Question

Canadian Metal, Mining, and Petroleum Company are analyzing two projects for possible investment. Only one investment will be made. The first project is an oil? drilling project in Alberta at a cost of $500 million that will produce $100 million per year in Years 5 through 10 and $200 million per year in Years 11 through 20. The second project is an expansion of an aluminum smelter in Mapletree, Quebec, and will cost $500 million and will produce $87 million per year for Years 2 through 20. The cost of capital is 12 percent.

a. Which investment should be made?

b. If the oil?well project justifies an extra 4 percent premium over the normal cost of capital because of its riskiness and relative uncertainty of flows, does the investment decision change?

Answer 1

Project 1:

Present value at year 4 for cash flows in year 5 through 10 = annuity [ 1 - / / ( 1 + r)ⁿ] / r

Present value at year 4 for cash flows in year 5 through 10 = 100,000,000[ 1 - 1 / ( 1 + 0.12)⁶] / 0.12

Present value at year 4 for cash flows in year 5 through 10 = 100,000,000 * 4.111407

Present value at year 4 for cash flows in year 5 through 10 = 411,140,732.4

Present of  411,140,732.4 = 411,140,732.4 / ( 1 + 0.12)⁴

Present of  411,140,732.4 = 261,287,368.2

Present value at year 10 for cash flows in year 11 through 20 = 200,000,000[ 1 - 1 / ( 1 + 0.12)¹⁰] / 0.12

Present value at year 10 for cash flows in year 11 through 20 = 200,000,000 * 5.650223

Present value at year 10 for cash flows in year 11 through 20 = 1,130,044,606

Present value of 1,130,044,606 = 1,130,044,606 / ( 1 + 0.12)¹⁰

Present value of 1,130,044,606 = 363,844,119.3

Total present value of cash inflows = 363,844,119.3 + 261,287,368.2 = 625,131,487.5

NPV = present value of cash inflows - present value of cash outflows

NPV = 625,131,487.5 - 500,000,000 = 125,131,487.5

project 2:

Present value at year 1 for cash flows = 87,000,000 [ 1 - 1 / ( 1 + 0.12)¹⁹] / 0.12

Present value at year 1 for cash flows = 640,822,586.8

Present value = 640,822,586.8 / ( 1 + 0.12)

Present value = 572,163,023.9

NPV = 572,163,023.9 - 500,000,000 = 72,163.023.97

Since Oil well has a higher NPV, oil well project investment should be made.

b)

If cost of capital is 12% + 4% = 16%

Present value at year 4 for cash flows in year 5 through 10 = annuity [ 1 - / / ( 1 + r)ⁿ] / r

Present value at year 4 for cash flows in year 5 through 10 = 100,000,000[ 1 - 1 / ( 1 + 0.16)⁶] / 0.16

Present value at year 4 for cash flows in year 5 through 10 = 368,473,590.8

Present of  368,473,590.8 = 368,473,590.8 / ( 1 + 0.16)⁴

Present of  368,473,590.8 = 203,504,684

Present value at year 10 for cash flows in year 11 through 20 = 200,000,000[ 1 - 1 / ( 1 + 0.16)¹⁰] / 0.16

Present value at year 10 for cash flows in year 11 through 20 = 966,645,495.7

Present value of 966,645,495.7= 966,645,495.7/ ( 1 + 0.16)¹⁰

Present value of 966,645,495.7 = 219,122,684.2

Total present value of cash inflows = 203,504,684 + 219,122,684.2 = 422,627,368.2

NPV = present value of cash inflows - present value of cash outflows

NPV = 422,627,368.2 - 500,000,000 = -77,372,631.78

Since it has a negative NPV now, we should invest in aluminum shelter project