INVESTMENT DECISION-MODULE III (1) (3).pptx

Module III
Finance &Investment Decision
3.1 Time value of Money
3.2 Practical Applications of Compounding and Present
Value Techniques
3.3 Conceptual Framework of Risk and Return.
3.4 Cost of Capital, Cost of Different Sources of Finance-
Weighted Average Cost of Capital.
3.5 Leverage, Operating Leverage, Application of operating
leverage, Financial Leverage, Combined Leverage .
3.6 Capital Budgeting Decisions and Techniques

Time Value of Money—Concept
A rupee which is received today ,is more valuable than a
rupee receivable in future .The amount that is received
in earlier period can be reinvested and it can earn an
additional amount. For example, a rupee received today
can be reinvested and it can earn some interest, but the
rupee receivable in future cannot be reinvested.

Rationale Of Time Preference For Money
There are three reasons that may be attributed to the
individual’s time preference for money.
1. Uncertainty: future is uncertain and it involves risk. An
individual is not certain about future cash inflows.
Hence he/she would like to prefer to receive cash today
instead of in the future. For example, there is a bird in
your hand and there are two birds in the bush. The one
that is in your hand is preferred because nobody knows
whether there are two birds in the bush or not, if at all
they are there, you may be able to catch or you may not
be able to catch them.

2.Current Consumption: Most of the people generally
prefer to use the present money for satisfying the
present needs. It may be due to the urgency of their
present wants or because of the risk of not being in a
position to enjoy the future consumption.
3.Possibility of investment opportunity: Another reason
why individuals prefer present money is due to the
possibility of investment opportunity through which
they can earn additional cash.For example,if one has
Rs.100 today,he/she can put it in bank account and earn
some interest.

If the interest rate is 6%,the principal amount would earn
Rs.6 and he/she would have Rs.106 at the end of one
year. Investment opportunity is the one main reason for
individual or the firm’s justification for time preference
for money lies simply in the availability of investment
opportunities.

Practical Applications of Compounding and Present
Value Techniques.
Simple Interest
Simple interest is the interest paid on the original amount
or principal amount. It is a function of three
components such as principal amount, interest per
annum and the number of years for which the interest
rate is calculated.
Symbolically
SI= P0 (I) (n), where SI is Simple Interest, Po is Principal
amount at year ‘0’,
I = Interest rate per annum, n= Number of years for which
interest is calculated.

Example:
Mr.A who has deposited Rs.100000 in a savings bank
account at 6 percent simple interest and was interested
to keep the deposit for a period of 5 years. He requested
you to give accumulated interest at the end of five years.
Solution
SI=P0 (I) (n)
= 100000x0.06x5 = Rs.30000.

If an investor wants to know his total future value at the
end of ‘n’ years, future value is the sum of accumulated
interest and the principal amount. Symbolically,
FVn = SI +P0
= 100000+ 30000 = Rs.130000
Problem 2
Krishna’s annual savings are Rs.1000, which is invested
in a bank saving fund account that pays a 5% simple
interest. Krishna wants to know his total future value
or terminal value at the end of 8 years period.

Compound Interest
The interest that is earned on a given deposit and has
become part of principal at the end of a specified
period.
Compound Value of a Single Amount
Compound value or future value on an account can be
calculated by the following formula .
CV= P0 (1+I)n
Where CV = Compound Value, P0 = Principal amount
I=Interest per annum n=Number of years for which compound is done.

Suppose you have Rs.1000000 today and you deposit it
with a financial institute, which pays 8% compound
interest for a period of 5 years. Show how the deposit
would grow.
Solution
CV = P0 (1+I)n
CV = 1000000(1+0.08)5
= 1000000 (1.08)5 = 1000000(1.469) =Rs.1469000

Variable Compounding Periods
Generally compounding is done once in a year. If the
investor is promised to pay compound interest for
variable periods(like semi-annual, quarter
etc.).Compound value with variable compound periods
is determined with the following formula:
CVn = P0(1+ I/M)mxn
Where CVn=Compound value at the end of year ‘n’
P0 = Principal amount at the year ‘0’
I= Interest rate per annum
m =Number of times per year compounding is done.
n=Maturity period

Semi-annual Compounding
How much does a deposit of Rs.40000 grow to at the end
of 10 years at the rate of 6 percent interest and
compounding is done semi annually.
Solution
CV10 = 40000(1+0.06/2)2x10
= 40000(1.806) =Rs.72240.
Compound value for one rupee table for the year 20 at 3
percent interest.

Quarterly compounding
Suppose that a firm deposits Rs.50 lakhs at the end of
each year for 4 years at the rate of 8% interest and
compounding is done on quarterly basis.What is the
compound value at the end of the fourth year
Solution
CV4 = P0(1+I/M)mxn
= 5000000(1+0.08/4)4x4= 5000000x1.373=Rs.6865000
(Compound factor table: 16 years with 2% interest,that is 1.373)

 Doubling Period
 Doubling period is that period required to double the
amount invested at a given rate of interest. For example,
if you deposit Rs.10000 at 6% interest, and it takes 12
years to double the amount.
 Doubling period can be computed by adopting two
rules:
 (i) Rule of 72 : To get doubling period,72 is divided by
interest rate.
 Doubling Period (Dp) = 72÷I where I= Interest rate
 Dp= Doubling period in years

If you deposit Rs.500 today at 10% rate of interest, in how
many years will this amount double‽
(2) Rule of 69: Rule of 72 may not give exact doubling
period, but Rule of 69 gives a more accurate doubling
period. The formula to calculate doubling period is
Dp = 0.35+69÷I
Effective Rate of Interest In Case of Doubling Period
Sometimes investors may get a doubt that what is the
effective interest rate applicable if a financial institute
pays double amount at the end of a given number of
years.

Effective rate of interest can be defined with the use of
the following formula:
(a)In case of Rule of 72
ERI = 72 ÷Doubling Period(Dp)
Where ERI=Effective Rate of Interest
Dp= Doubling Period
(b) In case of Rule of 69
ERI = 69÷Dp +0.35

Problem
A financial institute has come with an offer to the public,
where the institute pays double the amount invested
in the institute at the end of 8 years.Mr.A who is
interested to deposit with the institute wants to know
the effective rate of interest that will be given by the
institute. Calculate ERI by applying rule of 72 and rule
of 69.

PRESENT VALUE
It is concerned with determining the present value of a
future amount, assuming that the decision-maker has
an opportunity to earn a certain return on his/her
money. This return is referred in financial literature as
discount rate, cost of capital or an opportunity cost.

Present Value of a single amount
PV = FVn (1/1+I)n
Where PV is Present Value
I=Interest Rate or discounting factor or cost of capital
n =Duration of the cash flow

An investor wants to find the present value of Rs.40000
due 3 years. His interest rate is 10%.
PV = FV3 (1/1+I)n
=40000(1/1+0.10)3
=40000x0.751 =Rs.30040
Present Value of a Series of Cash Flows
In capital budgeting decisions, there is a need to convert
the future cash inflows into present values to take
decisions and in case of raising funds through debt, also
needs to convert the future cash outflows into present
values. Cash flows over a period may be even or uneven.

Present Value of Uneven Cash Flows
PV= CIF1 + CIF2 + …………+CIFn
(1+I)1 ( 1+I)2 ( 1+I)n
Where PV=Present Value
CIF = Cash Inflow
I = Interest rate or discounting factor or cost of capital
n =Duration of cash inflows stream

From the following information, calculate the present value at
10 percent interest rate.
Year 1 2 3 4 5
Cash
Inflow(Rs.) 3000 4000 5000 4500 5500
Solution
Year Cash Inflow P V Factor Present Value
( Rs.) (10%) (Rs.)
1 3000 0.909 2727
2 4000 0.826 3304
3 5000 0.751 3755
4 4500 0.683 3073.5
5 5500 0.621 3415.5
Total Present
Value 16275

Concept of Risk and Return
The risk-return tradeoff states that the potential return rises
with an increase in risk. Using this principle, individuals
associate low levels of uncertainty with low potential returns,
and high levels of uncertainty or risk with high potential
returns. According to the risk-return tradeoff, invested
money can render higher profits only if the investor
will accept higher possibility of losses.
Meaning of Risk
According to the dictionary meaning, 'existence of volatility in
the occurrence of an expected incident is called risk’. Higher
the unpredictability greater is the risk. Risk and returns are
the two sides of the investment coin. Risk is associated with
the possibility of not realising return or realising less return
than expected.

