Future Worth: $10K investment, $1800 1st yr, $100 more after

[tn2k7]

Your uncle has almost convinced you to invest in his peach farm. It would require a $10,000 initial investment on your part. He promises you revenue (before expenses) of $1800 per year the first year, and increasing by $100 per year thereafter. Your share of the estimated annual expenses is $500. You are planning to invest for six years. Your uncle has promised to buy out your share of the business at that time for $12000. You have decided to set a personal MARR of 15% per year. Use the FW method to determine the profitability of this investment project. Include a cash flow-diagram.

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First of all, I made a table of the total profit every year:

Year, Revenue, Profit (Revenue-$500)
1, 1800, 1300
2, 1900, 1400
3, 2000, 1500
4, 2100, 1600
5, 2200, 1700,
6, 2300, 1800

Using this data, there is a geometric gradient of G=100, therefore A=1300. Here is my cash flow diagram:

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Now when it comes to finding the actual FW, (assuming I've done everything right up to this point,) I'm not sure how to handle the Gradient. I'm not sure whether the Gradient should be positive, or negative. Also, I made it present value first, then made a future value. This is what I've done, (making the Gradient positive). :

FW(15%) = 12000 + 1300(F/A, 15%, 6) + 100(P/G, 15%, 6)(F/P, 15%, 6) - 10000(F/P, 15%,6) =

FW(15%) = 12000 + 1300(8.7537) 100(7.937)(2.3131) - 10000(2.3131) =

2084.72 > 0, project is acceptable.

I'm fairly confident I did everything, other than the Gradient, correctly. Any and all help would be greatly appreciated!

 

[Denis]

Re: Future Worth Method Problem

Well, your result is correct; really, this is the "workings":

f = 1300(1.15^5) + 1400(1.15^4) + 1500(1.15^3) + 1600(1.15^2) + 1700(1.15^1) + 1800(1.15^0)

10000(1.15^6) - 12000 - f = ~2085.07

You end up with 2084.72 due to rounding your factors.