You are considering the following two mutually exclusive projects. Both projects
ID: 2628546 • Letter: Y
Question
You are considering the following two mutually exclusive projects. Both projects will be depreciated using straight-line depreciation to a zero book value over the life of the project. Neither project has any salvage value
Year
Project(A)
Project (B)
0
-$30,000
-$25,000
1
10,000
8,000
2
11,000
8,000
3
12,000
8,000
4
13,000
8,000
The required rate of return is 10%.
(a) What is the NPV for each of the projects? Which project should be accepted if NPV method is applied? Explain why.
(b) What is the IRR for each of the projects? Which project should be accepted if IRR method is applied? Explain why.
(c) What is the payback period for each of the projects? Which project should be accepted if payback period method is applied? Explain why.
(d) What is the discounted payback period for each of the projects? Which project should be accepted if discounted payback period method is applied? Explain why.
(e) What is the profitability index for each of the projects? Which project should be accepted if profitability index method is applied? Explain why.
(f) Find the crossover rate. Show the equation.
(g) Sketch the NPV profile. You must plot at least 5 points for the profile: two points on the x and y axis each, and the cross-over rate on the x axis.
Year
Project(A)
Project (B)
0
-$30,000
-$25,000
1
10,000
8,000
2
11,000
8,000
3
12,000
8,000
4
13,000
8,000
Explanation / Answer
Depreciation is a non cash expense. We will not consider for calculating NPV. However depreciation is a tax deductible. Tax yield should be added. As in this sum there is no tax rate we will ignore the depreciation.
Project A initial investment= 30000
Project B initial investment= 25000
Year
Project A
PV@10%
Project B
PV @10%
1
10000
9091
8000
7273
2
11000
9091
8000
6612
3
12000
9016
8000
6011
4
13000
8879
8000
5464
NPV
36077
25360
1. NPV= PV of inflow - Initial outflow
Project A= 36077-30000 i.e $6077
Project B= 25360-25000 i.e $360
Project A should be accepted since NPV of project A is higher. If NPV>0 The project is expected to create shareholder wealth. Therefore accepted in this case.
2. IRR is that discount rate where outflow is equal to inflow.
IRR of project A is: Say 13%
= 10000/1.13 + 11000/1.13^2 + 12000/1.13^3 + 13000/1.13^4
= 33755
If, 13%= 33755
IRR = 30000
IRR= 11.5% project accepted Coz IRR is greater than Required rate of return.
IRR of project B= say 7%
= 8000PVIFA(7%, 4) . here compute PV of annuity
= 27098
If, 7% = 27098
IRR = 25000
= 6.5%
Since IRR is less than reqd. rate of return therefore reject.
3.) Payback period:-
Project A = 2yrs & 9000/12000= 9mth.
= 2.9yrs
Project B = 3yrs & 1000/8000= .125
= 3.125Yrs
Project A should be accepted.
d. Discounted Payback period
PROJECT A = 3yrs and 2803/8879= .3
= 3.3yrs
PROJECT B= 3yrs and 51041/5464 = 9
= 3.9yrs.
e) PROFITABILITY INDEX= Pv of inflow/Initial Investment
Project A= 36077/30000= i.e 1.2
Project B= 25360/25000= i.e 1.01
If profitability index generates what is generated oout of the project for one rupee of invetsment. Project A should be accepted.
f) Crossover rate is the cost of capital at which the net present values of two projects are equal. It is the point at which the net present value profile of one project crosses over (intersects) the net present value profile of the other project.
Year
Project A
PV@10%
Project B
PV @10%
1
10000
9091
8000
7273
2
11000
9091
8000
6612
3
12000
9016
8000
6011
4
13000
8879
8000
5464
NPV
36077
25360
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