The degree of risk varies on the basis of the features of the
assets, investment instruments, the mode of
investment ,the issuer of securities etc. The objective of
risk management is not elimination of risk but proper
assessment of the risk and deciding whether it is worth
taking or not.
Risk and Uncertainty
Though risk and uncertainty go together, but they differ
in perception. Risk refers to a situation where the
decision maker knows the possible consequence of a
decision and their related likelihoods. Uncertainty
involves a situation about which the likelihood of
possible outcome is not known.

Present Value
Present value is exact contrary to compound value.
Compound value is helpful to know the interest added
to principal amount at a given compound interest rate
and given number of years, whereas in the present value
we know the present value of a sum that is receivable in
the future. In sample, under compounded approach the
sum invested will appreciate whereas in present
value,the sum receivable in future will depreciate due to
discounting.
The present value of a future cash inflow(or outflow) is
the amount of current cash that is of equivalent value
to the present value.The process of determining present
value of a future cash flows(cash inflow or outflow)

Uncertainty cannot be quantified whereas risk can be
quantified of the likelihood of future outcomes. The degree
of risk depends upon the features of assets,investment
instruments, mode of investment etc.
Types of Risk
1.Systematic Risk
Systematic risk refers to that portion of variation in return
caused by factors that affect the price of all securities. The
effect in systematic return causes the prices of all individual
securities to move in the same direction. This movement is
generally due to the response to economic, social and
political changes. The systematic risk cannot be avoided. It
relates to economic trends which affect the whole market. It
cannot be eliminated by diversification of portfolio because
every share/bond is influenced by the general market trend.

Examples:
Market Risk: Variations in prices sparked off due to real
social, political and economic events is referred to as
market risk.
Interest Rate Risk: Generally price of securities tend to
move inversely with changes in the rate of interest. The
market activity and investor perceptions are influenced
by the changes in interest rates which in turn depend on
nature of instruments, maturity periods,
creditworthiness of the issuer of securities etc.

2.Unsystematic Risk
Unsystematic risk refers to that portion of the risk which
is caused due to factors unique or relate to a firm or
industry. This risk is a company specific risk and can be
controlled if proper measures are taken. As it is unique
to a particular firm or industry, it is caused by factors
like labour unrest, management policies, recession in a
particular industry etc.
Examples:
Business Risk : Business risk can be internal as well as
external. Internal risk is caused due to improper product
mix, non-availability of raw materials, incompetence to
face competition, absence of strategic management etc.

External business risk involves change in operating
conditions caused by conditions thrust upon the firm
which are beyond its control such as business cycles,
government controls etc.
Financial Risk :Financial risk is associated with the
capital structure of a company. A company with no debt
financing has no financial risk. The extent of financial
risk depends on the leverage of the firm’s capital
structure.
Credit or default risk :It deals with the probability of
meeting with a default. It is primarily the probability
that a buyer will default. The borrower’s credit rating
might have fallen suddenly and he became default
prone and in its extreme form it may lead to insolvency

Cost of Capital ---Concept
The term cost of capital is a concept having different
meanings. Cost of capital from the three view points are:
1.The Investor’s View Point: It may be defined as ‘the
measurement of the sacrifice made by him /her in order
to capital formation. For example,Mr.A an investor
invested in a company’s equity shares, an amount of
Rs.100000 instead of investing in a bank deposit which
pays seven percent interest. Here investor had sacrificed
seven percent interest for not having invested in the
bank.

Cost of capital represents the rate of return that a firm
must pay to the suppliers of capital for use of their
funds. In other words, cost of capital is the weighted
average cost of various sources of finance used by the
firm in capital formation. The sources are equity shares,
preference shares, long-term debt and short-term debt.
Thus it is said that cost of capital is the minimum rate of
return which a firm must and is expected to earn on its
investments so as to maintain the market value of its
shares. It is also known as Weighted Average cost of
capital, composite cost of capital or combined cost of
capital. It is expressed in terms of percentage.

2.The Firm’s View Point –It is the minimum required
rate of return needed to justify the use of capital. For
example, a firm raised Rs.50 lakhs through the issue of
10% debentures, for justifying this issue it has to earn a
10% minimum rate of return on investment.
3.Capital Expenditure’s View Point: The cost of capital
is the minimum required rate of return or the hurdle
rate or target rate or cut off rate or any discounting rate
used to value cash flows. For example, Firm A is
planning to invest in a project, that requires Rs.20 lakhs
as an initial investment and it provides cash flows for
five years period, here for conversion of the future cash
inflows into present values we need cost of capital.

Importance Of Cost Of Capital
1.Designing Optimal Capital Structure
Cost of capital is helpful in formulating a sound and
economical capital structure for a firm. The debt
capacity of a firm is significantly influenced by the cost
consideration. Capital structure involves determination
of proportion of debt and equity in capital structure
where cost of capital is minimum.
While designing a firm’s capital structure ,financial
executives always keep in mind minimisation of the
overall cost of capital and to maximise the value of the
firm. The measurement of specific cost of each source
of fund and calculation of weighted average cost of
capital helps to come to a balanced capital structure.

2.Investment (Capital Budgeting) Evaluation
Capital expenditure means investment in long-term
projects like investment on new machinery. It is also
known as Capital Budgeting expenditure. Capital
Budgeting decisions require a financial standard (cost
of capital) for evaluation. For instance, in the Net
Present Value Method(NPV),an investment project is
accepted if the present value of cash inflows are greater
than the present value of cash outflows. The present
value of cash inflows are calculated by discounting with
a discount rate known as cost of capital. The concept of
cost of capital is very much useful in capital budgeting
decisions, particularly if a firm is adopting discounted
cash flow methods of project evaluation.

3.Financial Performance Appraisal
Cost of capital framework can be used to evaluate the
financial performance of top management. Financial
performance evaluation involves a comparison of actual
profitability of the project with the project’s overall cost
of capital. If the actual profitability rate is more than the
projected cost of capital, then the financial performance
may be said to be satisfactory and vice versa.

Computation of Cost Of Capital
A. Computation of cost of specific source of finance and
B. Computation of weighted average cost of capital.
Computation of Specific Source of Finance
Computation of each specific source of finance such as debt,
preference share capital, equity share capital and retained
earnings.
I. Cost of Debt
1.1 Cost of Perpetual/Irredeemable debt
The cost of debt is the rate of interest payable on debt.
a. Before-tax cost of debt:
Kd = I/NP where
Kd = Cost of debt, I=Interest, NP=Net Proceeds

(i) When debt is issued at par: NP=Face Value – Issue
Expenses.
(ii) When debt is issued at premium,
NP = Face Value+Premium – Issue Expenses
(iii) When debt is issued at discount,
NP=Face Value – Discount –Issue Expenses.
After-tax cost of debt
Kd = I/NP (1-t), where Kd =Cost of debt
t=Rate of tax.

Problem 1
A company issues Rs.100000 10% debentures at par.
Calculate the before-tax cost of debt.
Solution
Kd = I/NP,I =10% of Rs.100000,that is Rs.10000.
NP=Rs.100000.
Kd= 10000/100000 )=0 .1,that is 0.1x100=10%

Problem 2
(a) X Ltd. issues Rs.50000 8%debentures at par. The tax
rate applicable to the company is 50%. Compute the
cost of debt capital.
(b) Y Ltd.++issues Rs.50000 8% debentures at a premium
of 10%.The tax rate applicable to the company is
60%.Compute cost of debt capital.
(c) A Ltd.issues Rs.50000 8% debentures at a discount of
5%.The tax rate is 50%.Compute the cost of debt
capital.
(d) B Ltd. issues Rs.100000 9% debentures at a premium
of 10%.The costs of floatation are 2%.The tax rate
applicable is 60%.Compute cost of debt capital.

Kd = I/NP (1-t)
(a) Interest = 50000x8/100 = Rs.4000, NP =Rs.50000
t= 0.50, Therefore,Kd = 4000/50000 (1-0.50)
=0.08x0.50=0.04 x100=4%
(b) NP=Face value+Premium-Issue expenses
=50000+5000=Rs.55000,Interest=8% of
50000=Rs.4000,t=0.60
Kd=I/NP (1-t)=4000/55000 (1-0.60)=2.91%
© Interest =Rs.4000,NP=Face value-discount-issue
expenses.
NP=50000-2500 =Rs.47500,t=0.50
Kd=4000/47500(1-0.50)=4.21%

(d) Interest =100000x9/100=rs.9000,
NP=100000+10000-2200=Rs.107800
t=0.60
Kd= 9000/107800 (1-0.60)=3.34%.

