You are evaluating two projects with the following cash flows: Year Project X Project Y0 −$544,200 −$514,0001 219,100 208,8002 229,000 218,6003 236,200 226,5004 195,900 187,300 What is the crossover rate for these two projects?
Question
You are evaluating two projects with the following cash flows: Year Project X Project Y0 −514,0001 219,100 208,8002 229,000 218,6003 236,200 226,5004 195,900 187,300 What is the crossover rate for these two projects?
Solution
The crossover rate is the cost of capital at which the Net Present Values (NPV) of two projects are equal. To find the crossover rate, we first need to find the difference in the cash flows of the two projects for each year.
Here are the differences for each year:
Year 0: -514,000) = -219,100 - 10,300 Year 2: 218,600 = 236,200 - 9,700 Year 4: 187,300 = $8,600
Now, we have a new set of cash flows:
Year 0: -10,300 Year 2: 9,700 Year 4: $8,600
We then set the NPV of these cash flows to zero and solve for the discount rate, which is the crossover rate. The NPV formula is:
NPV = ∑ [CFt / (1+r)^t] = 0
Where: CFt = cash flow at time t r = discount rate t = time period
This is a complex equation to solve and usually requires the use of financial calculator or software. The solution to this equation will give you the crossover rate.
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