Question

ZZY, LLC, has identified the following two mutually exclusive projects:

Year	Cash Flow for A in $	Cash Flow for B in $
0	-65,000	-65,000
1	34,000	19,000
2	27,000	25,000
3	21,000	29,000
4	17,000	34,000

Below what discount rate is B the better project than A? (Hint: You need to find the crossover rate). Answer in percent to two decimals.

Answer 1

Year 0 Incremental cash flow of B wrt A = -65000-(-65000) = 0
Year 1 Incremental cash flow of B wrt A = 19000-(34000) = -15000
Year 2 Incremental cash flow of B wrt A = 25000-(27000) = -2000
Year 3 Incremental cash flow of B wrt A = 29000-(21000) = 8000
Year 4 Incremental cash flow of B wrt A = 34000-(17000) = 17000

Cross over rate is the rate at which incremental cash flows are discounted to 0
CF/(1+r)^t = 0
0 + -15000/(1+r) + -2000/(1+r)² + 8000/(1+r)³ + 17000/(1+r)⁴ =0
Hence crossover rate r = 16.31%

Below 16.31% Project B is better than Project A

Best of luck. God Bless