Appendix G
Financial measures used in cost benefit
analysis
PAYBACK
The payback may be defined as the amount of time, usually expressed in
years and months, required for the original investment amount to be
repaid by the cash-in flows. This measure is sometimes used with
nominal cash-in flows and sometimes used with discounted cash-in
flows. Nominal cash flows are the amounts unadjusted for the time value
of money. The most popular form of payback used today is referred to as
the exhaust method. The exhaust method of payback calculation
involves the deduction of each year's cash-in flow from the original
investment until the original amount is reduced to zero. This method
should be contrasted with the average payback method which only gives
a rough approximation of the period of time required to recover the
investment amount when the cash-in flows are relatively constant.
Exhaust method
Payback in time (years, months, etc) = investment–cumulative benefit
The calculation of the payback by the exhaust method is a reiterative
process which requires the cumulative benefit to be subtracted from the
investment until the result is zero. The time at which the result is zero
represents the period which is required for the investment amount to be
returned.
Average method
Payback in time
=
Investment
Average annual benefit
This average method is only useful if the annual benefits do not
materially vary from the average. If there is any substantial variability in
the annual benefits this method will produce meaningless results. Many
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firms use the payback as the primary criterion for deciding whether an
investment is suitable or not.
It is generally considered that the cash flows used to calculate the
payback should have first been discounted. This is referred to as a
discounted payback. If this is done it will produce a time-value-based
payback measure which will reflect the cost of capital. A discounted
payback will always show a longer period than one based on nominal
values.
NET PRESENT VALUE (NPV)
The net present value may be defined as the difference between the sum
of the values of the cash-in flows, discounted at an appropriate cost of
capital, and the present value of the original investment. Provided the
NPV is greater than or equal to zero the investment will earn the firm's
required rate of return. The size of the NPV may be considered as either
a measure of the surplus which the investment makes over its required
return, or as a margin of error in the size of the investment amount.
Present value of benefit =
Benefit
(1+i)n
Where
i = rate of interest
n = number of years
NPV =  Present value of benefit — Present value of investment
The interpretation of the NPV should be based on the following rules:
If NPV>=0 then invest
If NPV <0 then do not invest
The size of the NPV represents the margin of error which may be made
in the estimate of the investment amount before the investment will be
rejected.
PROFITABILITY INDEX (PI)
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The profitability index is defined as the sum of the present values of the
cash-in flows divided by the present value of the investment. This shows
a rate of return expressed as the number of discounted pounds and pence
which the investment will earn for every pound originally invested.
PI =  Present value of benefits
Present value of investment
INTERNAL RATE OF RETURN (IRR)
The internal rate of return is the rate of interest which will cause the
NPV to be zero. It is the internally generated return which the
investment will earn throughout its life. It is also frequently referred to
as the yield of the investment.
IRR = i such that NPV=0
RATE OF RETURN OR RETURN ON INVESTMENT (ROI)
The rate of return or return on investment, which is sometimes referred
to as the simple return on investment, is calculated by considering the
annual benefit divided by the investment amount. Sometimes an average
rate of return for the whole period of investment is calculated by
averaging the annual benefits while on other occasions the rate of return
is calculated on a year by year basis using individual benefit amounts.
ROI = Annual benefit
Investment amount
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