Question

Canfly Airlines is considering two mutually exclusive projects, Project A and Project B. The projects have the following cash flows (in millions of dollars):

Year	Project A Cash Flow	Project B Cash Flow
0	-$4.0	-$4.5
1	2.0	1.7
2	3.0	3.2
3	5.0	?

The crossover rate of the two projects’ NPV profiles is 9 percent. What is the cash flow for Project B at t = 3?

(Ans: 5.79 million)

Answer 1

We know, cross over rate is the rate where the NPV for both the alternative is equal. NPV is the present value of future cashflows discounted at the required rate of return.
Calculation of NPV of Project A
			(Amount in million$)
Year	Cashflow	Discounting factor @ 9%	PV of cashflows
0	-4	1	-4.00
1	2	0.917431193	1.83
2	3	0.841679993	2.53
3	5	0.77218348	3.86
		NPV	4.22
Calculation of NPV of Project B
			(Amount in million$)
Year	Cashflow	Discounting factor @ 9%	PV of cashflows
0	-4.5	1	-4.50
1	1.7	0.917431193	1.56
2	3.2	0.841679993	2.69
3	x	0.77218348	0.77x
		NPV	-0.25+0.77x
Let the cashflow in year 3 for project B be x
As the NPV are equal at cross over rates, therefore equating the equation we get,
-0.25+0.77x=4.22
0.77x=4.47
x= 5.80
Therefore, cashflow for Project B at t=3 is $5.80 millions
* figures are rounded off to two decimal places