The answer is listed but I just can\'t seem to get the work right. Problem 1 Con

Question

The answer is listed but I just can't seem to get the work right.

Problem 1 Consider a plant costing $1,000,000 to build that produces a product A. For the same capital outlay a different plant can be erected to produce an alternative product B. Conditions are such that each plant will only be in operation for eight years and then both will be scrapped. The cash flows in each of the eight years obtained by product A and B are shown in the table below (Note that the -1,000,000 in year 0 shows the investment). A choice is being made about which plant is more profitable, considering MARR-10%.

Explanation / Answer

Calculation of IRR of product A

NPV at 10% = Present value of cash inflows - Present value of cash outflows

= 2,136,200 - 1,000,000

= $1,136,200

IRR is the rate at which NPV is zero.

Since at 10%, NPV is positive, hence we must calculate NPV at a higher rate.

Let us calculate NPV at 30%.

NPV at 30% = Present value of cash inflows - Present value of cash outflows

= 940,200 - 1,000,000

= -$59,800

At 30%, NPV is negative, hence the IRR of the project must lie between 10% to 30%. Exact IRR can be calculated as under:
IRR = Lower rate + {NPV at lower rate/(NPV at lower rate - NPV at higher rate)} x (Higher rate - lower rate)
= 10% + {1,136,200/(1,136,200 + 59,800)} x (30% - 10%)
= 10% + (1,136,200/1,196,000) x 20%
= 10% + 18.27%
= 28.27%
Hence, IRR of the product A is 28.27%(Approx.)

Similar calculations can be made for product B also.

Year Cash inflows PVF Present value of cash inflows 1 100,000 0.909 90,900 2 200,000 0.826 165,200 3 300,000 0.751 225,300 4 400,000 0.683 273,200 5 500,000 0.621 310,500 6 600,000 0.564 338,400 7 700,000 0.513 359,100 8 800,000 0.467 373,600 $2,136,200

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