accounting chapter 26
TRANSCRIPT
Capital Investment Decisions
Chapter 26
26-1Copyright © 2014 Pearson Education, Inc. Publishing as Prentice Hall
Learning Objectives
1. Describe the importance of capital investments and the capital budgeting process
2. Use the payback and the accounting rate of return methods to make capital investment decisions
26-2Copyright © 2014 Pearson Education, Inc. Publishing as Prentice Hall
Learning Objectives
3. Use the time value of money to compute the present values of lump sums and annuities
4. Use discounted cash flow methods to make capital investment decisions
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Learning Objective 1
Describe the Describe the importance of capital importance of capital investments and the investments and the
capital budgeting capital budgeting processprocess
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Methods of Analyzing Potential Capital Investments
1. Payback
2. Accounting rate of return (ARR)
3. Net present value (NPV)
4. Internal rate of return (IRR)
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Stages of Capital Investing
1. Screen the potential capital investments using one or both of the methods that do not incorporate the time value of money
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Stages of Capital Investing
1. Screen the potential capital investments using one or both of the methods that do not incorporate the time value of money
2. Further analyze the potential investments using the net present value and/or internal rate of return methods
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Pass
Focus of GAAP versusFocus of Capital Budgeting
GAAP Capital Budgeting
Accrual accounting Cash flows
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Capital Investment Cash Flows
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Life Cycle of Capital Investments
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Match the following business activities to the steps in capital budgeting process:
Steps in the capital budgeting process:a. Develop strategiesb. Planc. Actd. Control
Business activities:
1. A manager evaluates progress one year into the project.
2. Employees submit suggestions for new investments.
3. The company builds a new factory.
4. Top management attends a retreat to set long-term goals.
5. Proposed investments are analyzed.
6. Proposed investments are ranked.
7. New equipment is purchased.
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Match the following business activities to the steps in capital budgeting process:
Steps in the capital budgeting process:a. Develop strategiesb. Planc. Actd. Control
Business activities:
d 1. A manager evaluates progress one year into the project.
2. Employees submit suggestions for new investments.
3. The company builds a new factory.
4. Top management attends a retreat to set long-term goals.
5. Proposed investments are analyzed.
6. Proposed investments are ranked.
7. New equipment is purchased.
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Match the following business activities to the steps in capital budgeting process:
Steps in the capital budgeting process:a. Develop strategiesb. Planc. Actd. Control
Business activities:
d 1. A manager evaluates progress one year into the project.
b 2. Employees submit suggestions for new investments.
3. The company builds a new factory.
4. Top management attends a retreat to set long-term goals.
5. Proposed investments are analyzed.
6. Proposed investments are ranked.
7. New equipment is purchased.
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Match the following business activities to the steps in capital budgeting process:
Steps in the capital budgeting process:a. Develop strategiesb. Planc. Actd. Control
Business activities:
d 1. A manager evaluates progress one year into the project.
b 2. Employees submit suggestions for new investments.
c 3. The company builds a new factory.
4. Top management attends a retreat to set long-term goals.
5. Proposed investments are analyzed.
6. Proposed investments are ranked.
7. New equipment is purchased.
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Match the following business activities to the steps in capital budgeting process:
Steps in the capital budgeting process:a. Develop strategiesb. Planc. Actd. Control
Business activities:
d 1. A manager evaluates progress one year into the project.
b 2. Employees submit suggestions for new investments.
c 3. The company builds a new factory.
a 4. Top management attends a retreat to set long-term goals.
5. Proposed investments are analyzed.
6. Proposed investments are ranked.
7. New equipment is purchased.
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Match the following business activities to the steps in capital budgeting process:
Steps in the capital budgeting process:a. Develop strategiesb. Planc. Actd. Control
Business activities:
d 1. A manager evaluates progress one year into the project.
b 2. Employees submit suggestions for new investments.
c 3. The company builds a new factory.
a 4. Top management attends a retreat to set long-term goals.
b 5. Proposed investments are analyzed.
