The Utah Mining Corporation is set to open a gold mine near Provo, Utah. Accordi

Question

The Utah Mining Corporation is set to open a gold mine near Provo, Utah. According to the treasurer, Monty Goldstein, This is a golden opportunity. The mine will cost $901,000 to open and will have an economic life of 11 years. It will generate a cash inflow of $173,000 at the end of the first year, and the cash inflows are projected to grow at 7 percent per year for the next 10 years. After 11 years, the mine will be abandoned. Abandonment costs will be $124,000 at the end of year 11. Required: (a) What is the IRR for the gold mine? (Do not include the percent sign (%). Round your answer to 2 decimal places. (e.g., 32.16)) IRR % (b) The Utah Mining Corporation requires a 11 percent return on such undertakings. Should the mine be opened?

Explanation / Answer

let internal rate of return be r%

at t=0,

cash out flow = 901000 + 124000/(1+r)11

cash inflow = 173000[1/(1+r) + 1.07/(1+r)2 + (1.07)2/(1+r)3 +.... + (1.07)10/(1+r)11]

= [173000/(1+r)] [ 1 - [1.07/(1+r)]11]/ [ 1- 1.07/(1+r)]

= 173000/(r - 0.07) [ 1 - [1.07/(1+r)]11] = 901000 + 124000/(1+r)11

solving for r we get, r = 20.5 % approx

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