Highland Mining and Minerals Co. is considering the purchase of two gold mines.

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 $1,630,000 and will produce $342,000 per year in years 5 through 15 and $537,000 per year in years 16 through 25. The U.S. gold mine will cost $2,054,000 and will produce $295,000 per year for the next 25 years. The cost of capital is 8 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.)

Which investment should be made?

Assume the Australian mine justifies an extra 3 percent premium over the normal cost of capital because of its riskiness and relative uncertainty of cash flows. Calculate the new net present value given this assumption. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.)

Calculate the net present value for each project. (Do not round intermediate calculations and round your answers to 2 decimal places.)

Explanation / Answer

a-1

Australian Gold Mine

Both types of cash flows are in the form of deferred annuity, We can use following formula to calculate PV of deferred annuity.

PV of deferred annuity = pmt x PVIFA(n,r%) xPVIF(m,r%)

PV of cash flows = 342,000 xPVIFA(11,8%)x PVIF(4,8%) +537,000 xPVIFA(10,8%) xPVIF(15,8%)

                                =342000x7.139 x0.73503    +537,000 x6.7101x0.3152

                                = 2,930,371.31

NPV = PV of cash flows – initial investment

                =2,930,371.31-1,630,000

                =1,300,371.31

US Gold mine

Here the cash flow in in the form of ordinary annuity

PV of annuity = pmt x PVIFA(n,r%)

PV of cash flows = 295000 xPVIFA(25,8%)

                                = 295,000 x 10.6748

                                = 314,9058.92

NPV = PV of cash flows – initial investment

                =314,9058.92-2,054,000

                =1,095,058.92

a-2

Since NPV of Australian Gold mine is higher, Australian Gold mine should be chosen.

b-1

Australian Gold Mine

Both types of cash flows are in the form of deferred annuity, We can use following formula to calculate PV of deferred annuity.

PV of deferred annuity = pmt x PVIFA(n,r%) xPVIF(m,r%)

PV of cash flows = 342,000 xPVIFA(11,11%)x PVIF(4,11%) +537,000 xPVIFA(10,11%)x PVIF(15,11%)

                                =342000x6.20652 x0.658731    +537,000 x5.88923x0.20900

                                = 2,059,208.03

NPV = PV of cash flows – initial investment

                =2,059,208.03-1,630,000

                =429,208.03

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