The project took 10 years of planning and a cost of $4,000,000, which was spent
ID: 1180062 • Letter: T
Question
The project took 10 years of planning and a cost of $4,000,000, which was spent equally at $400,000 in years 1 through 10. Fishing and recreation activities, estimated at $270,000 per year, will begin in year 11 and are expected to continue in perpetuity. Determine the rate of return on the venture using tabulated factors. We have the following info, p = -$4,000,000 n = 10 A = $400,000 F = $270,000 i = ? So the equation should look like this? 0 = -4,000,000 + 400,000(P/A, i, 10) + 270,000(P/F, i, 10) So since this is a trial and error method, I select 5% and 6%. When I do the interpolation, I get 4.84%. This is way off from the answer in the back of the book of 5.32%. Even using Excel Rate(n,A,P,F) I get a totally different answer. Any help is greatly appreciated. Thank you.Explanation / Answer
The answer 5.32% is correct. You included 4,000,000 twice in cash flows. It is given that the 4,000,000 is distributed over ten years. Convert this to equivalent cash flow at year 0.Assume interest rate i.
[400000/i]* [1 - 1/(1+i)10]
Fishing provides income. This is not expenditure. It starts at year 11 and continues perpetually. Convert these cash flows to equivalent at year 10 and then convert this to year 0.
Equivalent at year 10 = 270000/i
Equivalent at year 0 = 27000/i*(1+i)10
Total income at year 0 = total expenditure at year 0.
[400000/i]* [1 - 1/(1+i)10] = 27000/i*(1+i)10
Solving this we get 5.32%
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