1.2 Cost of Redeemable Debt
(i) Before-tax cost of redeemable debt
Kd= I+1/n (RV –NP)
½ (RV+ NP)
Where I = Annual Interest, n=Number of years in which
debt is to be redeemed,
RV=Redeemable value of debt,
NP=Net Proceeds of debentures.
(ii) After-tax cost of redeemable debt
Kd= I(1-t)+1/n (RV-NP)
½ (RV+NP)
Where I=Annual Interest, t=Tax rate, n=Number of years
in which debt is to be redeemed,RV=redeemable Value of
debt,NP=Net Proceeds of debentures.

Problem 3
A company issues Rs.1000000 10% redeemable
debentures at a discount of 5%.The costs of floatation
amount to Rs.30000.The debentures are redeemable
after 5 years. Calculate before-tax and after-tax cost of
debt assuming a tax rate of 50%.
Solution
(i)Before-tax cost of redeemable debt
Kd = I+1/n (RV-NP)
½ (RV+ NP)
I= 1000000x10/100 =Rs.100000,n=5,RV=Rs.1000000,
NP=1000000-50000-30000=Rs.920000.

Kd= 100000+1/5(1000000-920000)
½(1000000+920000)
=100000+16000 = 0.1208x100 =12.08%
960000
(ii)After-tax cost of redeemable debt
Kd= I(1-t)+1/n(RV-NP)
½(RV+NP)
= 100000(1-0.50)+1/5(1000000-920000)
½(1000000+920000)
=50000+16000 = 66000 = 0.06875x100 = 6.875%
960000 960000

Problem 4
A 5 year Rs.100 debenture of a firm can be sold for a net
price of Rs.96.50.The coupon rate of interest is 14% per
annum and the debenture will be redeemed at 5%
premium on maturity.The firm’s tax rate is
40%.Compute the before-tax and after-tax cost of
debenture.
Solution
Before-tax cost of redeemable debt
Kd= 1+1/n(RV-NP)
½(RV+NP)
14+1/5(105-96.50) =15.70 = 15.58%
½(105+96.50) 100.75

After-tax cost of debt
Kd=1(1-t)+1/n(RV-NP)
½(RV+NP)
=14(1-0.40)+1/5(105-96.50) = 8.40+1.70 =10.025%
½(105+96.50) 100.75
Assuming that a firm pays tax at 50% rate,compute the
after-tax cost of debt capital in the following cases:
(i) A perpetual bond Rs.100 sold at par,coupon rate of
interest being 7%.
(ii) A 10 year,8% Rs.1000 bond sold at Rs.950 less 4%
underwriting commission.

Solution
(i) Cost of a perpetual bond
Kd= I/NP(1-t)=7/100(1-0.50)=0.035x100=3.5%
(ii) Cost of redeemable bond
Kd= I(1-t)+1/n(RV-NP)
½(RV+NP)
=80(1-0.50)+1/10(1000-912)
½(1000+912)
= 40+8.8 =0.0510x100=5.10%
956

II Cost of Preference Capital
A fixed rate of dividend is payable on preference shares.
The cost of preference capital is a function of dividend
expected by its investors,that is its dividend.
A. Cost of Perpetual/Irredeemable Preference Capital
Kp =D/NP where Kp =Cost of Preference Capital
D=Annual fixed Preference Dividend,NP=Net
proceeds of preference shares.

B.Cost of Redeemable Preference Shares
Kp= D+MV-NP/n
½ (MV+NP)
Where Kp =Cost of preference shares.
D=Annual Preference dividend
MV=Maturity Value of preference shares
NP=Net Proceeds of preference shares.
Problem 1
A company issues 10000 10% Preference Shares of Rs.100
each. Cost of issue is Rs.2 per share. Calculate cost of
preference capital if these shares are issued (a)at par
(b)at a premium of 10% and (c ) at a discount of 5%.

Cost of Preference Capital
Kp=D/NP
(a) Issued at par
Dividend=10000x100=1000000x10/100=Rs.100000
NP=Face Value-Issue expenses,1000000-20000=Rs.980000
Kp=100000/980000 x100 =10.2%
(b) Issued at a premium of 10%
NP=FV+Premium-Issue expenses,1000000+100000-
20000=Rs.1080000.
Kp=100000/1080000 x100=9.26%

(c) Issued at a discount of 5%
NP=FV-Discount-Issue expenses,1000000-50000-
20000=Rs.930000.
Kp=100000/930000 x100=10.75%
Problem 2
A company issues 10000 10%preference shares of Rs.100
each redeemable after 10 years at a premium of 5%.The
cost of issue is Rs.2 per share.Calculate the cost of
preference capital.
Solution
Kp= D+(MV-NP)/n
½ (MV+NP)

D=1000000x10/100=Rs.100000,n=10 years,NP=Face Value-
Issue expenses,1000000-20000=Rs.980000
MV=1000000+50000=Rs.1050000.
Kp= 100000+(1050000-980000)/10 = 107000/1015000x100
½(1050000+980000)
=10.54%
Problem 3
A company issues 1000 7% preference shares of Rs.100
each at a premium of 10% redeemable after 5 years at
par. Compute the cost of preference capital.

III. Cost of Equity Share Capital
The cost of equity capital is a function of the expected
return by its investors. Shareholders invest money in
equity shares on the expectation of getting dividend
and the company must earn this minimum rate so that
the market price of the shares remains unchanged.
Whenever a company wants to raise additional funds by
the issue of new equity shares, the expectations of the
shareholders have to be evaluated.

The cost of equity share capital can be computed in the
following ways:
(a) Dividend Yield Method or Dividend Price Method
According to this method,the cost of equity capital is
the discount rate that equates the present value of
expected future dividends per share with the net
proceeds or current market price of a share.
Ke = D/NP or D/MP
Where Ke = Cost of Equity Capital
D =Expected dividend per share
NP=Net Proceeds per share
MP=Market Price per share.

Problem 1
A company issues 1000 equity shares of Rs.100 each at a
premium of 10%.The company has been paying 20%
dividend to equity shareholders for the past five years
and expects to maintain the same in the future also.
Compute the cost of equity capital. Will it make any
difference if the market price of equity share is Rs.160‽
Solution
Ke=D/NP, Dividend per share=Rs.20
NP/share=FV+Premium, that
is,100000+10000=Rs.110000/1000 = Rs.110
Ke=20/110 x100 = 18.18%.

If the market price of an equity share is Rs.160
Ke =D/MP ,20/160 x100=12.5%
(b) Dividend Yield plus Growth in Dividend Method.
When the dividends of the firm are expected to grow at a
constant rate and the dividend payout ratio is constant,
this method may be used to compute the cost of equity
capital. According to this method,the cost of equity
capital is based on the dividends and the growth rate.
Ke = D/NP +g or D/MP+g where
Ke =Cost of equity capital, D=Expected dividend per share.
NP=Net proceeds per share,MP=Market price per share,
g=Growth rate in dividends.

Problem
(a) A company plans to issue 1000 new shares of Rs.100
each at par.The floatation costs are expected to be 5%
of the share price.The company pays a dividend of
Rs.10 per share initially and the growth in dividends is
expected to be 5%.Compute the cost of new issue of
equity shares.
(b) If the current market price of an equity share is
Rs.150,calculate the cost of existing equity share
capital.

(a)Ke = D/NP +g
D=Rs.10,
NP= 1000x100=rs.100000-issue expenses,(5% of 100000)
=100000-5000 = rs.95000
Net Proceeds per share=95000/1000 =Rs.95
,g=5%=0.05
Ke= 10/95 + 0.05 x100 =15.52%
(b) Ke = D/MP +g
10/150 + 0.05 x100=11.67%

Problem 2
Equity shares of a paper manufacturing company is
currently selling at Rs.100.It wants to finance its capital
expenditure of Rs.1 lakh either by retaining earnings or
selling new shares. If the company seeks to sell
share,the issue price will be Rs.95. The expected
dividend for the next year is Rs.4.75 and it is expected to
grow at 6% perpetually. Calculate the cost of equity
capital.
Ke = D/NP +g

(c) Earning Yield Method (Earning Price Method)
According to this method,the cost of equity capital is the
discount rate that equates the present values of
expected future earnings per share with the net
proceeds or current market price of a share.
Ke= Earnings per share
Net Proceeds per share = EPS/NP
or
Earnings per share = EPS/MP
Market price per share

A firm is considering an expenditure of Rs.60 lakhs for
expanding its operations.The relevant information is as
follows:
Number of existing equity shares Rs.10 lakhs
Market value of existing share Rs.60
Net earnings Rs.90 lakhs.
Compute the cost of equity share capital and of new
equity capital assuming that new shares will be issued at
a price of Rs.52 per share and the costs of new issue will
be Rs.2 per share.

