Mid-State Electric Company must clean up the water released from its generating plant. The company's cost of capital is 10 percent for average projects, and that rate is normally adjusted up or down by 2 percentage points for high- and low-risk projects. Clean-up Plan A, which is of average risk, has an initial cost of -$1,000 at Time 0, and its operating cost will be -$100 per year for its 10-year life. Plan B, which is a high-risk project, has an initial cost of -$300, and its annual operating cost over Years 1 to 10 will be -$200. What is the proper PV of costs for the better project?
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A. B. C. D. E.Explanation
The first thing to note is that risky cash outflows should be discounted at a lower discount rate, so in this case we would discount the riskier Project B's cash flows at 10% - 2% = 8%. Project A's cash flows would be discounted at 10%.
Now we would find the PV of the costs as follows:
Project AProject B -
CF(0) = -1,000CF(0) =-300 -
CF(1-10) = -100CF(1-10)=-200 -
I =10.0I= 8.0 -
Solve for NPV = -$1,614.46. Solve for NPV = -$1,642.02.
Project A has the lower PV of costs. If Project B had been evaluated with a 12% cost of capital, its PV of costs would have been -$1,430.04, but that would have been wrong.