You are contemplating investing into two different projects. Both projects are o
ID: 2614094 • Letter: Y
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.
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
Explanation / Answer
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
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
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