Cost of existing equity share capital
Ke = EPS/MP
EPS =Net Earnings/Number of equity shares,that
is,9000000/1000000 =Rs.9
Ke=9/60 x100=15%
Cost of new equity capital
Ke=EPS/NP, 9/52-2 x100 =18%

IV.Cost of Retained Earnings
It is sometimes argued that retained earnings do not
involve any cost because a firm is not required to pay
dividends on retained earnings.However,the
shareholders expect a return on retained profits.
Retained earnings accrue to a firm only because of some
sacrifice made by the shareholders is not receiving the
dividends out of the available profits.
The cost of retained earnings is the opportunity cost of
dividends foregone by the shareholders.

It is important to note that shareholders cannot obtain
the entire amount of retained profits by way of
dividends even if there is 100 percent pay out ratio. It is
so because the shareholders are required to pay tax on
their dividend income. So some adjustment has to be
made for tax.Moreover,if shareholders wish to invest
their after-tax dividend income in alternative securities,
they may have to incur some costs of purchasing the
securities such as brokerage. Thus the cost of retained
earnings may be calculated as:
Kr =ke (1-t)(1-b)
Where Kr=Cost of retained earnings
t=Tax rate
b=Brokerage

Problem 1
A firm’s Ke(return available to shareholders) is 15%,the
average tax rate of shareholder is 40% and it is
expected that 2% is brokerage cost that shareholders
will have to pay while investing their dividends in
alternative securities. What is the cost of retained
earnings‽
Solution
Cost of Retained Earnings
Kr=Ke (1-t)(1-b)
Ke=15%,t=0.40,b=0.02
Kr=15%(1-0.40)(1-0.02)=15%x0.6x0.98=8.82%

Problem 2
The following particulars relate to Ambuja Ltd.
Rs.
Equity share capital 100000 shares of Rs.10 1000000
Profit after tax 900000
Current market price of equity share 75
(a) Calculate the cost of equity.
(b) What is the cost of retained earnings if the average
personal tax rate of sharehoder’s is 30% and the
brokerage cost for making new investment is 2%‽

2.Ravi is a shareholder in India Polyester Ltd.The
earnings of the company have varied considerably.Ravi
feels that the long run average dividend would be Rs.3
per share. He expects that the same pattern would
continue in future. Ravi expects a minimum rate of
earning of 15%.Calculate the market price of a share.
3.The market price of an equity share of GLtd. is
Rs.80.The dividend expected a year hence is Rs.1.60 per
share. The shareholders anticipate a growth of 7% in
dividends. Calculate the cost of equity capital.

B. Computation of Weighted Average Cost of Capital
Weighted average cost of capital is the average cost of
the costs of various sources of financing. Weighted
average cost of capital is also known as composite cost of
capital, overall cost of capital or average cost of capital.
Once the specific cost of individual sources of finance is
determined, we can compute the weighted average cost
of capital by putting weights to the specific costs of
capital in proportion of the various sources of funds to
the total. The weights may be given either by using the
book value of the source or market value of the source. If
there is a difference between market value and book
value weights, the weighted average cost of capital
would also differ.

Weighted average cost of capital, Kw =∑XW
∑W
where, Kw=Weighted average cost of capital
X=Cost of specific source of finance
W= Weights,proportion of specific source of
finance.

Problem 1
A firm has the following capital structure and after-tax
costs for the different sources of funds used”
Sources of funds Amount Rs. After tax cost(%)
Debt 1500000 5
Preference Shares 1200000 10
Equity Shares 1800000 12
Retained Earnings 1500000 11
Total 6000000

Solution
Sources of funds Weights Cost(%) Weighted Cost
Rs. (W) X (XW)
Debt 1500000 0.25 5 1.25
Preference
Shares 1200000 0.2 10 2
Equity
shares 1800000 0.3 12 3.6
Retained
Earnings 1500000 0.25 11 2.75
Weighted Average Cost
Of Capital 9.6%

Problem 2
A firm has the following capital structure as the latest
statement.Compute Weighted average cost of capital.
Source of Finance Amount (Rs.) After-tax cost(%)
Debt Capital
Preference shares
Equity shares
Retained earnings
3000000
1000000
2000000
4000000
4.0
8.5
11.5
10.0
Total 10000000

Problem 3
XYz Company supplied the following information to
you and requested to compute cost of capital based
on book values as well as market values.
Source of
Finance
Book
Value(Rs.)
Market
Value(Rs.)
After-tax
cost(%)
Equity Capital
Long-term debt
Short-term debt
1000000
800000
200000
1500000
750000
200000
12
7
4
Total 2000000 2450000

Marginal cost of capital
Companies may raise additional funds for expansion.
Here a financial manager may be required to calculate
the cost of additional funds to be raised. The cost of
additional funds is called marginal cost of capital. The
weighted average cost of new or incremental capital is
known as the marginal cost of capital.Thus marginal
cost of capital is the weighted average cost of new
capital using the marginal weights.The marginal
weights represent the proportion of various sources of
funds to be employed in raising additional funds.

Problem 4
HLL has provided the following information and
requested you to calculate (a)WACC using book-value
weights and (b)weighted marginal cost of capital
(assuming that specific cost do not change)
Source of finance
to
Amount Rs. After-tax
cost(X)
%
Equity Capital
Preference Capital
Debenture Capital
Total
1400000
800000
900000
3100000
9
12
16

HLL wishes to raise an additional capital of Rs.1200000
for the expansion programme.The details of sources of
funds are as follows:
Equity Capital Rs.600000
Preference Capital Rs.300000
Debenture Capital Rs.300000

Problem 5
From the following information of Excel Ltd.,determine
the WACC using (a)book value weights and (b)market
value weights. How are they different ‽ Can you think a
situation where the WACC would be the same using
either of the weights ‽
Source of finance Bok
value
Rs.
Market value
Rs.
Cost (%)
Equity capital
Retained earnings
Preference capital
Debt capital
300000
100000
50000
200000
600000
60000
190000
15
13
8
6
Total 650000 850000

Leverages
While constructing capital structure, a firm can use fixed cost
bearing securities for maximization of shareholders’ wealth.
Leverage has been defined as the action of a lever and
mathematical advantage gained by it. In other words,
leverage allows accomplishing certain things that are
otherwise not possible. From the financial management
point of view, the term leverage is commonly used to
describe the firm’s ability to use fixed cost assets or sources
of funds to magnify the returns to its owners. According to
James Home, ‘leverage is the employment of an asset or
sources of funds for which the firm has to pay a fixed cost or
fixed return'. Here fixed cost or fixed returns remains
constant irrespective of the level of output.

Types of Leverages
There are basically two types of leverages. In addition to these
two kinds of leverages ‘composite leverage ‘ is also computed
to determine the combined effect of the leverages.
1.Operating Leverage :Operating leverage is present anytime in
a firm when it has operating fixed costs regardless of the
level of production. These fixed costs do not vary with sales,
they must be paid regardless of the amount of revenue
available. Hence operating leverage may be defined as the
firm’s ability to use operating costs to magnify the effects of
changes in sales on its earnings before interest and taxes.
Operating leverage results from the presence of fixed
operating expenses with firm’s income stream.

The operating costs are categorised into three—(1)Fixed
costs which do not vary with the level of production.For
example,depreciation on plant and machinery,insurance
etc.,(2)Variable costs which vary directly with the level
of production.Eg.rawmaterials,direct labour costs etc.
(3)Semi-variable costs which partly vary and partly
fixed.Eg.Indirect materials,Telephone charges etc.
The degree of operating leverage may be defined as the
change in the percentage of operating income(EBIT) for
a given change in percentage of sales revenue.The
degree of operating leverage at any level of output is
arrived at by dividing the percentage change in EBIT
with percentage change in sales.

Operating Leverage = Contribution
EBIT (Operating profit)
EBIT=Earnings Before Interest and Tax
Degree of Operating Leverage(DOL)=
Percentage change in EBIT
Percentage change in sales
Operating leverage may be favourable or
unfavourable.High degree of operating leverage
indicates higher degree of risk. Operating risk(business
risk) is the risk of the firm for not being able to cover its
fixed operating costs.

