The document discusses the concept of cost of capital. It defines cost of capital as the minimum rate of return that a company must earn on an investment to make that project worthwhile. It then discusses different methods to calculate the cost of various components of capital, including: 1. Cost of equity can be calculated using the dividend valuation model or capital asset pricing model. 2. Cost of preference shares is the annual dividend divided by the issue price. 3. Cost of debt is the after-tax interest rate on bonds or loans. The document provides examples of calculating each of these costs and compares the dividend valuation model to CAPM. It emphasizes that the cost of capital incorporates the risk and return considerations for

1. Cost of Capital
 Minimum rate of return which a company is
expected to earn from a proposed project so as to
make no reduction in the earning per share to equity
shareholders and its market price.
 In economic terms there are two approaches to
define CoC:
1. It is the borrowing rate of the firm, at which it can
acquire funds to finance the proposed project
2. It is the lending rate which the firm could have
earned if the firm would have invested elsewhere
CoC is a combined cost of each type of source
by which a firm raises funds.

2. CoC
Also referred to as cut-off rate, target rate,
hurdle rate, minimum required rate of return,
standard return, etc.
Assumption: that the firm’s business and
financial risks are unaffected by the acceptance
and financing of projects.
Business risk – is the risk to the firm of being
unable to cover fixed operating costs.
Measured by: (ΔEBIT/EBIT)/ (ΔSales/Sales)
Financial risk – is the risk of being unable to
cover required financial obligations such as
interest, preference dividends. Measured by:
(ΔEPS/EPS)/ (ΔEBIT/EBIT)

3. Importance of CoC
Capital Budgeting Decisions
Designing the Corporate Financial Structure
Deciding about the method of financing – in lieu with
capital market fluctuations
Performance of top management
Other areas – eg., dividend policy, working capital

4. Measuring CoC
A realistic measure of CoC should have the following
qualities of capital expenditure decisions:
1. It must account for the general uncertainty of
expected future returns from investment proposals.
2. It must allow for the various degrees of uncertainty
of expected future returns associated with different
uses of funds.
3. It must allow for the effects of uncertainty associated
with an incremental investment and the uncertainty
of returns from the entire asset portfolio of the firm.
4. It must account for a variety of financing means
available to a firm.
5. It must allow for the differential effects of financing
combination on the amount and quality of residual
net benefits accruing to shareholders.
6. It must reflect the changes in the capital market.

5. Basic costs of capital
1. Cost of Equity Capital: the cost of obtaining funds
through the sale of common stock.
2. Cost of Preference Shares
3. Cost of Debt
4. Cost of Retained Earnings

6. Cost of Equity Capital
Ke is defined as the minimum rate of return that a
firm must earn on the equity-financed portion of an
investment project in order to leave unchanged the
market price of the shares.
It is the rate at which investors discount the expected
dividends of the firm to determine its share value.
The two approaches to measure ke are i. Dividend
valuation approach and ii. Capital asset pricing
model.

7. Cost of Equity
Most difficult and controversial cost to work out.
Conceptually, the cost of equity ke may be defined as
the minimum rate of return that a firm must earn on
the equity financed portion of an investment project
in order to leave unchanged the market price of the
shares.
The cost of equity capital is higher than that of
preference and debt because of greater uncertainty of
receiving dividends and repayment of principal at the
end.

8. 2 approaches to measure Ke
1. Dividend approach – dividend valuation model:
assumes that the value of a share equals the
present value of all future dividends that it is
expected to provide over an indefinite period.
Ke accordingly is defined as the discount rate that
equates the present value of all expected future
dividends per share with the net proceeds of the
sale (or the current market price) of a share.

9. Formula
N
Po(1-f)=Σ D1/(1+ke)+ D2/(1+ke)2
+….+∞
n=1
N
=Σ D1(1+g)n-1
/(1+ke)n
n=1
Po(1-f) = D1/(ke–g) or
Ke = (D1/Po) + g; where
D1 = expected dividend per share
Po = net proceeds per share/current market price
g = growth in expected dividends

10. Assumptions of the Dividend
Approach
The market value of shares depends upon the
expected dividends.
Investors can formulate subjective probability
distribution of dividends per share expected to be
paid in various future periods. The initial dividend
is greater than 0.
Dividend payout ratio is constant.
Investors can accurately measure the riskiness of
the firm so as to agree on the rate at which to
discount the dividends.

