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AAE 320 Farming Systems Management Problem Set #6 Key
1) Answer the following questions using methods from the time value of money section.
Show
your work for potential partial credit.
a) How much would $7,000 invested at 7% compounded annually be worth in 7 years?
FV = PV(1 + r)
t
= 7000(1 + 0.07)
7
= $11,240.47
b) Suppose you will replace your irrigation well in 5 years at a cost of $40,000 then.
You made
lots of money this year marketing your grain, and so can set the money aside now.
How much
money invested this year at 6% interest compounded annually would be worth $40,000 in 5
years?
Suppose you could only find an investment offering 3% interest compounded annually,
how much would you have to invest at this rate today to have $40,000 in 5 years?
PV = FV/[(1 + r)
t
] = 40000/[(1 + 0.06)
5
] = $29,890.33
40000/[(1 + 0.03)
5
] = $34,504.35
c) Suppose you could buy a plot of land today at $3,500/ac and sell it in 3 years for $5,000,
paying cash for the land by withdrawing equity from your farm.
What is your rate of return,
expressed as an annually compounded interest rate?
If you typically earn 8% annual return on
your equity, is this a good deal if you are trying to make as much money as possible, or should
you leave the equity in your farm?
r = (FV/PV)
1/t
– 1 = (5000/3500)
1/3
– 1 = 0.1262 = 12.62%
Compared to the 8% return earned on equity in the farm, this is a good investment.
d) Assuming a 10% discount rate, what is the net present value of a strawberry patch that costs
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 Spring '08
 MITCHELL

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