Highland Mining and Minerals Co. is considering the purchase of two gold mines.
ID: 2647783 • Letter: H
Question
Highland Mining and Minerals Co. is considering the purchase of two gold mines. Only one investment will be made. The Australian gold mine will cost $1,621,000 and will produce $307,000 per year in years 5 through 15 and $570,000 per year in years 16 through 25. The U.S. gold mine will cost $2,086,000 and will produce $281,000 per year for the next 25 years. The cost of capital is 12 percent. Use Appendix D for an approximate answer but calculate your final answers using the formula and financial calculator methods. (Note: In looking up present value factors for this problem, you need to work with the concept of a deferred annuity for the Australian mine. The returns in years 5 through 15 actually represent 11 years; the returns in years 16 through 25 represent 10 years.)
Calculate the net present value for each project. (Do not round intermediate calculations and round your answers to 2 decimal places.)
Highland Mining and Minerals Co. is considering the purchase of two gold mines. Only one investment will be made. The Australian gold mine will cost $1,621,000 and will produce $307,000 per year in years 5 through 15 and $570,000 per year in years 16 through 25. The U.S. gold mine will cost $2,086,000 and will produce $281,000 per year for the next 25 years. The cost of capital is 12 percent. Use Appendix D for an approximate answer but calculate your final answers using the formula and financial calculator methods. (Note: In looking up present value factors for this problem, you need to work with the concept of a deferred annuity for the Australian mine. The returns in years 5 through 15 actually represent 11 years; the returns in years 16 through 25 represent 10 years.)
Explanation / Answer
Calculation for The Australian Mine is as follows:
We have 2 periods from period 0-15 years and 16-25 years
So, in order to calculate the deffered annuity we need to find the Present value at the year 15th for cashflow of $570,000 from the table the PV factor for 10 years i.e; from year 16 through 25 is 5.62022
Therefore, Present value of cashflow at the end of 15th year is $570,000 * 5.62022 = $3,220,625
Now we need to find the Present value at the end of 4th year for the cash flow of $307,000
Since we have 11 periods from 5th year through 15th year from the annuity table the PV factor is 5.93770
So the present value at the end of 4th year would be $307,000 * 5.93770 = $1,822,874
Now since we have the two present value at end of 4th year and at the end of 15th year we will discount them to get the Net Present value at year 0
This can be done by the following formula :
PV at year 4 / (1+r)t + PV at year 15 / (1+r)15
= 1,822,874 / (1+.12)4 + $3,220,625 / (1+.12)15
= 1,822,874 / 1.5735 + $3,220,625 / 5.4735 = $1,158,484 + $588,403 = $1,746,887
Net Present value for the Australian Mine = Cash Inflow - Cash outflow = $1,746,887 - $1,621,000
= $125,887
Calculation for US Mine is as follows:
Year Cash Flow PV Factor Present Value 0 ($2,086,000) 1 ($2,086,000.00) 1 $281,000 0.892857 $250,892.86 2 $281,000 0.797194 $224,011.48 3 $281,000 0.711780 $200,010.25 4 $281,000 0.635518 $178,580.58 5 $281,000 0.567427 $159,446.95 6 $281,000 0.506631 $142,363.35 7 $281,000 0.452349 $127,110.13 8 $281,000 0.403883 $113,491.19 9 $281,000 0.360610 $101,331.42 10 $281,000 0.321973 $90,474.48 11 $281,000 0.287476 $80,780.79 12 $281,000 0.256675 $72,125.70 13 $281,000 0.229174 $64,397.95 14 $281,000 0.204620 $57,498.17 15 $281,000 0.182696 $51,337.65 16 $281,000 0.163122 $45,837.19 17 $281,000 0.145644 $40,926.06 18 $281,000 0.130040 $36,541.12 19 $281,000 0.116107 $32,626.00 20 $281,000 0.103667 $29,130.36 21 $281,000 0.092560 $26,009.25 22 $281,000 0.082643 $23,222.55 23 $281,000 0.073788 $20,734.42 24 $281,000 0.065882 $18,512.87 25 $281,000 0.058823 $16,529.35 Net Present Value $117,922.09Related Questions
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