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This question states that a company is considering investing $10,000 immediately in a 1 year project with the following cash flows (which arise at years end):
income =$100,000 exp=$35,000
and eventually asked to find NPV. there was inflation of 10%In the answer, the NPV was [(110,000-35,000) x DF1] – 10,000
what i don’t understand:
why is the 10,000 investment not included added to the 35,000 to give 45,000? I’m thinking it should be added since the question mentions “immediately”, while the cash flows are at year end so at years end the total outflow would have been the investment amount plus the expenses.There is an outflow of cash of $10,000 immediately, followed by inflows of cash of $65,000 (100,000 – 35,000).
The NPV is the net of the inflows less the outflow (obviously after discounting were relevant).
If the NPV is positive, then it means were are getting back more than the 10,000 we paid out (and therefore it is worthwhile), whereas if the NPV is negative it means we are getting back less than the $10000 we paid out (and therefore it would not be worthwhile)
So John, are you saying that from the answer provided, the “-10,000” is dependent on the [110,000-35,000] being positive or negative?….why can the 10,000 invested not be included in the outflow to give 55,000 as the net inflow which is then multiplied by the DF?…why does it have to be separate?
10000 is paid out immediately – i.e. now, or time 0.
In 1 years time we receive 100,000 and pay out 35,000 – a net 65,000, but this net receipt is at the end of the year – i.e. in 1 years time.
The whole point of discounting is to account for the interest involved. Receiving 65,000 in 1 years time is not worth the same as receiving 65,000 now (because of the interest element). Similar paying out 10,000 now is not the same as paying out 10,000 in 1 years time.
So…..we bring everything back to present values by discounting to account for the interest.
10,000 paid now is 10,000 now.
The present value of 65000 receivable in 1 years time is 65,000 x the discount factor for 1 year at 10% (I assume that you mistyped and that 10% is the interest rate, not the inflation rate!), which is 59085
So doing this investment is equivalent to paying out 10,000 now, and receiving 59,085 now.
So the NPV is 49,085 and because it is positive (a surplus) the project is worth doing.
(I think it will help you to watch the Paper F2 lectures on investment appraisal. In Paper F2 we go through all of the discounting ‘mechanics’ and the reason for doing the discounting.) )
Thanks john, that was a very good explanation. There was 10% inflation and 8% cost of capital……but I understand what you’re saying.
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