posted by Gibbons on .
A company is considering the purchase of a forest that is estimated to yield an annual return of $50,000 for 10 years, after which the forest will have no value. The company wants to earn 8% on its investment and set up a sinking fund to replace the purchase price. If the money is placed in the fund at the end of each year and earns 6% compounded annually, find the price the company should pay for the forest.
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If I understand the investment instructions correctly, this is how it works:
The company would invest an amount P which should yield net 8% return each year for 10 years.
The revenue generated is constant each year at $50,000, and includes profit and capital repayment. The capital is repaid from a sinking fund that pays 6% p.a. and should generate the original capital at the end of 10 years. The annual payment into the sinking fund (out of the revenue) is $x.
x=annual investment into sinking fund
For the 8% profit over 10 years, we have
P*(0.08*10) = 50000*10 - 10x ...(1)
and that the amount x over 10 years at 6% p.a. should yield exactly P:
P = x*1.06^10/(1.06-1.0) ...(2)
Substituting (2) into (1)
x*1.06^10/(1.06-1.0)*(0.08*10) = 50000*10 - 10x
Solve for x to get $14758.85
and from (2)
P = $440514.32
Substitute the amounts into the scenarios and check.