Earnings available to equity shareholders
Particulars Amount Rs.
Sales Revenue xxxx
Less:Variable cost xxx
Contribution xxxx
Less:Fixed cost xxx
Earnings Before Interest and Tax(EBIT ) xxxx
Less:Interest xxx
Earnings Before Tax (EBT) xxxx
Less:Tax xxx
Earnings After Tax(EAT) xxxx

Less:Preference dividend xxx
Earnings Available to Equity Shareholders xxxx
Problem 1
ABC Ltd. produced and sold 100000 units of a product at
the rate of Rs.10 per unit.For production of 100000 units
it has spent a variable cost of Rs.600000 at the rate of
Rs.6 per unit and a fixed cost of Rs.250000.The firm has
paid interest of Rs.5000 at the rate of 5% of rs.100000
debt. Calculate operating leverage.

Solution
EBIT or Operating Profit
Computation of EBIT
Particulars Amount Rs.
Sales Revenue(100000x10) 1000000
Less:Variable cost(100000x6) 600000
Contribution 400000
Less:Fixed cost 250000
EBIT 150000
Operating Leverage = 400000 = 2.66 times
150000

Problem 2
From the following particulars of ABC Ltd.,calculate
degree of operating leverage.
Particulars Previous Year 2019
Rs.
Current Year 2020
rs.
Sales Revenue
Variable Cost
Fixed Cost
1000000
600000
250000
1250000
750000
250000

Degree of Operating Leverage= Percentage change in EBIT
Percentage change in sales
Particulars
Sales Revenue
Less: Variable cost
Contribution
Less: Fixed cost
EBIT
2019 Rs.
1000000
600000
400000
250000
150000
2020 Rs.
1250000
750000
500000
250000
250000
Percentage
change
25%
25%
25%
--
66.67%
DOL =66.67/25
=2.667 times
Operating Leverage
2.667 indicates that
when there is 25%
change in sales,the
change in EBIT is
2.667 times.

Financial Leverage: Firms may need long-term funds for
long-term activities like
expansion,diversification,modernisation etc.Finance
manager’s job is to raise the required funds with
different composition of sources .The required funds
may be raised by two major sources, debt and equity.
Use of various sources to compose capital is known as
capital structure. The use of fixed charge sources of
funds such as debt and preference share capital along
with equity share capital in capital structure is
described as financial leverage.It is the ability of the
firm to use fixed financial charges to magnify the effects
of changes in EBIT on the firm’s earnings per share.

In other words, financial leverage may be defined as the
payment of fixed rate of interest for the use of fixed
interest bearing securities to magnify the rate of return
on equity shares. It is also known as trading on equity.
Hence financial leverage results from the presence of
fixed financial charges in the income statement.
Financial Leverage is computed by the formula:
Financial Leverage = EBIT(Operating Profit)
EBT(Earnings Before Tax)
Degree of Financial Leverage(DFL) =
Percentage change in EPS
Percentage change in EBIT

Financial leverage may be positive or negative. Higher the
degree of financial leverage leads to high financial risk
which refers to the risk of the firm for not being able
cover its fixed financial costs.
Problem 3
A firm has sales of 100000 units at Rs.10 per unit.Variable
cost of the produced products is 60% of the total sales
revenue. Fixed cost is Rs.200000.The firm has used a
debt of Rs.500000at 20% interest. Calculate the
operating and financial leverage.

Problem 4
From the following particulars of PQR Company,
calculate operating and financial leverages. The
company’s current sales revenue is Rs.1500000 and sales
are expected to increase by 25%.Rs.900000 incurred on
variable expenses for generating Rs.15 lakhs sales
revenue.The fixed cost is Rs.250000.The company has
Rs,20 lakhs equity share capital and Rs.20 lakhs ,10%
debt capital. Rs.10 per equity share and 50% tax rate.

EBIT
Financial Leverage = EBIT
EBT
Degree of Operating Leverage = % change in EBIT
% change in Sales
Degree of Financial Leverage= % change in EPS
% change in EBIT

Computation of Earnings Per Share
Particulars Current
position
Expected
change
% change
Sales
Less:Variable cost
Contribution
Less:Fixed cost
EBIT
Less:Interest
EBT
Less:Tax @50%
Less:Preference
dividend
Earnings available
to equity
shareholders
1500000
900000
600000
250000
350000
200000
150000
75000
----
75000
1875000
1125000
750000
250000
500000
200000
300000
150000
---
150000
25%
42.86%

EPS = Earnings available to equity shareholders
No. of equity shares
EPS= 75000/200000 =0.375 (Current position)
EPS = 150000/200000 = 0.75 ( Expected change)
% change in EPS =0.75-0.375 x100 = 0.375/0.375 x100=100%
0.375
Operating Leverage = Contribution = 600000 = 1.714times
EBIT 350000
DOL = 42.86 /25 = 1.714 times.
Financial Leverage = 350000/150000 =2.33 times
DFL= 100/42.86 = 2.33 times

3. Combined Leverage
The operating leverage has its effects on operating risk
and is measured by the percentage change in EBIT due
to the percentage change in sales. The financial leverage
has its effects on financial risk and is measured by the
percentage change in EPS due to the percentage change
in EBIT.Since both these leverages are closely related
with the ascertainment of firm’s ability to cover fixed
charges(fixed operating costs in case of operating
leverage and fixed financial costs in case of financial
leverage),the sum of them gives us the total leverage or
combined leverage and the risk associated with
combined leverage is known as the total risk.

The degree of combined leverage is defined as the
percentage change in EPS due to the percentage change
in sales.
% change in EBIT x % change in EPS
% change in Sales % change in EBIT
= % change in EPS
% change in Sales
Or Contribution x EBIT = Contribution
EBIT EBT EBT

Problem 5
VST Corporation has sales of Rs.40 lakhs,variable cost
70 percent of the sales and fixed cost is Rs.800000.The
firm has raised Rs.20 lakhs funds by issue of
debentures at the rate of 10 percent. Compute
operating, financial and combined leverage.
Problem 6
Penta Four Ltd. currently has an all equity capital
structure consisting of 15000 equity shares of Rs.100
each.The management is planning to raise another
Rs.25 lakhs to finance a major expansion programme
and is considering three alternative methods of
financing.

(i) To issue 25000equity shares of Rs.100 each.
(ii) To issue 25000,8% debentures of Rs.100 each.
(iii) To issue 25000,8% preference shares of Rs.100 each.
The company’s expected EBIT will be Rs.8lakhs.
Assuming a corporate tax rate of 46 percent.
Determine the EPS in each financial plan and
determine the best one and why .

The capital structure of XLtd. Consists of the following
securities.
10% Debentures Rs.500000
12% Preference shares Rs.100000
Equity shares of Rs.100 Rs.400000.
Operating Profit(EBIT) of Rs.160000 and the company
is in 50% tax bracket.
(1) Determine the company’s EPS.
(2) Determine the percentage change in EPS associated
with 30% increase and 30% decrease in EBIT.
(3) Determine the degree of financial leverage.

Capital Budgeting Decisions and Techniques.
Capital Budgeting is the process of making investment
decisions in capital expenditures. A capital expenditure
may be defined as an expenditure the benefits of which
are expected to be received over period of time
exceeding one year. The main characteristic of a capital
expenditure is that the expenditure is incurred at one
point of time whereas benefits of the expenditure are
realised at different points of time in future. Thus it is
the expenditure incurred for acquiring or improving the
fixed assets, the benefits of which are expected to be
received over a number of years in future.

The following are some of the examples of capital
expenditure.
(i) Cost of acquisition of permanent assets as land and
building, plant and machinery ,goodwill etc.
(ii)Cost of addition,expansion,improvement or alteration
in the fixed assets.
(iii)Cost of replacement of permanent assets.
(iv)Research and development project cost etc.

Definitions
1.Charles T Horngreen has defined capital budgeting as
“Capital budgeting is long term planning for making and
financing proposed capital outlays’.
2.In the words of Lynch,’Capital Budgeting consists in
planning and development of available capital for the
purpose of maximising the long term profitability of the
concern.’
Need and Importance of Capital Budgeting
1. Large Investments: Capital budgeting decisions generally
involve large investment of funds. But the funds available
with the firm are always limited and the demand for funds
far exceeds the resources. Hence it is very important for a
firm to plan and control its expenditure.

2. Long-term commitment of funds: Capital expenditure
involves not only large amount of funds but also funds for
long-term or more or less on permanent basis.The long-
term commitment of funds increases the financial risk
involved in the investment decision.
3.Irreversible Nature. The capital expenditure decisions are of
irreversible nature. Once the decision for acquiring a
permanent asset is taken, it becomes very difficult to dispose
of these assets without incurring heavy losses.
4.Long-term Effect on profitability: Capital budgeting
decisions have a long-term and significant effect on the
profitability of a concern. The future growth and
profitability of the firm depends upon the investment
decisions taken today.