6. Proposed investments are ranked.
7. New equipment is purchased.
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Match the following business activities to the steps in capital budgeting process:
Steps in the capital budgeting process:a. Develop strategiesb. Planc. Actd. Control
Business activities:
d 1. A manager evaluates progress one year into the project.
b 2. Employees submit suggestions for new investments.
c 3. The company builds a new factory.
a 4. Top management attends a retreat to set long-term goals.
b 5. Proposed investments are analyzed.
b 6. Proposed investments are ranked.
7. New equipment is purchased.
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Match the following business activities to the steps in capital budgeting process:
Steps in the capital budgeting process:a. Develop strategiesb. Planc. Actd. Control
Business activities:
d 1. A manager evaluates progress one year into the project.
b 2. Employees submit suggestions for new investments.
c 3. The company builds a new factory.
a 4. Top management attends a retreat to set long-term goals.
b 5. Proposed investments are analyzed.
b 6. Proposed investments are ranked.
c 7. New equipment is purchased.
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Learning Objective 2
Use the payback and Use the payback and the accounting rate of the accounting rate of
return methods to make return methods to make capital investment capital investment
decisionsdecisions
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Payback with Equal AnnualNet Cash Inflows
Smart Touch Learning is considering investing $240,000 in:
•Hardware and software to provide a business-to-business (B2B) portal. Smart Touch Learning expects the portal to save $60,000 per year for each of the six years of its useful life.
•An upgrade to its website. The company expects the upgraded website to generate $80,000 in net cash inflows each year of its three-year life.
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Payback with Equal AnnualNet Cash Inflows
Payback =Amount invested
Expected annual net cash inflow
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Payback with Equal AnnualNet Cash Inflows
Payback =Amount invested
Expected annual net cash inflow
Payback for B2B portal =$240,000
= 4 years$60,000 per year
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Payback with Equal AnnualNet Cash Inflows
Payback =Amount invested
Expected annual net cash inflow
Payback for B2B portal =$240,000
= 4 years$60,000 per year
Payback for website upgrade =$240,000
= 3 years$80,000 per year
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Payback—Equal AnnualNet Cash Inflows
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Payback—Unequal AnnualNet Cash Inflows
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Payback with Unequal AnnualNet Cash Inflows
Payback for Z80 portal = 3 years +$10,000 (amount needed to complete recovery in year 4)
= 3.2 years$50,000 (net cash inflow in year 4)
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Ranking by the Payback Method
Rank Project Payback Period
1 Website upgrade 3.0 years
2 Z80 portal 3.2 years
3 B2B portal 4.0 years
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Comparing Payback Periods Between Investments
Exhibit 26-6 Comparing Payback Periods Between Investments
Payback Period
0 1 2 3 4 5
Years
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B2B Portal - 4.0 Years($120,000 net cash inflow after payback period ignored)
Z80 Portal - 3.2 Years($150,000 net cash inflow after payback period
ignored)
Website Upgrade - 3.0 Years(No additional cash inflows)
Decision Rule for Payback
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DECISION RULE: Payback
Investments with shorter payback periods are moredesirable, all else being equal.