11. Note 1: if the growth rate is not uniform, then,
Po(1-f)or Po=D1/(1+ke)+ D1(1+g1)/(1+ke)2
+ D1(1+g1) (1+g2)/
(1+ke)3
….+∞
Note 2: if we limit the dividend payment upto N
years, then,
Po(1-f)or Po=D1/(1+ke)+ D1(1+g)/(1+ke)2
+…+ D1(1+g)N-1
/
(1+ke)N
+….+ PN/(1+ke)N
Where, PN is the share value at the end of the Nth year.
Example: Expected dividend is Rs.2 in 1st
year. Growth rate
expected 4% in perpetuity. Floatation cost is 2%. What is
the cost of equity? Assume market price of share is Rs. 20.
So, 20(1-0.02)=2/ke-0.04
ke=0.04+2/20(1-0.02)=14.20%
If there are no floatation costs, then,
ke=g+D1/P0=0.04+2/20=14%

12. The Fincon Ltd. is planning an equity issue in Jan
1998. it has an EPS of Rs.25 and declared a dividend of
Rs.15 per share in the current year. Its present P/E
ratio is 8. It wants to price the issue at market price
and floatation costs are expected to be 10% of the
issue price. Determine required rate of return for
equity shares before issue and after the issue. How
will dividend tax under the Indian Income Tax Act
affect your calculations?
Cost of present equity:
Ke=[EPS/P0(1-f)]=[D1/Po(1-f)]+g=reciprocal of P/E
multiple
g=%Retimes[EPS/Po(1-f)]
Ke=1/8=.125=12.5% OR Ke=15/200+25/200(1-
15/25)=.125=12.5%

13. Cost of equity for new issue:
Ke=15/200(1-0.10)+[25/200(1-0.10)](1-
15/25)=15/180+(25/180)(0.40)=.1388=13.9%
Under new tax laws:
Po=D1/(Ke-g) OR Ke=D1/P0+g
But 10% tax is paid by company out of profits. Thus,
retained earnings or g alone is affected. Thus, revised
formula for g is:
g=EPS/P0[1-DPS(1+dt)/EPS] or g=[EPS-DPS(1+dt)]/P0
where, dt is dividend tax
For existing issue, Ke=D1/P0+[EPS-DPS(1+dt)]/P0
Ke=15/200+[25-15(1+0.1)]/200=15/200+[25-
16.5]/200=15/200+8.5/200=.1175=11.75%

14. For further issue of equity, Ke=D1/P0(1-f)+[EPS-
DPS(1+dt)]/P0(1-f)
Ke=15/200(1-0.1)+8.5/200(1-
0.1)=15/180+8.5/200=23.5/180=0.13055=13.1%
The new tax laws would result in:
a.Lower cost of equity
b.Perhaps it would promote investment also.

15. Example: suppose current dividend (D0)=Rs. 2
Current share price P0=Rs.100
Company growth rate: upto 5th
year – 10%
6-10th
year=8%
11th
year & beyond=6%
Then, P0
5
=Σ 2*1.10(1.1)n-1
/(1+ke)n
+
n=1
10
Σ D6(1.08)n-1
/(1+ke)n
+
n=6
∞
Σ D6(1.06)n-1
/(1+ke)n
+

16. 2. Capital Asset Pricing Model
approach
The CAPM explains the behavior of security
prices and provides a mechanism whereby
investors could assess the impact of proposed
security investment on their overall portfolio risk
and return. In other words, it formally describes
the risk-return trade-off for securities.
The basic assumption of CAPM are related to
A. the efficiency of the market, and
B. investor preferences.

17. A. Efficient Market implies
All investors have common (homogeneous)
expectations regarding the expected returns,
variances and correlation of returns among all
securities;
All investors have the same information about
securities;
There are no restrictions on investments;
There are no taxes;
There are no transaction costs; and
No single investor can affect the market price
significantly.

18. B. Investors’ preference assumption is that all investors
prefer the security that provides the highest return for
a given level of risk or the lowest risk for a given level
of return. That is, investors are risk averse.

19. Risk to which security investment is exposed
to are of 2 types:
Diversifiable/unsystematic risk: is the portion of
the security’s risk that is attributable to firm-specific
random causes; can be eliminated through
diversification. Eg., management capabilities and
decisions, strikes, unique government regulations,
availability of raw materials, competition.

