Renfree Mines, Inc., owns the mining rights to a large tract of land in a mounta
ID: 2388333 • Letter: R
Question
Renfree Mines, Inc., owns the mining rights to a large tract of land in a mountainous area. The tract contains a mineral deposit that the company believes might be commercially attractive to mine and sell. An engineering and cost analysis has been made, and it is expected that the following cash flows would be associated with opening and operating a mine in the area:
Cost of equipment required $ 850,000
Annual net cash receipts $ 305,000*
Working capital required $ 225,000
Cost of road repairs in eight years $ 66,000
Salvage value of equipment in nine years $ 200,000
*Receipts from sales of ore, less out-of-pocket costs for salaries, utilities, insurance, and so forth.
The mineral deposit would be exhausted after nine years of mining. At that point, the working capital would be released for reinvestment elsewhere. The company
Explanation / Answer
I round up the PVs to 3 decimal places for a single future amount at 15%. Your table may be slightly different so just check them.
At the end of year
0: cost of equipment = -850,000
0: working capital = -225,000
1: net annual cash receipts 305,000*0.870=265,350
2: net annual cash receipts 305,000*0.756=230,580
3: net annual cash receipts 305,000*0.658=200,690
4: net annual cash receipts 305,000*0.572=174,460
5: net annual cash receipts 305,000*0.497=151,585
6: net annual cash receipts 305,000*0.432=131,760
7: net annual cash receipts 305,000*0.376=114,680
8: net annual cash receipts 305,000*0.327=99,735
8: cost of roads -66,000*0.327= - 21,582
9: net annual cash receipts 305,000*0.284=86,620
9: salvage value of the equipment 200,000*0.284=56,800
9: recovery of working capital 225,000*0.284=28,400
Sum them all up to get net present value $444,078
Since the net present value of the project is positive, the project can be accepted.
NOTE:
When you're good, you can do the shortcut for all the net annual cash receipts.
Just add all the present value (PV) factors from the table from year 1 all the way to year 9 and multiply it with 305,000 to get all 9 year sum.
(0.870+0.756+0.658+0.572+0.497+0.432+0.376+0.327+0.284) * 305,000 = 4.772 * 305,000 = 1,455,460
Then add the neg. cost of equipment (Y0), neg working capital (Y0), neg. cost of roads(Y8), salvage value (Y9) and recovery of workin capital (Y9) to get the same result.