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

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

Solutions

Expert Solution

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

jeff jeffy answered 1 year ago
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