5.Difficulties of investment decision: The long-term
investment decisions are difficult to be taken because
(i)decision extends to a series of years beyond the
current accounting period,(ii)uncertainties of future
and (iii) higher degree of risk.
6.Effect on other projects: While taking investment in
long-term assets decision, the impact of the proposed
project on the other projects must be examined .If the
effect is in terms of increase in profits ,then the
financial manager has to accept the project and vice
versa.

Capital Budgeting Process
1.Identification of Investment Proposals: The capital
budgeting process begins with the identification of
investment proposals. The proposal or the idea about
potential investment opportunities may originate from
the top management or may come from any officer from
any department of the organization. The department
head analyses the various proposals in the light of the
corporate strategies and submits the suitable proposals
to the capital expenditure planning committee in case
of large companies or to the officers concerned with the
process of long-term investment decisions.

2.Screening the Proposals: The Expenditure Planning
Committee screens the various proposals received from
different departments. The committee views these
proposals from various angles to ensure that these are in
accordance with the corporate strategies or selection
criterion of the firm and also do not lead to
departmental imbalances.
3.Evaluation of Various Proposals: The next step in the
capital budgeting process is to evaluate the profitability
of various proposals. There are many techniques which
may be used for this purpose such as pay back period
method, average rate of return method,net present
value method etc.

4.Fixing priorities: After evaluating various proposals, the
unprofitable or uneconomic proposals may be rejected
straight away. But it may not be possible for the firm to
invest immediately in all the acceptable proposals due to
limitation of funds. Hence it is very essential to rank the
various proposals and to establish priorities after
considering urgency, risk and profitability involved there in.
 5. Implementation
 After the completion of all the above steps, the investment
proposal under consideration is implemented, i.e., put into a
concrete project. There are several challenges that can be
faced by the management personnel while implementing
the projects as it can be time-consuming. So it is better to
assign responsibilities for completing the project within the
given time frame and cost limit so as to avoid unnecessary
delays and cost.

7.Performance Review: The last stage in the process of
capital budgeting is the evaluation of the performance
of the project. The evaluation is made through post
completion audit by way of comparison of actual
expenditure on the project with the budgeted one,and
also by comparing the actual return from the
investment with the anticipated return. The
unfavourable variances, if any should be looked into
and the causes of the same be identified so that
corrective action may be taken in future.

Kinds of Capital Budgeting Decisions
Capital Budgeting decisions are classified as:
1.Accpt Reject Decisions: Accept-reject decisions relate to
independent projects which do not compete with one
another.Such decisions are generally taken on the basis
of minimum return on investment. All those proposals
which yield a rate of return higher than the minimum
required rate of return or the cost of capital are
accepted and the rest are rejected.If the proposal is
accepted,the firm makes investment in it.And if it is
rejected,the firm does not invest in the same.

(ii)Mutually exclusive Project Decisions: Such decisions
relate to proposals which compete with one another in
such a way that acceptance of one automatically
excludes the accptance of the other. Thus one of the
proposals is selected at the cost of the other. For
example,a company may have the option of buying a
new machine,or a second hand machine,or taking an
old machine on hire .In such a case,the company may
select one best alternative out of the various options by
adopting some suitable technique or method of capital
busgeting.Once one alternative is selected,the others
are automatically rejected.

(iii) Capital Rationing Decisions: A firm may have several
profitable investment proposals but only limited funds to
invest.In such a case these various investment proposals
compete for limited funds and thus the firm has to ration
them.The firm selects the combination of proposals that
will yield the greatest profitability by ranking them in
descending order of their profit earning capacity.
(iv) Contingent Investments: Contingent projects are
dependent investments, acceptance of one option needs to
undertake one or more other projects. For example, location
of a factory in a backward area may need to construct
roads,quarters for employees,hospitals,schools without
which it is very difficult to attract employees.

Techniques of Capital Budgeting or Evaluation of
Investment Proposals
Evaluation techniques are divided into two broad
categories,namely
(A) Traditional Techniques or non-discounted
techniques:
1.Pay back Period Method (PBP)
2.Accounting Rate of Return or Average Rate of
Return(ARR).
(B) Modern Techniques or discounted cash flow
techniques:
1.Net Present Value Technique(NPV)

2.Internal Rate of Return technique(IRR)
3.Profitability Index technique(PI)
Traditional Techniques
1. Pay Back Period
Pay back period is one of the most popular and widely
recognised techniques of evaluating investment
proposals. Pay back period is defined as that period
required to recover the original cash outflow invested
in a project. In other words, it is the minimum
required number of years to recover the original cash
outlay invested in a project. The cash flow after taxes
is used to compute the pay back period.

Payback period can be calculated in two ways,(i)Using
formula and (ii)Using cumulative cash flow method.
The first method can be applied when the annual cash
flows stream of each year is equal, that is, uniform
cash flows for all the years. In this situation the
following formula is used to calculate pay back period.
Pay back period = Original Investment÷ Annual Cash
Inflows After Taxes.
The second method is applied when the annual cash
flows after taxes are unequal or not uniform over the
projects life period. In this situation, the pay back
period is calculated through the process of cumulative
cash flows, cumulative process goes up to the period

where cumulative cash flows equal to the actual cash
outflows. Symbolically:
PBP = Year before full recovery +(Unrecovered amount of
investment÷ Cash flows during the year)
Decision Rule
Acceptance or rejection of the project is decided based on
the comparison of calculated PBP with the standard pay
back period. Symbolically;
Accept: Calculated PBP< Standard PBP
Reject: Calculated PBP> Standard PBP

Proforma of Cash Inflows After Taxes(CFAT)
Particulars Amount (Rs.)
Sales Revenue xxxx
Less:Variable cost xxx
Contribution xxxx
Less: Fixed cost xxx
Earnings Before Depreciation and Taxes(EBDT) xxxx
Less: Depreciation xx
Earnings Before Taxes(EBT) xxx
Less:Taxes xx
Earnings After Taxes(EAT) xxx
Add:Depreciation xx
Cash Flows After Taxes xxx

Advantages of Pay Back Period
1.It is very simple and easy to understand.
2.It saves in cost, it requires lesser time and labour as
compared to other methods of capital budgeting.
Limitations of pay back period method
1.It ignores cash flows after pay back period.
2.It is not an appropriate method of measuring the
profitability of a project, as it does not consider all cash
inflows yielded by the investment.
3.It does not take into consideration time value of money.
4.There is no rationale basis for setting a minimum pay back
period.
5.It is not consistent with the objective of maximizing
shareholders’ wealth since share value does not depend on
pay back periods of investment projects.

Problem 1
A project costs Rs.100000 and yields an annual cash
inflow of Rs.20000 for 8 years. Calculate its pay back
period.
Solution
Pay back period =Original Investment ÷ Annual Cash
Inflows after taxes
=100000 = 5 years.
20000

Problem 2
There are two projects X and Y.Each project requires an
investment of Rs.20000.You are required to rank these
projects according to the pay back method from the
following information.
Net profit before depreciation and after tax
Years Project X (Rs.) Project Y (Rs.)
1 1000 2000
2 2000 4000
3 4000 6000
4 5000 8000
5 8000 ---

The pay back period for Project X is 5
years(1000+2000+4000+ 5000+8000=20000)and the
pay back period for Project Y is 4
years.(2000+4000+6000+8000=20000)
Hence Project Y is preferred or ranked first.
Problem 3
A company is considering expanding its production. It
can go in either for an automatic machine costing
Rs.224000 with an estimated life of 5 years or an
ordinary machine costing Rs.60000 having an
estimated life of 8 years. The annual sales and costs are
estimated as follows:

Automatic Machine(Rs.) Ordinary Machine (Rs.)
Sales 150000 150000
Costs:
Materials 50000 50000
Labour 12000 60000
Variable overheads 24000 20000
Calculate the pay back period. (Tax at 50%)

Cash Inflows After Taxes (CFAT)
Particulars Automatic
Machine(Rs.)
Ordinary
Machine(Rs.)
Sales 150000 150000
Less: Variable costs
Materia+Labour+
Variable overheads 86000 130000
Contribution 64000 20000
Less:Fixed cost
Earnings Before
Depreciation and
Taxes
Less:depreciation
---
64000
44800
---
20000
7500
Earnings Before Tax
Less:Tax 50%
Earnings After Tax
Add:depreciation
CFAT
19200
9600
9600
44800
54400
12500
6250
6250
7500
13750

Depreciation= Original Investment-Scrap Value
Estimated life
Automatic machine=224000/5 =Rs.44800
Ordinary machine =60000/8 = rs.7500
Pay back period= Original Investment÷Annual Cash
Inflows
Automatic machine=224000/54400 =4.11 years
Ordinary machine =60000/13750 =4.36 years

Problem 4
A project costs Rs.20 lakhs and yields annually profit of
Rs.300000 after depreciation at 12 ½ % but before tax at
50%. Calculate pay back period and suggest whether it
should be accepted or rejected based on 6 years
standard pay back period.

