Problem 10-13 NPV and IRR Analysis Cummings Products Company is considering two
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Problem 10-13
NPV and IRR Analysis
Cummings Products Company is considering two mutually exclusive investments whose expected net cash flows are as follows:
Construct NPV profiles for Projects A and B.
Select the correct graph.
The correct graph is C-Select-ABCDItem 1 .
What is each project's IRR? Round your answers to two decimal places.
Project A %
Project B %
Calculate the two projects' NPVs, if you were told that each project's cost of capital was 10%. Round your answers to the nearest cent.
Project A $
Project B $
Which project, if either, should be selected?
Project A-Select-Project AProject BItem 6
Calculate the two projects' NPVs, if the cost of capital was 18%. Round your answers to the nearest cent.
Project A $
Project B $
What would be the proper choice?
Project B-Select-Project AProject BItem 9
What is each project's MIRR at a cost of capital of 10%? (Hint: Note that B is a 7-year project.) Round your answers to two decimal places.
Project A %
Project B %
What is each project's MIRR at a cost of capital of 18%? (Hint: Note that B is a 7-year project.) Round your answer to two decimal places.
Project A %
Project B %
What is the crossover rate? Round your answer to two decimal places.
%
What is its significance?
I-Select-IIIIIIItem 15
I.The crossover rate has no significance in capital budgeting analysis.
II.If the cost of capital is greater than the crossover rate, both the NPV and IRR methods will lead to the same project selection.
III.If the cost of capital is less than the crossover rate, both the NPV and IRR methods lead to the same project selections.
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IRRA = 18.84%; IRRB = 24.41%.
At r = 10%, Project A has the greater NPV, specifically $303.34 as compared to Project B's NPV of $222.37. Thus, Project A would be selected. At r = 18%, Project A has an NPV of $80.74 which is higher than Project B's NPV of $22.66. Thus, choose Project B if r = 18%.
Here is the MIRR for Project A when r = 10%:
Now, MIRR is that discount rate which forces the PV of $2,459.6 in 7 years to equal $958.82:
$958.82 = $2,459.6/(1 + MIRR)7
MIRRA = 14.41%.
Similarly, $430 = $1,033.89/(1 + MIRR)6 (Note: B is a 7-year project)
MIRRB = 16.75%.
At r = 18%,
MIRRA = 16.12%.
MIRRB = 16.75%.
To find the crossover rate, construct a Project which is the difference in the two projects' cash flows:
IRR = Crossover rate = 14.12%.
Projects A and B are mutually exclusive, thus, only one of the projects can be chosen. As long as the cost of capital is greater than the crossover rate, both the NPV and IRR methods will lead to the same project selection. However, if the cost of capital is less than the crossover rate the two methods lead to different project selections — a conflict exists. When a conflict exists the NPV method must be used.
Because of the sign changes and the size of the cash flows, Project has multiple IRRs. Thus, the IRR function for some calculators will not work (it will work, however, on a BAII Plus). The HP can be "tricked" into giving the roots by selecting an initial guess near one of the roots. Similarly, Excel can also be used.
Solution
Correct Response
Click here to read the eBook: Net Present Value (NPV) Click here to read the eBook: Internal Rate of Return (IRR)
Problem 10-13
NPV and IRR Analysis
Cummings Products Company is considering two mutually exclusive investments whose expected net cash flows are as follows:
Construct NPV profiles for Projects A and B.
Select the correct graph.
The correct graph is C-Select-ABCDItem 1.
What is each project's IRR? Round your answers to two decimal places.
Project A %
Project B %
Calculate the two projects' NPVs, if you were told that each project's cost of capital was 10%. Round your answers to the nearest cent.
Project A $
Project B $
Which project, if either, should be selected?
Project A-Select-Project AProject BItem 6
Calculate the two projects' NPVs, if the cost of capital was 18%. Round your answers to the nearest cent.
Project A $
Project B $
What would be the proper choice?
Project B-Select-Project AProject BItem 9
What is each project's MIRR at a cost of capital of 10%? (Hint: Note that B is a 7-year project.) Round your answers to two decimal places.
Project A %
Project B %
What is each project's MIRR at a cost of capital of 18%? (Hint: Note that B is a 7-year project.) Round your answer to two decimal places.
Project A %
Project B %
What is the crossover rate? Round your answer to two decimal places.
%
What is its significance?
II-Select-IIIIIIItem 15
I.The crossover rate has no significance in capital budgeting analysis.
II.If the cost of capital is greater than the crossover rate, both the NPV and IRR methods will lead to the same project selection.
III.If the cost of capital is less than the crossover rate, both the NPV and IRR methods lead to the same project selections.
