Question

Products Inc. is analysing a 5 -year project that produces sales of £100 million per year (in years 1 through 5). Under the assumption that accounts receivable are 10% of current year sales, the project has a positive NPV of £5 million. However, the management is concerned that customers will pay at a slower rate, which will put accounts receivable for the project at 20% of current year sales. The project’s discount rate is 10%. The NPV of the project under this alternative scenario is closest to
a. £1.55 million
b. £4 million
c. £2.7 million

Answer 1

Present Value (PV) of increase in accounts receivable when accounts receivable is 10% of sales:

Year 1 increase = -10%*100 = -10; Year 2 to Year 4 = 0 (since every year accounts receivable remains at 10 million); Year 5 increase = 10 (Year 1 increase in returned in Year 5)

PV of increase in accounts receivable = -10/(1+10%) + 10/(1+10%)^5 = 2.88 million

Now if accounts receivable is doubled to 20 million, the PV of increase in accounts receivable will become 2.88*2 = 5.76 million. So, NPV should decrease by the amount by which this PV is increasing which is 2.88 million.

So, new NPV should be 5 - 2.88 = 2.12 million

This is closest to option (a) which is 1.55 million. (Answer)