Problem 5
(when cash inflows are uneven)
ABC Ltd. is considering two projects. Each project
requires an investment of Rs.10000.The firm’s cost of
capital is 10%.The company has fixed 3 years PBP as the
cut-off point. State which project should be accepted.
The net cash inflows from investments in two projects
X and Y are as follows:
Year 1 2 3 4 5
Project
X(Rs.)
5000 4000 3000 1000 ---
Project
Y(Rs.)
1000 2000 3000 4000 5000

Calculation of Pay Back Period
Year ProjectX Project Y
CFAT(Rs.) Cumulative
CFAT(Rs.)
CFAT(Rs.) Cumulative
CFAT(Rs.)
1
2
3
4
5
5000
4000
3000
1000
---
5000
9000
12000
13000
1000
2000
3000
4000
5000
1000
3000
6000
10000
15000

Pay back period= Year before full recovery+(Unrecovered
amount÷Cash flows during the year)
Project X = 2+(1000÷3000)=2+0.33= 2.33 years
Project Y = 4 years.
Prroject X should be accepted since 2.33 years is less than
3 years cut-off point.

Problem 6
Calculate the pay back periods of the following projects
each requiring a cash outlay of Rs.100000.Suggest
which projects are acceptable if the standard pay back
period is 5 years.
Year Cash Inflows
project A Project B Project C
1 30000 30000 10000
2 30000 40000 20000
3 30000 20000 30000
4 30000 10000 40000
5 30000 5000 ---

Accounting Rate of Return Method (ARR)
Accounting rate of return method uses accounting
information as revealed by financial statements to
measure the profitability of the investment proposals.It
is also known as Average Rate of Return (ARR).Average
annual earnings after depreciation and taxes are used
to calculate ARR.It is measured in terms of percentage.
ARR may be calculated in two ways:
(i) Whenever it is clearly measured as Accounting Rate
of Return
If the accounting rate of return is given in the problem,
return on original investment method should be
used to calculate accounting rate of return

Accounting Rate of Return (ARR)=
Average Annual EAT or PAT x100
Original Investment
Original Investment=Original Investment+Additional
Net working capital +Installation charges
+Transportation charge.
(ii) Whenever it is clearly mentioned as Average Rate of
Return
If average rate of return is given in the problem, return on
average investment method should be used to calculate
average rate of return.

ARR = Average Annual EAT x100
Average Investment
Average Investment = (Original Investment-Scrap
Value)1/2+Additional Net working capital +Scrap value.
Decision Rule
Accept: Calculated ARR>Pre-determined ARR
Reject: Cal ARR< Pre-determined ARR.
Advantages of ARR Method
1.It is very simple to understand and easy to calculate.
2.Information can easily be drawn from accounting records as
this method is based upon accounting concept of profits.
3.It takes into account all profits of the project’s life period.

Limitations of ARR Method
1.It uses accounting profits instead of actual cash flows
after taxes in evaluating the projects. Accounting profits
are inappropriate for evaluating and accepting projects
since they are computed based on arbitrary
assumptions and choices and also include non-cash
items.
2.It ignores the concept of time value of money.
3.It does not differentiate between the size of the
investment required for each project.
4.It is incompatible with the objective of wealth
maximisation to the equity shareholders.
5.It uses arbitrary cut-off as yardstick or standard for
acceptance or rejection rule.

Problem 1
A project requires an investment of Rs.500000 and has a
scrap value of Rs.100000. Its stream of income before
depreciation and taxes during the five years amounting
to Rs.100000,Rs.120000,Rs.140000,Rs.160000 and
Rs.200000 .Calculate the accounting rate of return on
the investment. Also state whether you recommend the
project for investment when the management expects a
rate of return of 10%.Tax rate is 50%
Solution
Accounting Rate of Return =
Average Annual Earnings After Tax x100
Original Investment

Total earnings or profit
=100000+120000+140000+160000+200000=Rs.720000
Average earnings= 720000/5 = Rs.144000
Less: depreciation 80000
Average Earnings Before Tax 64000
Less:Tax @50% 32000
Average Earnings After Tax 32000
Depreciation= Original investment-scrap value
Estimated life
=500000-100000 =Rs.80000
5

ARR = 32000 x 100 =6.4%
500000

Problem 2
A limited company has under consideration the following
two projects:
Project X(Rs.) Project Y(Rs.)
Investment in machinery 1000000 1500000
Working capital 500000 500000
Life of machinery(years) 4 6
Scrap value(%) 10 10
Tax rate(%) 50 50
Compute average rate of return and suggest which project
is to be preferred.
Income before depreciation and tax at the end of

Year 1 2 3 4 5 6
X(Rs.) 800000 800000 800000 800000
Y(Rs.) 1500000 900000 1500000 800000 600000 300000

Solution
Average Rate of Return =
Average annual earnings after taxes x100
Average Investment
Average Annual EAT
Particulars Project X(Rs.) Project Y (Rs.)
Average EBDT 800000 933333
Less: depreciation 225000 225000
Average EBT 575000 708333
Less:Tax 50% 287500 354167
Average EAT 287500 354167

Average Investment= (Original investment-Scrap value)1/2+Additional Net
working capital+ Scrap value.
Project X=(1000000-100000)1/2+500000+100000=Rs.1050000.
Project Y=(1500000-150000)1/2+500000+150000=Rs.1325000
ARR-Project X=287500 x100=27.38%
1050000
ARR,Project Y= 354167 x 100 = 26.73%
1325000
Working Note
Depreciation= Original cost-Scrap value
Estimated life
Project X = 1000000-100000 = 900000 = rs.225000
4 4
Project Y = 1500000-150000 = 1350000 = Rs.225000
6 6

Problem 3
From the following data,determine the Accounting Rate
of Return.
Particulars Machine A(Rs.) Machine B(Rs.)
Original cost 56125 56125
Additional
Net working capital 5000 6000
Estimated life(years) 5 5
Estimated salvage value 3000 3000
Average income tax rate(%) 55 55

Annual estimated income after depreciation and
taxes(EAT)
Year 1 2 3 4 5
Machine A(Rs.) 3375 5375 7375 9375 11375
Machine B(Rs.)11375 9375 7375 5375 3375
Depreciation has been charged on straight line basis.

Modern or Discounted Cash Flow Techniques
Modern techniques are again subdivided into three:
1.Net Present Value method 2. Internal Rate of Return
method and 3.Profitability Index
Net present value (NPV)
NPV can be defined as present value of benefits minus
present value of costs. It is the process of calculating
present values of cash outflows from the present value
of cash inflow and find the net present value which
may be positive or negative. Positive net present value
occurs when the present value of cash inflows is higher
than the present value of cash outflows and vice versa.

Decision Rule
Accept:NPV>zero
Reject:NPV<zero
Advantages
1.It takes into account the time value of money.
2.It uses all cash inflows occurring over the entire life
period of the project.
3.It is particularly useful for the mutually exclusive
projects.
4.It is consistent with the objective of maximisation of
shareholders’ wealth.
5.It takes into consideration the changing discount rate.

Limitations
1.It is difficult to understand when compared with pay
back period and Accounting rate of return methods.
2.It may not give good results while comparing projects
with unequal life period as the project having higher
net present value but realised in a longer life span may
not be as desirable as a project having something lesser
net present value achieved in a much shorter span of
life of the asset.
3.It may not give good results while comparing projects
with unequal investment of funds.
4.It is not easy to determine an appropriate discount rate.

Steps involved in the computation of NPV
(i)Forecasting of cash inflows of the investment project
based on realistic assumptions.
(ii)Computation of cost of capital which is used as a
discounting factor for conversion of future cash inflows
into present values.
(iii)Calculation of present value of cash inflows using
cost of capital as discounting rate.
(iv)Finding out Net Present Value by subtracting present
value of cash outflows from present value of cash
inflows.

