Q. During the next 3 years, a business decides to invest £10,000, at thebeginningof each year.

The revenue at theendof each year is:

Year 1 = £5,000

Year 2 = £20,000

Year 3 = £50,000

Calculate the NPV using a discount rate of 4%, compounded annually.

A. My answer was £39,997.85. The textbook answer (Ian Jacques) is £38,887.69.

I drew out a timeline, like this:

Year 1 = -£10,000 +£5,000 = -£5,000

Year 2 = -£10,000 + £20,000 = £10,000

Year 3 = -£10,000 + £50,000 = £40,000

Year 1 = -£5,000 x (1.04)^(-1) = -£4,807.69

Year 2 = £10,000 x (1.04)^(-2) = £9,245.56

Year 3 = £40,000 x (1.04)^(-3) = £35,559.85

Total = £39,997.72.

This is higher than the answer, so I was thinking the £10,000 investments who should be increased by 4% compounded annually, and minus them from the future revenues.

Year 1 = -£10,000 +£5,000 = -£5,000

Year 2 = -£10,400 + £20,000 = £9,600

Year 3 = -£10,816 + £50,000 = £39,184

Year 1 = -£5,000 x (1.04)^(-1) = -£4,807.69

Year 2 = £9,600 x (1.04)^(-2) = £8,875.74

Year 3 = £39,184 x (1.04)^(-3) = £34,834.43

Total = £38,902.48

Where am I going wrong?

Thanks (as always) for your help.

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