000 – (100,000 *5%) = 95,000; n= 10
Kpr = [Dp+ (MV-NP)/n] / [(MV+NP)/2]
Kpr= [14,000 + (100,000 – 95,000)/10] = 0.1487 or 14.87%
22. 3. Cost of Equity Capital
1. It is not the out of pocket cost of using equity
capital, as the equity shareholders are not paid
dividend at a fixed rate every year.
2. Moreover payment of dividend is not a legally
binding on the part of the company.
3. The equity shareholders invest their funds in
shares with the expectation of getting dividend from
the company.
4. Therefore equity shares carry a cost which is
highest among all the sources of funds as they
involve highest degree of risk.
23. i) Dividend Yield or Dividend Price Approach: The cost of equity share is
calculated on the basis of required rate of return in terms of future
dividends to be paid on equity shares for maintaining their present market
price.
Ke = D/ NP (or) D / MP
Where, Ke – Cost of equity capital; NP – Net proceeds per share;
D – Expected dividend per share; MP – Market price per share;
ii) Dividend Yield plus Growth in Dividend Approach: The cost of equity
share capital is calculated on the basis of expected dividend rate plus rate
of growth in dividend.
Ke = (D/ NP) + g (or) (D / MP) + g
Where, Ke – Cost of equity capital; NP – Net proceeds per share;
D – Expected dividend per share; MP – Market price per share;
g – Expected rate of growth in dividend;
24. iii) Earning Price Approach: The cost of equity share capital is
equal to the rate which must be earned on incremental issue of
equity shares so as to maintain the present value of investment
intact.
Ke = EPS/ NP (or) EPS / MP
EPS = Total earnings / Number of shares outstanding
Where, Ke – Cost of equity capital; NP – Net proceeds per share;
EPS – Earnings per share; MP – Market price per share;
iv) Realized Yield Approach: The cost of equity share capital is
calculated on the basis of past records of dividends actually
realised by the equity shareholders which is discounted at the
present value factor and then compare with the value of
investment.
25. Example:7
A company offers for public subscription the shares of Br 10 at a
premium of 10%.The commission cost for the company is 5%. The
dividend rate is 20%. Calculate the cost of equity.
Solution:
D= 10*20% = 2; NP = 10 + 10*10% = 10+1 =11
NP = 11- (5% of 11) = 10.45
Ke = D/ NP = 2 / 10.45 = 0.1914 or 19.14%
Example:8
A company s share of face value Br 10,has a market value of Br
15. The expected dividend to be paid is 20% of the face value.
Calculate the cost of equity.
Solution:
D= 10*20% = 2; MP = 15
Ke = D/ MP = 2 / 15 = 0.1333 or 13.33%
26. Example:9
A company's share has a market price of Br 20.
The company pays a dividend of Br 1 per share.
The shareholders expect a growth rate of 5%
per year. Calculate the cost of equity.
Solution:
D= 1; MP = 20; g =5%
Ke = (D/ MP ) +g = (1 / 20) + 0.05 = 0.10 or 10%
27. 4. Cost of Retained earnings
Retained earnings are the accumulated amount of
undistributed profits belonging to the equity shareholders. It
provides a major source of financing expansion and
diversification projects.
If these were distributed to the shareholders, they would have
reinvested them in the same company by purchasing its equity
and earn on these additional shares the same rate of return as
they are earning on their existing shares. Thus the cost of
retained earnings is the same as the cost of equity capital.
28. Cost of Retained earnings
Kr = Ke (1-T) (1-B)
Where, Kr – Required rate of return on retained earnings;
Ke- Shareholders required rate of return;
T - Shareholders marginal tax rate;
B – Brokerage cost;
Example:10
Calculate the cost of retained earnings. Current market price of a
share Birr 140. Cost of floatation/brokerage per share 3% on
market price. Growth in expected dividends 5%. Expected
dividend per share on new shares Birr 14. Shareholders
marginal/personal tax rate 30%.
Solution:
D= 14; MP = 140; g =5%
Ke = (D/ MP ) +g = (14 / 140) + 0.05 = 0.15 or 15%
Kr = Ke (1-T) (1-B) = 15% (1-0.30) (1-0.03) =10.19%
29. 5. Weighted average cost of capital
Weighted average is an average of the costs of specific source
of capital employed in a business, properly weighted by the
proportion, they hold in the firms capital structure.
As against the simple average, weighted average is useful due
to the fact that the proportion of various sources of funds in the
capital structure of a firm is different.
A) Advantages of Weighted Average Cost of Capital
In financial decision making the weighted average cost of
capital is more relevant.