Problem 1
From the following information calculate the net present
value of the two projects and suggest which of the two
projects should be accepted assuming a discount rate of
10%.
Project X Project Y
Initial investment Rs.20000 Rs.30000
Estimated Life 5 years 5 years
Scrap value Rs.1000 Rs.2000

The profits before depreciation and after taxes are as
follows:
Year 1 Year 2 Year 3 Year 4 Year 5
Rs. Rs. Rs. Rs. Rs.
Project X 5000 10000 10000 3000 2000
Project Y 20000 10000 5000 3000 2000
Solution

Calculation of Net Present Value
Project X
Year Cash Flows (rs.) Present value of
Re.1@10%(discou
factor)
Present value of
cash inflows(rs.)
1
2
3
4
5
5(scrap value)
5000
10000
10000
3000
2000
1000
.909
.826
.751
.683
.621
.621
4545
8260
7510
2049
1242
621
Net Present
Value(NPV) =
Present value of
cash inflows –
Present value of
cash outflows.
NPV=24227-20000
24227
=Rs.4227

Project Y
Year Cash
flows(Rs.)
PV of Re.1@10% Present Value
of cash inflows
1
2
3
4
5
5
20000
10000
5000
3000
2000
2000
.909
.826
.751
.683
.621
.621
18180
8260
3755
2049
1242
1242
NPV of project Y
and hence it is
suggested that
project Y should
be selected
is higher than
NPV=34728-
30000 =
projectX
34728
Rs.4728

Problem 2
No project is acceptable unless the yield is 10%.Cash
inflows of a certain project along with cash outflows are
given below:
Years Cash outflows(Rs.) Cash Inflows(Rs.)
0 150000 ----
1 30000 20000
2 30000
3 60000
4 80000
5 30000
The salvage value at the end of the 5th year is
Rs.40000.Calculate the Net Present Value.

 Present value of cash outflows
 150000
 30000x.909= 27270
 Total = 177270

Problem 3
A firm has two investment opportunities, each costing
Rs.100000 and each having an expected profit as shown
below:
Year 1 2 3 4
Project A(Rs.) 50000 40000 30000 10000
Project B (Rs.)20000 40000 50000 60000
After giving due consideration to the risk criteria in each
project the management has decided that project A should
be evaluated at 10% cost of capital and project B,a risky
project with a 15% cost of capital. Compute the NPV and
suggest the course of action for the management of if:
(a)Both the projects are independent
(b) Both are mutually exclusive.

Problem 4
A company is considering investment in a project that
costs Rs.200000.The project has an expected life of 5
years and zero salvage value.The company uses straight
line method of depreciation.The company’s tax rate is
40%.The estimated earnings before depreciation and
before tax from the project are as follows:

Year Earnings before depreciation &tax Present value
Rs. factor at 10%
1 70000 .909
2 80000 .826
3 120000 .751
4 90000 .683
5 60000 .621
You are required to calculate the net present value at
10% and advise the company.

Calculation of NPV
Year
1
2
3
4
5
Cash
Inflows(Rs.)
58000
64000
88000
70000
52000
Present value
factor at 10%
.909
.826
.751
.683
.621
Present value of
cash inflows
(Rs.)
52722
52864
66088
47810
32292
251776
Since NPV is
positive,the
project can be
accepted.

Internal Rate of Return (IRR)
This method is also known as Trial and Error Method or
Time adjusted rate of return method. Internal rate of
return is defined as that discounting factor at which
the present value of cash inflows equals to the present
value of cash outflows. It takes into account the
magnitude and timing of cash flows.In case of NPV
method,the discount rate is the required rate of return
and that is pre-determined,where as IRR is based on
facts which depends entirely on the initial cash outlay
and cash proceeds of the proposed project.

Computation of IRR
It is based on cash flows after taxes.IRR is
mathematically represented as ‘r’. It can be found out
by trial and error method. In this method the evaluator
selects any discount rate to compute the present value
of cash inflows .Otherwise cost of capital is taken as
first trial. If the calculated present value of the cash
inflows is higher than the present value of the cash
outflows, then the evaluator can try at a higher
discount rate.
 On the other hand, if the present value of cash inflows
is lower than the present value of cash outflows ,then
the evaluator has to try lower discounting factor. This
process will be repeated till the present value of cash
inflows equals to the present value of cash outflows.

 Generally IRR may be between two discounting factors, in
that case the analyst has to use interpolation formula for
calculation of IRR. The formula is :
 IRR = LDF%+( Delta DF x PVLDF-COF )
 PVLDF-PVHDF
 Where,
 LDF=Lower discount factor
 Delta DF = Difference between low discount factor and high
discount factor.
 PVLDF = Present value of cash inflows at low discounting
factor.
 PVHDF = Present value of cash inflows at high discounting
factor.
 COF = Cash outflows

 Decision Rule
 Accept or reject rule of the project is decided based on
the calculated IRR and cost of capital.
 Accept: IRR is greater than Cost of capital.
 Reject :IRR is less than Cost of capital (Ko)
 Advantages of IRR
 1.It takes into account the time value of money.
 2.It considers cash flows throughout the project’s life.
 3.It does not use the concept of required rate of return
or the cost of capital. it itself provide a rate of return
which is indicative of profitability.
 4.It gives more psychological satisfaction to the user
since it is calculated by the method of trial and error.

 Limitations of IRR
 1.It is difficult to understand and to calculate since it
involves tedious calculations.
 2.It implies that profits can be reinvested at internal
rate of return which is not logical.
 3.It produces multiple rate of returns which can be
confusing.
 4.It does not help evaluation of mutually exclusive
projects, since a project with highest IRR would be
selected.
 5.It may not give fruitful results in case of unequal
projects life, unequal cash outflows and difference in
the timing of cash flows.

A company has to select one of the following two projects:
Year 0 1 2 3 4
Project X(Rs.)11000 6000 2000 1000 5000
ProjectY(Rs.)10000 1000 1000 2000 10000
Calculate IRR.Suggest the best alternative on the above
basis.

Solution
Project X
Year CFAT (Rs.) DF PV(Rs.)
10% 12% 10% 12%
1 6000 .909 .893 5454 5358
2 2000 .826 .797 1652 1594
3 1000 .751 .712 751 712
4 5000 .683 .636 3415 3180
present value of cash inflows 11272 10844
Less:PV of cash outflows 11000 11000
NPV 272 -156

IRR = LDF%+ ( ΔDFx PVLDF-COF )
PVLDF-PVHDF
=10% +( 2 x 11272 -11000) = 10% + 2x 272 =10%+544
11272-10844 428 428
=10%+1.27 = 11.27%

Project Y
Year CFAT (Rs.) DF PV(Rs.)
10% 15% 10% 15%
1 1000 .909 .870 909 870
2 1000 .826 .756 826 756
3 2000 .751 .658 1502 1316
4 10000 .683 .572 6830 5720
present value of cash inflows 10067 8662
Less:PV of cash outflows 10000 10000
NPV 67 -1338
PV of cash inflows at 10%= Rs.10067
PV of cash inflows at 15% = Rs.8662

IRR = 10% + (5 x 10067 -10000)
10067-8662
=10% + 5x 67 = 10%+ 335 = 10%+0.24 =10.24%.
1405 1405
Project X is preferred as it has higher IRR.

Profitability Index (PI)
This method is similar to Net present value method.It is
also called as Benefit-cost ratio or ‘Desirabilty factor’ is
the relationship between present value of cash inflows
and the present value of cash outflows.
Profitability Index (PI)= Present Value of cash inflows
Present value of cash outflows
Advantages
1.It gives due consideration to time value of money.
2.It considers all cash flows to determine PI.
3.It will help to rank projects according to their PI.
4.It is consistent with the objectives of maximisation of
shareholders’ wealth.

Problem 1
The initial cash outlay of a project is Rs.50000 and it
generates cash inflows of Rs.20000,Rs.15000,Rs.25000
and Rs.10000 in four years. Using profitabilityindex
method, appraise profitability of the proposed
investment assuming 10% rate of discount.
Solution
Year Cash inflows(Rs.) Present value Present Value (rs.)
factor at 10%
1 20000 .909 18180
2 15000 .826 12390
3 25000 .751 18775
4 10000 .683 6830

Total Present Value of cash inflows Rs.56175
Less :cash outflows 50000
6175
Profitability Index = Present value of cash inflows
Present value of cash outflows
= 56175 = 1.1235
50000
Problem 2
The initial cash outlay of a project is Rs.100000 and it
generates cash inflows of Rs.40000,Rs.30000,Rs.50000
and Rs.20000.Assume a 10% rate of discount. Calculate
profitability index.

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