20. Systematic/Non-diversifiable risk: is the
relevant portion of a security’s risk that is
attributable to market factors that affect all firms;
cannot be eliminated through diversification. Eg.,
interest rate changes, inflation or purchasing
power change, changes in investor expectations
about the overall performance of the economy and
political changes.
Since diversifiable risks can be eliminated through
diversification, investors should be concerned with
only non-diversifiable risks.

21. Market Portfolio
Systematic risk can be measured in relation to
the risk of a diversified portfolio which is
commonly referred to as the market portfolio
of the market. According to CAPM, the non-
diversifiable risk of an
investment/security/asset is assessed in terms
of the beta coefficient.
Beta is the measure of the volatility of a
security’s return relative to the returns of a
broad-based market portfolio. Beta coefficient
of 1 would imply that the risk of the specified
security is equal to the market.

22. Formula
ke = rf + ß(km – rf);
Where,
ke = cost of equity capital;
rf = the rate of return required on a risk free
asset/security/investment
km = required rate of return on the market portfolio
of assets that can be viewed as the average rate of
return on all assets
ß = the beta coefficient.
ß for market portfolios is 1, while it is 0 for risk-free
investments.

23. rf
ke
ß
rm
1

24. Difference b/w CAPM and Dividend Valuation
method
Valuation model does not consider the risk as
reflected in beta.
CAPM model suffers from the problem of collection
of data.
Beta measures only systematic risk.
Example: ß=1.4, rf=8%, km=12%
ke=8%+1.4(12%-8%)
=8%+1.4*4%=13.6%

25. Note: CAPM approach is theoretically sound but has
limitations:
1. It does not incorporate floatation costs.
2.Difficult to get ß values.
3. Poorly diversified investors would be concerned with
not only systematic but total risk.
So, dividend approach is better.

26. Cost of Preference Capital
They are a hybrid security between debt and equity.
The shareholders are paid a dividend yearly. Though,
this payment is not tax-deductible but the company is
required to make payments; since, if it does not pay, it
can’t pay dividends to the equity holders. Also,
preference dividend, if unpaid, gets accumulated over
years. Preference shares may be
redeemable/irredeemable. (now irredeemable
preference shares are not allowed. Have to be redeemed
in maximum 10 years)
Cost of preference share capital is the annual
preference share dividend divided by the net proceeds
from the sale of preference shares.
Perpetual security (irredeemable)
Cost of redeemable preference share

27. Cost of Preference Shares
The preference shareholders carry a prior right to
receive dividends over the equity shareholders.
Moreover, preference shares are usually cumulative
which means that preference dividend will keep
getting accumulated unless it is paid.
Further, non-payment of preference dividend may
entitle their holders to participate in the management
of the firm as voting rights are conferred on them in
such cases.
Above all, the firm may encounter difficulty in raising
further equity capital mainly because the non-payment
of preference dividend adversely affects the prospects
of ordinary shareholders.

28. A. Irredeemable (perpetual)
kp=dp/P0(1-f); where,
dp=constant annual dividend,
P0=expected sales price of preference share
f= floatation costs
Example: a 12% irredeemable preference share of face value
of Rs.100, f=5%. What is kp if preference share issued at i.
par, ii.10% premium, iii. 10% discount
i. At par, kp=12/100(1-0.05)=12/95=12.63%
ii.At 10% premium, kp=12/110(1-0.05)=11.48%
iii.At 10% discount, kp=12/90(1-0.05)=14.03%

29. B. Redeemable preference shares
N
Po(1-f)=Σ dp/(1+kp)n
+PN/(1+kp)N
;
n=1
Example: 14% preference dividend on face value of
Rs.100 to be redeemed after 10 years. Floatation cost is
5%. Kp?
N
100(1-0.05)=Σ 14/(1+kp)n
+100/(1+kp)10
;
n=1
By trial and error – kp=15% approximately.

30. Cost of Debt
Debt is the cheapest form of long-term debt from
the company’s point of view as:
It’s the safest form of investment from the point of
view of creditors because they are the first
claimants on the company’s assets at the time of
its liquidation. Likewise they are the first to be
paid their interest. Another, more important
reason for debt having the lowest cost if the tax-
deductibility of interest payments.

