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A company is considering a two-year project which has two annual internal rate of return namely 10% and 25%. The sum of the undiscounted cash flows is positive.
The project will necessarily have a positive NPV when the annua cost of capital is ?
A) more than 25%
B) more than 10%
C) between 10% and 25%
D) less than 25%The answer is A , could please explain why!?
You will know from my lectures that if there are 2 IRR’s then there must be two changes in sign. i.e. there must be an outflow at time 0, and inflow at time 1, and an outflow at time 2.
Since the sum of the cash flows is positive, it must mean that the inflow at time 1 must be bigger than the outflow at time 0.
Therefore if we have a graph of the NPV against the rate of interest, then initially the curve will have a positive NPV (because at interest of 0% the NPV must be positive). The curve will slope downwards, crossing the axis at 10% and the NPV will then be negative. Later it will start sloping upwards crossing the axis again at 25% and from then on will continue to slope upwards and have a positive NPV.
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