Problem 10-13
NPV and IRR Analysis
Cummings Products Company is considering two mutually exclusive investments whose expected net cash flows are as follows:
EXPECTED NET CASH FLOWS Year Project A Project B 0 -$280 -$430 1 -387 134 2 -193 134 3 -100 134 4 600 134 5 600 134 6 850 134 7 -180 134Construct NPV profiles for Projects A and B.
Select the correct graph.
The correct graph is C-Select-ABCDItem 1 .
What is each project's IRR? Round your answers to two decimal places.
Project A %
Project B %
Calculate the two projects' NPVs, if you were told that each project's cost of capital was 10%. Round your answers to the nearest cent.
Project A $
Project B $
Which project, if either, should be selected?
Project A-Select-Project AProject BItem 6
Calculate the two projects' NPVs, if the cost of capital was 18%. Round your answers to the nearest cent.
Project A $
Project B $
What would be the proper choice?
Project B-Select-Project AProject BItem 9
What is each project's MIRR at a cost of capital of 10%? (Hint: Note that B is a 7-year project.) Round your answers to two decimal places.
Project A %
Project B %
What is each project's MIRR at a cost of capital of 18%? (Hint: Note that B is a 7-year project.) Round your answer to two decimal places.
Project A %
Project B %
What is the crossover rate? Round your answer to two decimal places.
%
What is its significance?
I-Select-IIIIIIItem 15
I.The crossover rate has no significance in capital budgeting analysis.
II.If the cost of capital is greater than the crossover rate, both the NPV and IRR methods will lead to the same project selection.
III.If the cost of capital is less than the crossover rate, both the NPV and IRR methods lead to the same project selections.
Explanation / Answer
Calculation of IRR:
IRR of Project A:
IRR is the rate at which NPV is '0' i.e., PV of cash inflows =PV of cash outflows
Applying trial and error method:
At 19%, NPV
= {[-387/(1+0.18)]+[-193/(1+0.18)2]+[-100/(1+0.18)3]+[600/(1+0.18)4+[600/(1+0.18)5]+[850/(1+0.18)6]+[-180/(1+0.18)7]]}-280
=$275.84 - $280
=-$4.16
At 18%, NPV
= {[-387/(1+0.18)]+[-193/(1+0.18)2]+[-100/(1+0.18)3]+[600/(1+0.18)4+[600/(1+0.18)5]+[850/(1+0.18)6]+[-180/(1+0.18)7]]}-280
= $302.66 -$280
= $22.66
For 1% decrease in IRR, NPV increased by $26.82
For how much decrease in IRR, NPV increases by $4.16?
4.16 / 26.82 = 0.15%
Therefore, IRR= 19 – 0.15 = 18.85%
IRR of Project B:
IRR is the rate at which NPV is '0' i.e., PV of cash inflows =PV of cash outflows
Applying trial and error method:
At 25%, NPV
= [134*PVAF(25%,7yrs)]-430
= $423.59 - $430
=-$6.41
At 24%, NPV
= [134*PVAF(24%,7yrs)]-430
=$434.47 - $430
=$4.47
For 1% decrease in IRR, NPV increased by $10.88
For how much decrease in IRR, NPV increases by $6.41?
6.41 / 10.88 = 0.589%
Therefore, IRR= 25 - 0.589= 24.41%
IRR of Project A = 18.85%
IRR of Project B = 24.41%
Selection of Project as per IRR decision rule:
A project with higher IRR should be selected as it gives the higher return.
Here, IRR of Project A is 18.85%
IRR of Project B is 24.41%
As project B is with higher IRR, project B should be accepted.
Where cost of capital is 10%, NPV of the Projects:
NPV of Project A:
NPV = PV of Cash inflows - PV of Cash outflows
={[-387/(1+0.10)]+[-193/(1+0.10)2]+[-100/(1+0.10)3]+[600/(1+0.10)4+[600/(1+0.10)5]+[850/(1+0.10)6]+[-180/(1+0.10)7]]}-280
= $583.34 - $280
= $303.34
NPV of Project B:
NPV = PV of Cash inflows - PV of Cash outflows
=[134*PVAF(10%,7yrs)]-430
=$652.368 - $430
=$222.37
Selection of Project as per NPV decision rule:
A project with higher NPV should be selected.
Here, NPV of Project A = $303.34
NPV of Project B = $222.37
As Project A is with higher NPV, Project A should be selected.
Where cost of capital is 18%, NPV of the Projects:
NPV of Project A:
NPV = PV of Cash inflows - PV of Cash outflows
={[-387/(1+0.18)]+[-193/(1+0.18)2]+[-100/(1+0.18)3]+[600/(1+0.18)4+[600/(1+0.18)5]+[850/(1+0.18)6]+[-180/(1+0.18)7]]}-280
= $302.66 - $280
= $22.66
NPV of Project B:
NPV = PV of Cash inflows - PV of Cash outflows
=[134*PVAF(18%,7yrs)]-430
=$510.75 - $430
=$80.75
Selection of Project as per NPV decision rule:
A project with higher NPV should be selected.