31. Cost of Debt
It is the interest rate which equates the present value
of the expected future receipts with the cost of the
project. The present value of tax-adjusted interest
costs plus repayments of the principal is equated with
the amount received at the time the loan is
consummated.

32. Cost of Debt
Cost of debt is the after-tax cost of long-term
funds through borrowing.
Net cash proceeds are the funds actually received
from the sale of security.
Flotation cost is the total cost of issuing and
selling securities.
Cost of perpetual/irredeemable debt
Cost of redeemable debt

33. Cost of Perpetual/Irredeemable debt
The nominal cost of debt is the periodical interest paid on it. The
interest rate/market yield is said to be cost of debt.
Suppose a bond is issued to procure perpetual debt. Then,
ki=I/SV; where I is annual interest payment (coupon payment);
SV is sale proceeds of bond/debenture.
kd=I(1-T)/SV; where T is tax rate.
Example: A 12% perpetual debt of nominal value of Rs.100000. Tax
rate is 50%. Cost of debt when issued at i. Par, ii. At discount of
5% and iii. premium of 10%.
i. At par ki=12000/100000=12%
kd=12%(1-0.5)=6%
ii. At discount of 5%, that is value received is 95,000.
ki=12000/95000=12.63%
kd=12.63%(1-0.5)=6.32%

34. iii. At a premium of 10%, that is value received is
110,000.
ki=12000/110,000=10.91%
kd=10.91%(1-0.5)=5.45%
So here (ii) 6.32% is highest cost followed by (i) 6%
or (iii) 5.45%.

35. Cost of Redeemable debt
To find the cost, initial net proceeds are to be
equated with net outflows.
∞
Co=Σ In/(1+kd)n
+PN/(1+kd)N
; if principal payment is made
n=1
at the end of Nth year
Or,
∞
Co=Σ In+PN /(1+kd)n
; if payment of principal is done in
n=1
installments

36. Example: 15% debentures of Rs.1000 (face value) to be
redeemed after 10 years. Net proceeds are after 5%
floatation costs and 5% discount. The tax rate is 50%.
What is the cost of debt?
Year Cashflows
0 1000-5%of 1000(floatation)-5%ofdiscount
=900
1-10 Rs. 15% of 1000(1-0.5)=Rs.75
10 Rs. 1000 (repayment)
10
So, 900= =Σ 75/(1+kd)n
+1000/(1+kd)10
n=1
By trial and error; kd =9% approx.
Note: ki route is preferred over kd route.

37. Example: of redemption on yearly basis (coupon
rate=15%). The par value of debenture is Rs.100000.
the floatation cost is 10%. Principal to be paid back in
5 equal installments at the year end. Tax rate is 50%.
Net proceeds=100000-10%=90000
Outflows: Net coupon Principal
Total
Yr 1 15000(1-0.5)=7500 20000 27500
Yr 2 80000*.15(1-0.5)=6000 20000 26000
Yr 3 60000*.15(1-0.5)=4500 20000 24500
Yr 4 40000*.15(1-0.5)=3000 20000 23000
Yr 5 20000*.15(1-0.5)=1500 20000 21500
So, 90000=27500/(1+kd)+26000/(1+kd)2
+24500/(1+kd)3
+23000/(1+kd)4
+21500/(1+kd)5
By trial and error, kd=12% approx

38. Cost of Retained Earnings
May be defined as the opportunity cost in terms of
dividends foregone by/withheld from the equity
shareholders.
Cost of retained earnings is the same as the cost of an
equivalent fully subscribed issue of additional shares,
which is measured by the cost of equity capital.
Retained earnings are “dividends withheld”, that is, if
were in the hands of the investors (shareholders) they
could have earned on these by investing somewhere
else. The assumption is that the firm is earning “at
least equal to ke on these retained earnings. So the
cost kr is approximately equal to ke (a little less than
ke because of floatation costs are not there, kr<ke)

39. Weighted Average Cost of
Capital (WACC)
This gives us the overall cost of capital. Weight
age is given to the cost of each source of funds by
assessing the relative proportion of each source of
fund to the total, and is ascertained by using the
book value or the market value of each type of
capital. The cost of capital of the market value is
usually higher than it would be if the book value is
used.

40. Steps in Calculation of WACC
(Ko)
Assigning weights to specific costs.
Multiplying the cost of each sources by the
appropriate weights.
Dividing the total weighted cost by the total weights.