The average cost of capital provides one single figure which
may be used as discount factor in computing the discounted
cash inflows of the future stream of earnings.
30. B) Disadvantages of Weighted Average Cost of Capital
The cost raising funds are independent to the value funds
raised.
It is presumed that the present cost of the various sources of
funds would remain the same in future also. Which is not
true in actual practical life.
The specific costs are based upon the existing capital
structure and these will change when additional funds have
been raised.
If the growth of the company are being changed, there will
be a change in the weighted average cost of capital.
Where there is a change in capital structure involving a
change in debt-equity mix. There will be a change in the
weighted average cost of capital.
31. Example:11
A firm’s after tax cost of capital of the specific sources is
as follows: Cost of debt – 4.77%; Cost of preference
shares – 10.53%; Cost of Equity capital – 14.59%; Cost
of retained earnings – 14.00%.
The following is the capital structure: Debt Br 300,000;
Preference capital Br 200,000; Equity capital Br
400,000; Retained earnings Br 100,000; Total Br
1,000,000.
Calculate the weighted average cost of capital using
book value weights (Proportion method).
32. Solution:
Computation of weighted average of cost of capital
(Book Value Weights)
Weighted average cost of capital = 0.1077 *100 =
10.77%
Sources of
funds
Amount Proportion Specific
after
tax cost
Weighte
d cost
Debt
Preference Capital
Equity capital
Retained earnings
300,000
200,000
400,000
100,000
(300,000/1,000,000)*100 = 30%
(200,000/1,000,000)*100 = 20%
(400,000/1,000,000)*100 = 40%
(100,000/1,000,000)*100 = 10%
0.30
0.20
0.40
0.10
0.0477
0.1053
0.1459
0.1400
0.0143
0.0210
0.0584
0.0140
Total 1,000,000 0.1077
33. Example:12
From the following information capital structure of a
company, calculate the overall cost of capital (Total cost
method) using a) book value weights and b) market
value weights
The after tax cost of different sources of finance is as
follows: Equity share capital – 14%; Retained earnings –
13%; Preference share capital – 10%; Debentures – 5%.
Sources Book Value Market value
Equity share capital (Br 10 shares) Br 45,000 Br 90,000
Retained earnings 15,000
Preference capital 10,000 10,000
Debentures 30,000 30,000
34. Solution:
Computation of weighted average of cost of capital
(Book Value Weights)
Weighted average cost of capital
=(10,750/100,000)*100
= 10.75%
Sources of funds Amount Specifi
c after
tax
cost
Total after tax
cost
Equity capital
Retained earnings
Preference Capital
Debentures
45,000
15,000
10,000
30,000
14%
13%
10%
5%
45,000*14%=
6300
15,000*13%=1950
10,000*10%=1000
30,000*5% = 1500
Total 100,000 10,750
35. Computation of weighted average of cost of capital
(Market Value Weights)
Weighted average cost of capital
=(15,100/130,000)*100
= 11.62%
Sources of funds Amount Specific
after tax
cost
Total after tax
cost
Equity capital
Preference Capital
Debentures
90,000
10,000
30,000
14%
10%
5%
90,000*14%= 12600
10,000*10%=1000
30,000*5% = 1500
Total 130,000 15,100
36. 4.6 MARGINAL COST OF CAPITAL
Cost of capital plays important roles in financial
analysis and asset valuation. A chief use of the marginal
cost of capital estimate is in capital-budgeting decision
making.
A way of determining the cost of obtaining just one
more dollar of capital.
The marginal cost will vary according to the type of
capital used. For example, raising funds through the use
of unsecured or subordinated debt, or
through debt that requires higher interest
rates to offset risk, will be more expensive than debt
that is backed by collateral, such as a secured bond.
37. A company's marginal cost of capital (MCC) may
increase as additional capital is raised, whereas
returns to a company's investment opportunities are
generally believed to decrease as the company
makes additional investments, as represented by the
investment opportunity schedule (IOS).
For an average-risk project, the opportunity cost of
capital is the company's WACC.
38. The following graph demonstrate the relationship
between cost of capital and investment returns.
39. The WACC or MCC corresponding to the average risk of
the company, adjusted appropriately for the risk of a given
project.
It plays a role in capital budgeting decision making based
on the net present value (NPV) of that project.
It is the difference between the present value of the cash
inflows, discounted at the opportunity cost of capital
applicable to the specific project, and the present value of
the cash outflows, discounted using that same opportunity
cost of capital.
NPV =Present value of inflows - Present value of outflows
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