Here, NPV of Project A = $22.66
NPV of Project B = $80.75
As Project B is with higher NPV, Project B should be selected.
Calculation of MIRR at a cost of capital of 10%:
Modified IRR = [FV(positive cash flows, cost of capital) / (-PV (negative cash flows, finance rate))]1/n - 1
Here only cost of capital is given. Hence, cost of capital is only considered as finance rate.
Cost of capital = 10%
n = Number of years = 7
Computation of Modified IRR of project A:
FV (positive cash flows, reinvestment rate)
= (600 (1+0.10)3) + (600 (1+0.10)2) + (850 (1+0.10)1))
=$798.6 + $726 + $935
=$2459.60
PV (negative cash flows, finance rate)
=($280/(1+0.10)0) +($387/(1+0.10)1)+ ($193/(1+0.10)2)+ ($100/(1+0.10)3)+ ($180/(1+0.10)7)
=$280+$351.82+$159.50+$75.13+$92.37
=$958.82
Modified IRR = [FV(positive cash flows, cost of capital) / (-PV (negative cash flows, finance rate))]1/n - 1
= ($2459.60/958.82)1/7 - 1
=2.5651/7-1
=1.144 - 1
=0.144 (approx.)
Computation of Modified IRR of project B:
FV (positive cash flows, reinvestment rate)
=134*FVAF(10%, 7yrs)
=$1398.41
PV (negative cash flows, finance rate)
=$430/(1+0.10)0
=$430
Modified IRR = [FV(positive cash flows, cost of capital) / (-PV (negative cash flows, finance rate))]1/n - 1
= (1398.41/430)1/7 - 1
=3.2521/7-1
= 1.183 - 1
=0.183 (approx.)
Modified IRR of Project A = 0.144 = 14.4%
Modified IRR of Project B = 0.183 = 18.3%
Calculation of MIRR at a cost of capital of 18%:
Modified IRR = [FV(positive cash flows, cost of capital) / (-PV (negative cash flows, finance rate))]1/n - 1
Here only cost of capital is given. Hence, cost of capital is only considered as finance rate.
Cost of capital = 18%
n = Number of years = 7
Computation of Modified IRR of project A:
FV (positive cash flows, reinvestment rate)
= (600 (1+0.18)3) + (600 (1+0.18)2) + (850 (1+0.18)1))
=$985.82 + $835.44 + $1003
=$2824.26
PV (negative cash flows, finance rate)
=($280/(1+0.18)0) +($387/(1+0.18)1)+ ($193/(1+0.18)2)+ ($100/(1+0.18)3)+ ($180/(1+0.18)7)
=$280+$327.97+$138.61+$60.86+$56.50
=$863.94
Modified IRR = [FV(positive cash flows, cost of capital) / (-PV (negative cash flows, finance rate))]1/n - 1
= ($2824.26/863.94)1/7 - 1
=3.2691/7-1
=1.184 - 1
=0.184(approx.)
Computation of Modified IRR of project B:
FV (positive cash flows, reinvestment rate)
=134*FVAF(18%, 7yrs)
=$1919.82
PV (negative cash flows, finance rate)
=$430/(1+0.10)0
=$430
Modified IRR = [FV(positive cash flows, cost of capital) / (-PV (negative cash flows, finance rate))]1/n - 1
= (1919.82/430)1/7 - 1
=4.46471/7-1
= 1.238 - 1
=0.238 (approx.)
Modified IRR of Project A = 0.184 = 18.4%
Modified IRR of Project B = 0.238 = 23.8%
Cross Over Rate:
The rate at which the company is indifferent to select either of the projects is the IRR where NPV of Project A equals NPV of project B.
Applying the trial and error method,
At 18%, NPV of Project A = $22.66
NPV of Project B = $80.75
Difference= $22.66 - $80.75
= -$58.09
At 10%, NPV of Project A = $303.34
NPV of Project B = $222.37
Difference= $303.34 - $222.37
= $80.97
For 8% decrease in IRR, difference increased by $139.06
For how much decrease in IRR, difference increases by $58.09?
58.09 / 139.06 = 0.4177%
IRR = 18 - 0.4177 =17.5823 (approx).
Therefore, the discount rate at which the company is indifferent to select either of the two projects is 17.58%
IRR of Project A = 18.85%
IRR of Project B = 24.41%
NPV of Projects:
At 10%, Project A = $303.34
Project B = $222.37
At 18%, Project A = $22.66
Project B = $80.75
MIRR of Projects:
At 10%, Project A =14.4&
Project B = 18.3%
At 18%, Project A = 18.4%
Project B = 23.8%
Cross over rate = 17.58%
Based on the above findings, we can say graph corresponding to option C is appropriate.
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