Consider the following two mutually exclusive projects: Cash Flow (X) Cash Flow
ID: 2743087 • Letter: C
Question
Consider the following two mutually exclusive projects: Cash Flow (X) Cash Flow (Y) Year -$16,400 $16,400 6,660 7,240 4,760 7,190 7,780 3 3,530 What is the IRR of Project X? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, 0.g 32.16.) IRR What is the IRR of Project Y? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places,o.g, 32.16.) 712 % 699 % What is the crossover rate for these two projects? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places,e.g, 32.16 Crossover rateExplanation / Answer
year
Cash Flow(X)
Cash Flow(Y)
Cross Over Rate
0
(16,400)
(16,400)
-
1
6,660
7,190
530
2
7,240
7,780
540
3
4,760
3,530
(1,230)
IRR
7.12%
6.99%
9.69%
Alternatively Let us try with PV 7 %
year
Cash Flow(X)
PV Factor @ 7%
PV
0
(16,400)
1.0000
(16,400)
1
6,660
0.9346
6,224
2
7,240
0.8734
6,324
3
4,760
0.8163
3,886
NPV
34
As NPV is positive, let us try with 8 % PV
year
Cash Flow(X)
PV Factor @ 8%
PV
0
(16,400)
1.0000
(16,400)
1
6,660
0.9259
6,167
2
7,240
0.8573
6,207
3
4,760
0.7938
3,779
NPV
(248)
IRR = R1 +[NPV1x(R2-R1)%]/(NPV1-NPV2)
=7 %+ [34 x (8-7) %/34 – (-248)
=7%+0.34/281
=7% +0.12%
Cash Flow(Y)
year
Cash Flow(Y)
PV Factor @ 6%
PV
0
(16,400)
1.0000
(16,400)
1
7,190
0.9434
6,783
2
7,780
0.8900
6,924
3
3,530
0.8396
2,964
NPV
271
year
Cash Flow(Y)
PV Factor @ 7%
PV
0
(16,400)
1.0000
(16,400)
1
7,190
0.9346
6,720
2
7,780
0.8734
6,795
3
3,530
0.8163
2,882
NPV
(3)
IRR = R1 +[NPV1x(R2-R1)%]/(NPV1-NPV2)
=6 %+ [271 x (7-6) %/271 – (-3)
=6%+2.71/275
=6% +0.99%
=6.99%
year
Cash Flow(X)
Cash Flow(Y)
Cross Over Rate
0
(16,400)
(16,400)
-
1
6,660
7,190
530
2
7,240
7,780
540
3
4,760
3,530
(1,230)
IRR
7.12%
6.99%
9.69%