14.5: Calculating Net Present Value and Internal Rate of Return for Mutually Exc
ID: 2421587 • Letter: 1
Question
14.5: Calculating Net Present Value and Internal Rate of Return for Mutually Exclusive Projects
Why:
For competing projects, the discounting method that consistently chooses the wealth-maximizing project should be used. NPV measures profitability in absolute terms, while IRR measures relative profitability. NPV measures the amount by which the value of the firm changes and thus is consistent with maximizing wealth.
Information:
Consider two pollution prevention designs: Design A and Design B. Both designs have a project life of 5 years. Design A requires an initial outlay of $180,000 and has a net annual after-tax cash inflow of $60,000 (revenues of $180,000 minus cash expenses of $120,000). Design B, with an initial outlay of $210,000, has a net annual cash inflow of $70,000 ($240,000 $170,000). The after-tax cash flows are summarized as follows:
CASH FLOW PATTERN
Year
Design A
Design B
0
$(180,000)
$(210,000)
1
60,000
70,000
2
60,000
70,000
3
60,000
70,000
4
60,000
70,000
5
60,000
70,000
The cost of capital for the company is 12%.
Required:
Calculate the NPV and the IRR for each project.
Solution:
DESIGN A: NPV ANALYSIS
Year
Cash Flow
Discount Factor*
Present Value
0
$(180,000)
1.00000
$(180,000)
1–5
60,000
3.60478
216,287
Net present value
$ 36,287
DESIGN A: IRR ANALYSIS
CASH FLOW PATTERN
Year
Design A
Design B
0
$(180,000)
$(210,000)
1
60,000
70,000
2
60,000
70,000
3
60,000
70,000
4
60,000
70,000
5
60,000
70,000
Explanation / Answer
Calculation of NPV and IRR of Design A:
NPV of Design A:
Year
Cash Flow
PVF (12%)
PV of Cash Flow
0
(180000)
1
(180000)
1-5
60000
3.60478
216287
36287
IRR of Design 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= {$60000 * PVAF (19%, 5yrs)]-$180000
= $183458 - $180000
= $3458
At 20%, NPV= {$60000 * PVAF (20%, 5yrs)]-$180000
=$ 179437 - $180000
= -$563
For 1% increase in IRR, NPV decreased by $4021
For how much increase in IRR, NPV decreases by $3458?
3458 / 4021 = 0.86%
Therefore, IRR= 19 + 0.86 = 19.86%
Calculation of NPV and IRR of Design B:
NPV of Design B:
Year
Cash Flow
PVF (12%)
PV of Cash Flow
0
(210000)
1
(210000)
1-5
70000
3.60478
252335
42335
IRR of Design 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 19%, NPV= {$70000 * PVAF (19%, 5yrs)]-$210000
= $214034 - $210000
= $4034
At 20%, NPV= {$70000 * PVAF (20%, 5yrs)]-$210000
=$ 209343 - $210000
= -$657
For 1% increase in IRR, NPV decreased by $4691
For how much increase in IRR, NPV decreases by $4034?
4034 / 4691 = 0.86%
Therefore, IRR= 19 + 0.86 = 19.86%
Design A
Design B
NPV
$36287
$42335
IRR
19.86%
19.86%
Year
Cash Flow
PVF (12%)
PV of Cash Flow
0
(180000)
1
(180000)
1-5
60000
3.60478
216287
36287
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