Problem 10-13 NPV and IRR Analysis Cummings Products Company is considering two
ID: 2716637 • Letter: P
Question
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 -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?
-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?
-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.
%
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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