Please Q4 a (ii) of DEC 2004 P5 (WOODS LTD)

What he has done is the same idea as calculating an IRR – two guesses and approximate.

I assume that you are happy with part (1) where he has calculated the NPV as (2866650) if sale drop by 10,000 units per year.

Since sales would have to therefore drop by more that 10,000 units to get zero NPV (at which stage you would be prepared to start dropping SuperKooler) he has made a guess at a drop of 20,000 units and recalculated the NPV as +1782850. (You could have guessed differently – a drop of 30000 for example – and continued as below).

Having got two NPVs (for 10000 units and for 20000 units drop) he then say that because one gave a – NPV and one gave a + NPV then for zero NPV is must be somewhere between 10000 and 20000. He then approximates between the two to get the drop giving an NPV of zero.

So…..between 10000 units and 20000 units is a difference of (20000 – 10000) 10000 units. At the same time the NPV changes from -2866650 to +1782850 = a change in NPV of 4649500.

If we start from 10000 units, (when the NPV is -2866650) then to get zero NPV we need the NPV to increase by 2866650.

We know that a change of 4649500 needs a change of 10000 units, and so a change of 2866650 needs a change of 2866650/4649500 x 10000 units, which equals 6165 units. Add this to the original 10000 and you get 16165 units.

(This assumes that the NPV changes linearly, which it will not do, so the answer is only approximate. If you had tried different that 20000 units for the second guess, then you would get a slightly different answer)

Hope that helps!!

It would be best to state that the 20000 is a guess.

It was a difficult question in the middle of an exam – these days it is much less likely to be that tricky.