radnorgardens
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- Joined
- Dec 2, 2014
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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.
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.