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 $1,602,000 and will produce $318,000 per year in years 5 through 15 and $559,000 per year in years 16 through 25. The U.S. gold mine will cost $2,033,000 and will produce $290,000 per year for the next 25 years. The cost of capital is 10 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.) a-1. Calculate the net present value for each project. (Do not round intermediate calculations and round your answers to 2 decimal places.) a-2. Which investment should be made? Australian mine U.S. mine b-1. Assume the Australian mine justifies an extra 4 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.) b-2. Does the new assumption change the investment decision? yes No

Answer 1

a-1

Australian mine initial investment = 1602000, US mine initial investment = 2033000

We know the

Present value of cash flow = Cash flow x PV Factor

PV Factor = Present value factor = 1 / ( 1 + r)ⁿ

where r = cost of capital and n = year of cash flow

Cash flow, PV factor, present value of cash flows are given in the table below

Year	Australian Mine			US Mine
	Cash flow	PV Factor at 10%	Present value of cash flow	Cash flow	PV Factor at 10%	Present value of cash flow
1	0	0.9091	0.000	290000	0.9091	263636.364
2	0	0.8264	0.000	290000	0.8264	239669.421
3	0	0.7513	0.000	290000	0.7513	217881.292
4	0	0.6830	0.000	290000	0.6830	198073.902
5	318000	0.6209	197452.981	290000	0.6209	180067.184
6	318000	0.5645	179502.710	290000	0.5645	163697.440
7	318000	0.5132	163184.282	290000	0.5132	148815.854
8	318000	0.4665	148349.347	290000	0.4665	135287.140
9	318000	0.4241	134863.043	290000	0.4241	122988.309
10	318000	0.3855	122602.766	290000	0.3855	111807.554
11	318000	0.3505	111457.060	290000	0.3505	101643.231
12	318000	0.3186	101324.600	290000	0.3186	92402.937
13	318000	0.2897	92113.273	290000	0.2897	84002.670
14	318000	0.2633	83739.339	290000	0.2633	76366.064
15	318000	0.2394	76126.672	290000	0.2394	69423.694
16	559000	0.2176	121654.687	290000	0.2176	63112.449
17	559000	0.1978	110595.170	290000	0.1978	57374.954
18	559000	0.1799	100541.064	290000	0.1799	52159.049
19	559000	0.1635	91400.967	290000	0.1635	47417.317
20	559000	0.1486	83091.788	290000	0.1486	43106.652
21	559000	0.1351	75537.989	290000	0.1351	39187.866
22	559000	0.1228	68670.899	290000	0.1228	35625.332
23	559000	0.1117	62428.090	290000	0.1117	32386.666
24	559000	0.1015	56752.809	290000	0.1015	29442.423
25	559000	0.0923	51593.463	290000	0.0923	26765.839
Sum of Present values of cash flows			2232982.997			2632341.605

Net present value = - Initial investment + Sum of present values of cash flows from year 1 to 25

Net Present value of Australian Mine = -1602000 + 2232982.997 = 630982.997 = 630983.00 (rounding to 2 places of decimal)

Net Present value of US Mine = -2033000 + 2632341.605 = 599341.605 = 599341.61 (rounding to 2 places off decimal)

a-2 As Net present of Australian mine is greater than US mine, therefore investment should be made in Australian mine

b-1 Risk premium =4% , New cost of capital = Normal Cost of capital + Risk premium = 10% + 4% = 14%

Hence we will calculate the sum of present value of cash flow of Australian mine using discount rate of 14%

Cash flow, PV factor and present value of cash flow are given in table below

Year	Australian Mine
	Cash flow	PV Factor at 14%	Present value of cash flow
1	0	0.8772	0.000
2	0	0.7695	0.000
3	0	0.6750	0.000
4	0	0.5921	0.000
5	318000	0.5194	165159.235
6	318000	0.4556	144876.522
7	318000	0.3996	127084.669
8	318000	0.3506	111477.779
9	318000	0.3075	97787.526
10	318000	0.2697	85778.531
11	318000	0.2366	75244.326
12	318000	0.2076	66003.795
13	318000	0.1821	57898.065
14	318000	0.1597	50787.777
15	318000	0.1401	44550.681
16	559000	0.1229	68696.433
17	559000	0.1078	60260.029
18	559000	0.0946	52859.674
19	559000	0.0829	46368.135
20	559000	0.0728	40673.803
21	559000	0.0638	35678.775
22	559000	0.0560	31297.171
23	559000	0.0491	27453.659
24	559000	0.0431	24082.157
25	559000	0.0378	21124.699
Sum of Present values of cash flows			1435143.440

New Net Present value of Australian Mine at 14% = - initial investment + Sum of present values of cash flows discounted at 14%

= -1602000 + 1435143.440 = -166856.560 = -166856.56

b-2 Investment decision will change because new NPV of Australian mine at 14% discount rate is negative.Also on the other hand NPV of US mine at 10% discount rate is positive and greater than new NPV of Australian mine at 14% discount rate

So Investment decision changes with the new assumption