# Thread: Investment+Revenue to NPV question using a discount rate of 4%, compounded annually

1. ## Investment+Revenue to NPV question using a discount rate of 4%, compounded annually

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

The revenue at the end of 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.

2. The 10000's are at "beginning" of each year.

So you have:
5000/1.04 + 20000/1.04^2 + 50000/1.04^3

-10000 - 10000/1.04 - 10000/1.04^2

3. Originally Posted by Denis
The 10000's are at "beginning" of each year.

So you have:
5000/1.04 + 20000/1.04^2 + 50000/1.04^3

-10000 - 10000/1.04 - 10000/1.04^2
Thanks Dennis. I hate when I thought I had tried every conceivable way, and yet that's one more I didn't try!

Got it now.

Thxs.

Thanks Dennis. I hate when I thought I had tried every conceivable way, and yet that's one more I didn't try!
On the positive side: you'll never forget that way again

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