Manual for Development Projects - Planning Commission

Chapter 5
of values such as cash flow can exist only when at least one value is negative. Although IRR of different projects
will vary, a project cannot with confidence be ranked on the basis of IRR. Only in a very general way will the IRR
tell us that one project is better than another, in the sense that it contributes more to national income relative to
resources used. If the discount rate remains 12%, we cannot know with certainty that the project with 25% return
contributes relatively more to national income than the one with 15% return, and we cannot say with confidence
that we should implement the project with 25% rate of return first. If we raise the opportunity cost (cut-off rate) to
18%, then the project with 15% economic rate of return drops out of the investment net and judgement in favour
of a 25% IRR project will be easy.
5.10 One cannot simply choose that discount rate which will make the incremental net benefit-stream equal to
zero. There is no formula for finding the internal rate of return straightaway. We are forced to resort to a
systematic procedure of trial and error to find that discount rate which will make the net present worth of
incremental net benefit-stream equal to zero. The most difficult aspect of the trial and error procedure is making
the initial estimates. If the estimate is too far from the final result, then several trials will have to be made to find
two rates close enough together to permit accurate interpolation (interpolation is the process of finding a desired
value between two other values). In practice, it is better not to interpolate between intervals greater than about
five percent because the wider intervals can easily introduce an interpolation error. The formula of interpolation is
given below:
IRR =
Lower
the difference {Present worth of incre- }
discount + Between two {mental net* benefits- }
rates Discount rates {stream (cash flow) at }
*Note that IRR can be calculated form any point in time; all points will give the same returns.
{the lower discount rate }
{Sum of the present worth}
{of incremental net bene-}
{fit-streams (cash flows)}
{at the two discount }
{rates (signs ignored) }
5.11 It may be noted that interpolation between discount rates that bracket the true internal rate of return always
somewhat overstates the true return. This is because the technique assumes, as we move from one discount rate
to another, that IRR will change following a straight line but the true value of IRR follows a concave curvilinear
function.
Net Benefit-Investment Ratio (NBIR) = (N/K Ratio)
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5.12 NBIR is simply the present worth of net benefits divided by the present worth of investment. To calculate this
measure, simply divide the sum of the present worth after the incremental net benefits-stream has turned positive
by the sum of the present worth of the negative incremental net benefits in the early years of the project. The
reason for calculating the net benefit-investment ratio in this manner is that we are interested in an investment
measure that selects projects on the basis of return to investment during the initial phases of a project. If the net
benefit - investment ratio is 1 or greater, when we are discounting at the opportunity cost of capital, choose the
project beginning with the largest ratio value and proceed until available investment funds are exhausted. It may
be used to rank projects in those instances in which, for one reason or another, sufficient funds are not available
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9/23/2010