Garage, Inc., has identified the following two mutually exclusive projects: Year
ID: 2709031 • Letter: G
Question
Garage, Inc., has identified the following two mutually exclusive projects:
Year
Cash Flow (A)
Cash Flow (B)
0
–$
29,700
–$
29,700
1
15,100
4,650
2
13,000
10,150
3
9,550
15,900
4
5,450
17,500
What is the IRR for each of these projects? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
Using the IRR decision rule, which project should the company accept?
If the required return is 12 percent, what is the NPV for each of these projects? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
Which project will the company choose if it applies the NPV decision rule?
At what discount rate would the company be indifferent between these two projects? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Year
Cash Flow (A)
Cash Flow (B)
0
–$
29,700
–$
29,700
1
15,100
4,650
2
13,000
10,150
3
9,550
15,900
4
5,450
17,500
Explanation / Answer
IRR
Project A = 20.14%
Project B = 18.34%
Based on IRR, project A should be chosen as it has a higher IRR compared to other project
NPV
Project A = 4406.74
Project B = 4982.18
Based on NPV, project B should be chosen as it provides a higher NPV value compared to project A
At a discount rate of 19.09%, the company will be indifferent between the two projects
Project A
Project B
Year
Cash Flow
Year
Cash Flow
0
-29700
0
-29700
1
15100
1
4650
2
13000
2
10150
3
9550
3
15900
4
5450
4
17500
Let rA be the rate of return which makes NPV of Project A equals zero. That is
-29700 + 15100/(1+rA) + 13000/(1+rA)^2 + 9550/(1+rA)^3 + 5450/(1+rA)^4 = 0
Let rA = 20%, then LHS is equal to
= -29700 + 15100/(1.20) + 13000/(1.20)^2 + 9550/(1.20)^3 + 5450/(1.20)^4
= -29700 + 15100/(1.20) + 13000/1.44 + 9550/1.728 + 5450/2.0736
= -29700 + 12583.33 + 9027.78 + 5526.62+ 2628.28
= 66.01
Let rA be equal to 21%, then LHS is equal to
= -29700 + 15100/(1.21) + 13000/(1.21)^2 + 9550/(1.21)^3 + 5450/(1.21)^4
= -29700 + 15100/1.21 + 13000/1.4641 + 9550/1.771561 + 5450/2.143589
= -29700+12479.34+8879.18+5390.73+2542..46
= -408.30
rA = 0.20 + [((66.01)*(0.20-0.21))/(-408.3-66.01)]
=0.20 + (-0.6601/-474.31)
= 0.20 + 0.00139
= 0.20139 or 20.14%
Let rB be the rate of return where NPV will be zero. Then
-29700 + 4650/(1+rB) + 10150/(1+rB)^2 + 15900/(1+rB)^3 + 17500/(1+rB)^4 = 0
Let rB = 18%, then LHS will be
= -29700 + 4650/(1.18) + 10150/(1.18)^2 + 15900/(1.18)^3 + 17500/(1.18)^4
= -29700 + 4650/1.18 + 10150/1.3924 + 15900/1.643032 + 17500/1.938778
= -29700 + 3940.678 + 7289.572+9677.231+9026.305
= 233.786
Let rB = 19%, then LHS would be
= -29700 + 4650/(1.19) + 10150/(1.19)^2 + 15900/(1.19)^3 + 17500/(1.19)^4
= -29700 + 4650/1.19 + 10150/1.4161 + 15900/1.685159 + 17500/2.005339
= -29700 + 3907.563 + 7167.573 + 9435.311 + 8726.703
= -462.850
rB = 0.18 + [((233.786)*(0.18 – 0.19))/(-462.85-233.786)]
rB = 0.18 + (-2.33786/-696.636)
rB = 0.18 + 0.003356
= 0.183356 or 18.34%
Project A
Year
0
1
2
3
4
Cash Flows
-29700
15100
13000
9550
5450
Discount Factor (1/1.12^year)
1
0.892857
0.797194
0.71178
0.635518
Discounted Flows
-29700
13482.14
10363.52
6797.501
3463.574
Net Present Value of Project A
4406.74
Project B
Year
0
1
2
3
4
Cash Flows
-29700
4650
10150
15900
17500
Discount Factor (1/1.12^year)
1
0.892857
0.797194
0.71178
0.635518
Discounted Flows
-29700
4151.786
8091.518
11317.31
11121.57
Net Present Value of Project B
4982.18
Calculation of discount rate at which the company will be indifferent between two projects
NPV of project A at 18.34%
Year
0
1
2
3
4
Cash Flows
-29700
15100
13000
9550
5450
Discount Factor (1/1.1834^year)
1
0.845023
0.714064
0.6034
0.509887
Discounted Flows
-29700
12759.84
9282.826
5762.47
2778.883
Net Present Value of Project A
884.02
NPV of project B at 20.14%
Year
0
1
2
3
4
Cash Flows
-29700
4650
10150
15900
17500
Discount Factor (1/1.2014^year)
1
0.832362
0.692827
0.576683
0.480009
Discounted Flows
-29700
3870.484
7032.193
9169.259
8400.16
Net Present Value of Project B
-1227.90
r = 0.1834 + [((884.02) * (0.1834-0.2014))/(-1227.90-884.02)]
= 0.1834 + (-15.91236/-2111.92)
= 0.1834 + 0.007535
= 0.190935 or 19.09%
Project A
Project B
Year
Cash Flow
Year
Cash Flow
0
-29700
0
-29700
1
15100
1
4650
2
13000
2
10150
3
9550
3
15900
4
5450
4
17500
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