41. Weighting can be using marginal or historical
weights
Why marginal weights? Because it is the new capital
being raised for new investment that is important so
the weighted cost of new capital is of relevance. Else,
projects with costs higher than managerial costs may
be accepted, giving negative results and vice-versa.
But the problem is that if we go by marginal weighting,
we may resort to too much borrowing and accept
many projects because of lower cost at the moment.
But, at a later date, company may have the problem of
raising more finance. Marginal weights ignore long
term view.
Thus, the fact that today’s financing affects tomorrow’s
costs, is not considered in using marginal weights.

42. Historical weights take a long term view and try to
raise financing also in the proportion of existing
capital structure – considered superior.
Historical weights can be divided into book value
weights and market value weights.
Calculations based on the book value weights are more
easy operationally while those based on market values
are more sound theoretically since the sale price of
securities is going to be more close to the market
value. But the problem is how to choose the market
value because they fluctuate widely sometimes and
almost everyday their values are different.

43. Example: capital structure (book value based)
Debt 30% (Rs.6000) cost kd=8%
Preference shares 30% (Rs.6000) cost kp=13%
Equity 40% (Rs.8000) cost k=14%
Ko=WACC= Σwiki=30%*8%+30%*13%+40%*14%
=2.4%+3.9%+5.6%=11.9%
Note: ko calculated on the basis of market value is likely to
be greater than the one calculated on the basis of book
value since market values of equity and preference shares
is usually higher than book value and hence their weight is
more with respect to debt. For example, in the above
example, market values are:

44. Debt 25% (Rs.60000) cost kd=8%
Preference shares 29.17% (Rs.70000) cost kp=13%
Equity 45.83% (Rs.110000) cost k=14%
Total=240000
Ko=WACC=
Σwiki=0.25*0.08+0.2917*0.13+0.4583*0.14=0.0200+0.03
792+0.06416=0.122082=12.21%

45. Market Value vs. Book Value
Weights
 MV sometimes preferred to BV for the MV
represents the true expectations of the investors.
However, it suffers from the following
limitations:
1. MV undergoes frequent fluctuations and have to
be normalized;
2. The use of MV tends to cause a shift towards
larger amounts of equity funds, particularly
when additional financing is undertaken.

46. MV more appealing than BV as:
Market values of securities closely approximate the
actual amount to be received from their sale
Costs of specific sources of finance which constitute
the capital structure of the firm are calculated using
prevalent market prices.

47. Advantages of BV weights
1. The capital structure targets are usually fixed in
terms of book value.
2. It is easy to know the book value.
3. Investors are interested in knowing the debt-
equity ratio on the basis of book values.
4. It is easier to evaluate the performance of a
management in procuring funds by comparing
on the basis of book values.

48. Relevant costs closely related to
CoC
1. Marginal cost of capital: average cost of new or
incremental funds raised by the firm. MC tens to
increase proportionately as the amount of debt
increases.
2. Explicit cost and implicit cost:
a. Explicit cost: of any source of finance is the
discount rate that equates the present value of the
cash inflows that are incremental to the taking of
the financial opportunity with the present value of
the incremental cash outflows. The explicit cost of
a debt would be 0 if it is interest free. The explicit
cost of a gift would be –100%.

49. b. Implicit cost: is the opportunity cost. It is the
“rate of return” associated with the best
investment opportunity for the firm and its
shareholders that will be foregone if the project
presently under consideration by the firm were
accepted. It is not concerned with any
particular source of finance.
The explicit cost include only the CoC to be paid
and ignores the other factors such as risk
involved, flexibility and leverage characteristics
which are adversely affected with an increase
in debt contents in its capital structure and
these changes imply additional but hidden
costs.

50. 3. Future cost and Historical cost
We always consider the projects’ expected internal
rate of return and compare it with the expected
(future) cost of capital while making capital
expenditure decision. Historical costs (past costs)
help in predicting the future costs and provide an
evaluation of the past performance

51. 4. Specific cost and
Inclusive/Combined/Composite CoC
a. Specific CoC is associated with a specific
component of capital structure.
b. Inclusive CoC is an aggregate of the CoC from all
sources. In other words, it is WACC.

52. 5. Spot costs and Normalized costs
a. Spot costs represent those costs prevailing in the
market at a certain time.
b. Normalized cost indicate an estimate of cost by some
averaging process from which cyclical element is
removed.