Question

Anderson Associates is considering two mutually exclusive projects that have the following cash flows: Project A Project B Year Cash Flow Cash Flow 0 -$11,000 -$9,000 1 3,500 6,000 2 3,000 4,000 3 5,000 3,000 4 9,000 2,000 At what cost of capital do the two projects have the same net present value? (That is, what is the crossover rate?) Enter your answer rounded to two decimal places. Do not enter % in the answer box. For example, if your answer is 0.12345 or 12.345% then enter as 12.35 in the answer box.

Answer 1

Cost of capital at which the both projects have same NPV is referred to as the Crossover rate.

Crossover rate can be derived as the IRR for the incremental cashflows from Project and Project B

Computation of Incremental cashflows

Year	0	1	2	3	4
Project A	(11,000.00)	3,500.00	3,000.00	5,000.00	9,000.00
Project B	(9,000.00)	6,000.00	4,000.00	3,000.00	2,000.00
Incremental cashflow	(2,000.00)	(2,500.00)	(1,000.00)	2,000.00	7,000.00

Compute NPV of Incremental cashflows @ 10% discount rate

Year	0	1	2	3	4
Incremental cashflow	(2,000.00)	(2,500.00)	(1,000.00)	2,000.00	7,000.00
PV factor @ 10%	1.0000	0.9091	0.8264	0.7513	0.6830
PV of incremental cashflows	(2,000.00)	(2,272.73)	(826.45)	1,502.63	4,781.09
NPV	1,184.55

Compute NPV of Incremental cashflows @ 20% discount rate

Year	0	1	2	3	4
Incremental cashflow	(2,000.00)	(2,500.00)	(1,000.00)	2,000.00	7,000.00
PV factor @ 10%	1.0000	0.8333	0.6944	0.5787	0.4823
PV of incremental cashflows	(2,000.00)	(2,083.33)	(694.44)	1,157.41	3,375.77
NPV	(244.60)

NPV at lower discount rate	1,184.550
Lower discount rate	10.000%
Value at higher discount rate	(244.599)
Higher discount rate	20.000%
Step 1 : Higher discount rate - Lower discount rate	10.000%
Step2 : NPV at lower discount rate x step1	118.455
Step3 : NPV at lower discount rate - NPV at higher discount rate	1,429.149
Step4 : Step2 / Step 3	8.289%
Step 5 : Lower discount rate + step4 ---Crossover rate	18.289%

Therefore the Crossover rate at which both projects would have the same NPV is 18.29%