18
Investment Analysis and
Break-even Analysis
________________________________________________________________________
Financial management is a vital function of management process since finance is the
heart and soul of every business. A key constituent of financial management is
investment analysis.
Time Value of Money The time value of money is an essential concept in relation to
financial management because cash flows from projects occur at various points in time. A
rational decision-maker would not value the opportunity to receive some money now
equally with the opportunity to receive the same amount at some later dates, say after a
year. Time value of money is the price of foregoing purchasing power currently and also
the uncertainties involved. Time preference for money is expressed by means of an
interest rate when the future is linked with the present and by a discount rate when the
present is linked to the future.
An amount P, called the principal amount, carrying an interest rate of i per period,
after n conversion periods would become compounded sum S, where
S = P(1 + i)n.
The expression (1 + i)n is called accumulation factor. For selected pairs of i and n, the
values of this expression are given in Table B5. For n = 5 and I = 6%, the value is 1.3382,
for example.
Opposite to the process of compounding is the discounting which involves finding the
present value P, of an amount S which is due on a future date after n periods. Thus,
P = S(1 + i)-n
Here (1 + i)-n is referred to as present value factor (PVF). Table B3 gives PV factors for
some combinations of i and n.
Annuities An annuity refers to a series of payments at regular intervals of time and
usually equal in amount. Annuities are classified on the basis of their terms as annuity
certain, perpetuity and contingent annuity, while on the basis of time of payments as
ordinary annuity, annuity due and deferred annuity.
For an ordinary annuity, where an amount A is paid (or received) at the end of each of
n time periods and i is the rate of interest per time period, the amount of such payments,
M is obtainable as:
A(Rn – 1)
M = ------------- ,
R–1
where R = 1 + i.
Present value of an ordinary annuity, V, on the other hand, can be obtained as follows:
A(1 – R n )
V = -------------R–1
Investment Analysis
The objective of investment decisions is to identify the real assets that are worth more
than what they cost. There are four methods for the measurement of investment worth.
Payback method It indicates the time period required to recover the original cash
investment in any project. If C0 is the initial investment and Ct is the cash inflow
in the tth year, then the payback period would be the value of k, such that
k
∑ Ct – C0 = 0.
t=0
Average rate of return
It is the average annual profit as a percentage of the average
investment. It suffers from the investment. It suffers from the limitation that it is
unable to take account of the timing of cash proceeds from the investment.
Net present value (NPV) method
It is the excess (shortage) of the present
(discounted) value of the inflows over present value of the outflows. A project is
acceptable if its NPV > 0. Symbolically,
n
NPV =
∑ Ct(1 + i)-t
t=0
Internal rate of return (IRR)
It is the rate of return (discount) which equates the
outflows with the inflows. In other words, it rate of discounts that makes the NPV
of a project equal to zero. If the IRR is found to be in excess of the required rate
of return, the project is accepted. Otherwise the project is rejected. Thus,
n
∑ Ct (1 + IRR)-t = 0.
t=0
Methods of Incorporating Risk
Being an indispensable factor in the real world
operations, risk should be given due importance in investment analysis. There are many
ways in which risk can be taken into account while investment decision-making. They are
discussed here.
Certainty equivalent approach
It represents a direct approach to incorporate the
management’s utility function into analysis. It uses certainty risk equivalents
which are employed to multiply the risky cash flows, before calculating NPV
using risk-free rate of discount.
Risk-adjusted discount rate method
In this method, the risk-free rate is adjusted
upward by adding a suitable risk premium. The risk premium is a compensation
the risk-averse investors in the market would require before they would consent to
the risks of the investment.
Statistical distribution approach
In this approach, the degree of risk associated
with a project is sought to be measured in terms of variance of NPV distribution,
and the investment decisions are taken considering the expected value and
standard deviation of the NPV distribution.
Decision trees
It provides a convenient means to use the probability distribution
information to assess risk inherent in a given project. It assumes importance in
cases where the cash flows can not be easily classified as either independent or
perfectly correlated and the correlation is of moderate order.
Simulation approach The simulation technique can be used for approximating the
NPV or the expected return and its dispersion about the expected value.
Sensitivity analysis It does not attempt to quantify risk but focuses on how sensitive
is NPV (or IRR) to changes in any of the input variables.
Break-even analysis
Also known as cost-volume-profit analysis, the break-even analysis deals with interrelationships between total revenue, cost and profit in order to determine the potential
effects of decisions necessary to achieve or maintain various levels of financial success.
Various relationships are shown here.
Selling price – Variable cost
Contribution (margin) – Fixed cost
= Contribution margin (can be obtained
on a per unit basis or on aggregate basis)
= Profit
Contribution margin/unit
P/V ratio
= --------------------------------- ×100
Selling price
S–V
= -------- ×100
S
Break-even Point It exists when total revenue is equal to total sales and is, therefore, a
situation of no-profit no-loss. It may be expressed in terms of number of units or rupee
sales. We have,
Fixed cost, FC
Break-even sales
= -------------------P/V ratio
Fixed cost, FC
= ------------------------------Unit contribution margin
Break-even point (units)
Margin of Safety It is the excess of actual (or budgeted) sales over break-even sales.
Also, margin of safety ratio can be calculated as the margin of safety expressed as a
percentage of the actual (or budgeted) sales.
Sensitivity Analysis If the interaction of selling price, variable cost and fixed cost are
taken into account, break-even formula can be adapted to reflect simultaneous changes in
all the variables. Thus, we have
FC ± ∆ FC
Break-even sales (new) = -----------------V±∆V
1 – ----------S±∆S
Break-even Analysis for Multi-product Case In a multi-product case, the break-even
point is calculated by dividing the amount of fixed cost into weighted contribution
margin ratio. The weighted contribution margin ratio is calculated as given below:
n
∑[qi (Si – Vi)]
t=0
Contribution margin ratio = -------------------n
∑ Si qi
t=0
Where, n = number of different products, qi = estimated sales volume for ith product, Si =
unit selling price for ith product and Vi = unit variable cost for the ith product.
Break-even sales
Fixed cost
= ---------------CM Ratio