Question

You are contemplating investing into two different projects. Both projects are of equally low risk and their cash flows are provided below.

Year	Project “Gold”	Project “Blue”
0	-$50,000	-$25,000
1	$22,500	$3,000
2	$18,750	$6,000
3	$15,250	$12,000
4	$15,000	$24,000

Determine the NPV of each project at a 6% cost of capital. Which is preferable?

Based on the profitability index, which would you prefer?

At what discount rate would you be indifferent between the projects (i.e., calculate the crossover rate)?

Graphically illustrate what an NPV Profile Chart would look like (generally) if a crossover rate exists? Include the crossover rate calculated (step c), the NPV’s from (step a) and other appropriate labels for the axes, and project plots, etc.

Answer 1

		Project Gold		Project Blue
Year	PV factors @6%	Cash flow	PV of cash flow	Cash flow	PV of cash flow
0	1.0000	-50000	-50000	-25000	-25000
1	0.9434	22500	21226	3000	2830
2	0.8900	18750	16687	6000	5340
3	0.8396	15250	12804	12000	10075
4	0.7921	15000	11881	24000	19010
NPV			12599		12256
According to NPV Project Gold is preferable
Profitablity Index of Project Gold is			PV of Cash in flows/PV of Cash outflows
		=	1.251988947
Profitablity Index of Project Gold is
		=	1.490233865
According to Profitability Index Project Blue is preferable
Coss Over rate calculation
For example take the interest rate of 10% and 7%
Year	Project Gold	Project Blue	Difference in cash flows	PV factor @10%	PV cashflow @10%	PV factor @7%	PV cashflow @7%
0	-50000	-25000	-25000	1	-25000	1	-25000
1	22500	3000	19500	0.909	17727.27	0.935	18224.30
2	18750	6000	12750	0.826	10537.19	0.873	11136.34
3	15250	12000	3250	0.751	2441.77	0.816	2652.97
4	15000	24000	-9000	0.683	-6147.12	0.763	-6866.06
					-440.89		147.55
			Cross over rate	7.75