Consider the following two mutually exclusive projects: Year Cash Flow (X) Cash
ID: 2775858 • Letter: C
Question
Consider the following two mutually exclusive projects: Year Cash Flow (X) Cash Flow (Y) 0 –$ 20,700 –$ 20,700 1 9,025 10,450 2 9,450 7,975 3 8,975 8,875 Calculate the IRR for each project. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) IRR Project X % Project Y % What is the crossover rate for these two projects? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Crossover rate % What is the NPV of Projects X and Y at discount rates of 0%, 15%, and 25%? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Discount rate Project X Project Y 0% $ $ 15% $ $ 25% $ $
Explanation / Answer
Calculation of IRR of the projects
Project X
Project Y
Year 0
$ (20,700.00)
$ (20,700.00)
Year 1
$ 9,025.00
$ 10,450.00
Year 2
$ 9,450.00
$ 7,975.00
Year 3
$ 8,975.00
$ 8,875.00
IRR=
15.57%
15.76%
Calculation of NPV of the projects
At Discount rate 0%
Cash Flows
PVF
PV
Year
0%
Project X
Project Y
A
B
C
A*C
B*C
Year 0
$ (20,700.00)
$ (20,700.00)
1
$ (20,700.00)
$ (20,700.00)
Year 1
$ 9,025.00
$ 10,450.00
1
$ 9,025.00
$ 10,450.00
Year 2
$ 9,450.00
$ 7,975.00
1
$ 9,450.00
$ 7,975.00
Year 3
$ 8,975.00
$ 8,875.00
1
$ 8,975.00
$ 8,875.00
NPV = Sum of PVs.
$ 6,750.00
$ 6,600.00
At Discount rate 15%
Cash Flows
PVF
PV
Year
15%
Project X
Project Y
A
B
C
A*C
B*C
Year 0
$ (20,700.00)
$ (20,700.00)
1
$ (20,700.00)
$ (20,700.00)
Year 1
$ 9,025.00
$ 10,450.00
0.869565217
$ 7,847.83
$ 9,086.96
Year 2
$ 9,450.00
$ 7,975.00
0.756143667
$ 7,145.56
$ 6,030.25
Year 3
$ 8,975.00
$ 8,875.00
0.657516232
$ 5,901.21
$ 5,835.46
NPV = Sum of PVs.
$ 194.59
$ 252.66
At Discount rate 25%
Cash Flows
PVF
PV
Year
25%
Project X
Project Y
A
B
C
A*C
B*C
Year 0
$ (20,700.00)
$ (20,700.00)
1
$ (20,700.00)
$ (20,700.00)
Year 1
$ 9,025.00
$ 10,450.00
0.80000
$ 7,220.00
$ 8,360.00
Year 2
$ 9,450.00
$ 7,975.00
0.64000
$ 6,048.00
$ 5,104.00
Year 3
$ 8,975.00
$ 8,875.00
0.51200
$ 4,595.20
$ 4,544.00
NPV = Sum of PVs.
$ (2,836.80)
$ (2,692.00)
Calculation of IRR of the projects
Project X
Project Y
Year 0
$ (20,700.00)
$ (20,700.00)
Year 1
$ 9,025.00
$ 10,450.00
Year 2
$ 9,450.00
$ 7,975.00
Year 3
$ 8,975.00
$ 8,875.00
IRR=
15.57%
15.76%
Calculation of NPV of the projects
At Discount rate 0%
Cash Flows
PVF
PV
Year
0%
Project X
Project Y
A
B
C
A*C
B*C
Year 0
$ (20,700.00)
$ (20,700.00)
1
$ (20,700.00)
$ (20,700.00)
Year 1
$ 9,025.00
$ 10,450.00
1
$ 9,025.00
$ 10,450.00
Year 2
$ 9,450.00
$ 7,975.00
1
$ 9,450.00
$ 7,975.00
Year 3
$ 8,975.00
$ 8,875.00
1
$ 8,975.00
$ 8,875.00
NPV = Sum of PVs.
$ 6,750.00
$ 6,600.00
At Discount rate 15%
Cash Flows
PVF
PV
Year
15%
Project X
Project Y
A
B
C
A*C
B*C
Year 0
$ (20,700.00)
$ (20,700.00)
1
$ (20,700.00)
$ (20,700.00)
Year 1
$ 9,025.00
$ 10,450.00
0.869565217
$ 7,847.83
$ 9,086.96
Year 2
$ 9,450.00
$ 7,975.00
0.756143667
$ 7,145.56
$ 6,030.25
Year 3
$ 8,975.00
$ 8,875.00
0.657516232
$ 5,901.21
$ 5,835.46
NPV = Sum of PVs.
$ 194.59
$ 252.66
At Discount rate 25%
Cash Flows
PVF
PV
Year
25%
Project X
Project Y
A
B
C
A*C
B*C
Year 0
$ (20,700.00)
$ (20,700.00)
1
$ (20,700.00)
$ (20,700.00)
Year 1
$ 9,025.00
$ 10,450.00
0.80000
$ 7,220.00
$ 8,360.00
Year 2
$ 9,450.00
$ 7,975.00
0.64000
$ 6,048.00
$ 5,104.00
Year 3
$ 8,975.00
$ 8,875.00
0.51200
$ 4,595.20
$ 4,544.00
NPV = Sum of PVs.
$ (2,836.80)
$ (2,692.00)