Part 1: Net Present Value (NPV) First, we need to calculate the annual cash flow. The net income is given, and since depreciation is a non-cash expense, we add it back to net income to find the cash flow: Annual Cash Flow = Net Income + Depreciation Annual Cash Flow = $200,000+ $200,000 Annual Cash Flow = $400,000 The project lasts for 8 years with an initial investment of $2,000,000. The NPV formula is: CE NPV - Initial Investment = t=1 where CF, is the annual cash flow, is the discount rate, and 12 is the number of years. NPV= 400,000 - 2,000,000 t=1 (1+0.10) Calculating each term: Year 1: Year 2: Year 3: 400,000 (1+0.10)1 400,000 (1+0.10)² 400,000 (1+0.10) 400,000 1.10 400,000 363, 636.36 330, 578.51 1.21 400,000 = 300, 525.98 1.331 Year 4: 400,000 400,000 (1+0.10)4 1.4641 400,000 400,000 273, 205.44 Year 5: 248, 368.58 (1+0.10)5 1.61051 Year 6: Year 7: Year 8: 400,000 400,000 (1+0.10)6 1.77156 400,000 400,000 (1+0.10)7 1.94872 400,000 400,000 (1+0.10)8 2.14359 225, 789.62 =205, 263.29 = 186, 602.99 Adding these present values together and subtracting the initial investment: NPV 363, 636.36 + 330, 578.51 +300, 525.98 +273, 205.44 + 248, 368.58 +225,789. NPV = 2,133,970.77-2, 000, 000 = 133,970.77 So, the NPV is $133,970.77. Part 2: Internal Rate of Return (IRR) The IRR is the discount rate that makes the NPV of the project zero. To find the IRR, we need to solve the following equation:
Part 1: Net Present Value (NPV) First, we need to calculate the annual cash flow. The net income is given, and since depreciation is a non-cash expense, we add it back to net income to find the cash flow: Annual Cash Flow = Net Income + Depreciation Annual Cash Flow = $200,000+ $200,000 Annual Cash Flow = $400,000 The project lasts for 8 years with an initial investment of $2,000,000. The NPV formula is: CE NPV - Initial Investment = t=1 where CF, is the annual cash flow, is the discount rate, and 12 is the number of years. NPV= 400,000 - 2,000,000 t=1 (1+0.10) Calculating each term: Year 1: Year 2: Year 3: 400,000 (1+0.10)1 400,000 (1+0.10)² 400,000 (1+0.10) 400,000 1.10 400,000 363, 636.36 330, 578.51 1.21 400,000 = 300, 525.98 1.331 Year 4: 400,000 400,000 (1+0.10)4 1.4641 400,000 400,000 273, 205.44 Year 5: 248, 368.58 (1+0.10)5 1.61051 Year 6: Year 7: Year 8: 400,000 400,000 (1+0.10)6 1.77156 400,000 400,000 (1+0.10)7 1.94872 400,000 400,000 (1+0.10)8 2.14359 225, 789.62 =205, 263.29 = 186, 602.99 Adding these present values together and subtracting the initial investment: NPV 363, 636.36 + 330, 578.51 +300, 525.98 +273, 205.44 + 248, 368.58 +225,789. NPV = 2,133,970.77-2, 000, 000 = 133,970.77 So, the NPV is $133,970.77. Part 2: Internal Rate of Return (IRR) The IRR is the discount rate that makes the NPV of the project zero. To find the IRR, we need to solve the following equation:
Chapter10: Capital Budgeting: Decision Criteria And Real Option
Section: Chapter Questions
Problem 21P
Related questions
Question
Transcribed Image Text:Part 1: Net Present Value (NPV)
First, we need to calculate the annual cash flow. The net income is given, and since depreciation is a
non-cash expense, we add it back to net income to find the cash flow:
Annual Cash Flow = Net Income + Depreciation
Annual Cash Flow = $200,000+ $200,000
Annual Cash Flow = $400,000
The project lasts for 8 years with an initial investment of $2,000,000. The NPV formula is:
CE
NPV - Initial Investment
=
t=1
where CF, is the annual cash flow, is the discount rate, and 12 is the number of years.
NPV=
400,000
- 2,000,000
t=1 (1+0.10)
Calculating each term:
Year 1:
Year 2:
Year 3:
400,000
(1+0.10)1
400,000
(1+0.10)²
400,000
(1+0.10)
400,000
1.10
400,000
363, 636.36
330, 578.51
1.21
400,000
=
300, 525.98
1.331
Transcribed Image Text:Year 4:
400,000 400,000
(1+0.10)4 1.4641
400,000 400,000
273, 205.44
Year 5:
248, 368.58
(1+0.10)5 1.61051
Year 6:
Year 7:
Year 8:
400,000 400,000
(1+0.10)6 1.77156
400,000 400,000
(1+0.10)7 1.94872
400,000 400,000
(1+0.10)8 2.14359
225, 789.62
=205, 263.29
= 186, 602.99
Adding these present values together and subtracting the initial investment:
NPV 363, 636.36 + 330, 578.51 +300, 525.98 +273, 205.44 + 248, 368.58 +225,789.
NPV = 2,133,970.77-2, 000, 000 = 133,970.77
So, the NPV is $133,970.77.
Part 2: Internal Rate of Return (IRR)
The IRR is the discount rate that makes the NPV of the project zero. To find the IRR, we need to solve
the following equation:
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