Accounting Rate ofReturn (ARR) Formula
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ARR =Average annual operating income
Average amount invested
Calculating Average AnnualIncome from Capital Investment
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Average Annual Operating Income
Total net cash inflows during operating life of the asset ($60,000 per year × 6 years) $ 360,000
Less: Total depreciation during operating life of the asset ($240,000 – $0) 240,000
Total operating income during operating life $ 120,000
Divide by: Asset’s operating life in years ÷ 6 years
Average annual operating income from asset $ 20,000
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Average Amount Invested
Average amount invested = (Amount invested + Residual value) / 2
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Average Amount Invested
Average amount invested = (Amount invested + Residual value) / 2
= ($240,000 + $0) / 2
= $120,000
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ARR of B2B
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ARR of B2B =Average annual operating income
Average amount invested
ARR of B2B
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ARR of B2B =Average annual operating income
Average amount invested
=$20,000
= 0.167 = 16.7%$120,000
Average Annual Operating Income
Total net cash inflows during operating life of the asset $ 360,000
(Add inflows from each year, not including residual value)
Less: Total depreciation during operating life of the asset ($240,000 – $30,000) 210,000
Total operating income during operating life $ 150,000
Divide by: Asset’s operating life in years ÷ 6 years
Average annual operating income from asset $ 25,000
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Average Amount Invested
Average amount invested = (Amount invested + Residual value) / 2
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Average Amount Invested
Average amount invested = (Amount invested + Residual value) / 2
= ($240,000 + $30,000) / 2
= $135,000
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ARR of Z80
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ARR of Z80 =Average annual operating income
Average amount invested
ARR of Z80
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ARR of Z80 =Average annual operating income
Average amount invested
=$25,000
= 0.185 = 18.5%$135,000
Decision Rule for AccountingRate of Return (ARR)
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DECISION RULE: Accounting Rate of Return (ARR)
If the expected ARR meets or exceedsthe required rate of return:
If the expected ARR is less thanthe required rate of return:
Invest Do not invest
Lockwood Company is considering a capital investment in machinery:
Initial investment $ 600,000
Residual value 50,000
Expected annual net cash inflows 100,000
Expected useful life 8 years
Required rate of return 12%
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8. Calculate the payback.
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8. Calculate the payback.
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Payback for machinery =$600,000
= 6 years$100,000 per year
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9. Calculate the ARR. Round the percentage to two decimal places.
Total net cash inflows during operating life of the asset ($100,000/yr. × 8 yrs.) $ 800,000
Less: Total depreciation during operating life of the asset ($600,000 – $50,000) 550,000
Total operating income during operating life $ 250,000
Divide by: Asset’s operating life in years ÷ 8 years
Average annual operating income from asset $ 31,250
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Average amount invested = (Amount invested + Residual value) / 2
= ($600,000 + $50,000) / 2
= $325,000
ARR =$31,250
= 0.0962 = 9.62%$325,000
9. Calculate the ARR. Round the percentage to two decimal places.
10. Based on your answers to the above questions, should Lockwood invest in the machinery?
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10. Based on your answers to the above questions, should Lockwood invest in the machinery?
Lockwood should not invest in the machinery. While it passes the payback analysis, the expected ARR of 9.62% is less than the company’s required rate of return of 12%.
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Learning Objective 3
Use the time value of Use the time value of money to compute the money to compute the present values of lump present values of lump
sums and annuitiessums and annuities
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Capital Investment Analysis Methods That Use the Time Value of Money
• Net present value (NPV)• Internal rate of return (IRR)
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Time Value of Money Depends on Several Key Factors
• The principal amount (p)
• The number of periods (n)
• The interest rate (i)
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Simple Interest versus Compound Interest—$10,000 at 6% for 5 Years
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Future Value and Present Value
$10,000 principal invested for five years at 6% interestFuture value = Principal + Interest earned
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Future Value and Present Value
$10,000 principal invested for five years at 6% interestFuture value = Principal + Interest earned
= $10,000 + $3,383
= $13,383
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Future Value and Present Value
$10,000 principal invested for five years at 6% interestFuture value = Principal + Interest earned
= $10,000 + $3,383
= $13,383
Future value = Present value + Interest earned
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Future Value and Present Value
$10,000 principal invested for five years at 6% interestFuture value = Principal + Interest earned
= $10,000 + $3,383
= $13,383
Future value = Present value + Interest earned
We can rearrange the equation as follows:
Present value = Future Value – Interest earned
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Future Value and Present Value
$10,000 principal invested for five years at 6% interestFuture value = Principal + Interest earned
= $10,000 + $3,383
= $13,383
Future value = Present value + Interest earned
We can rearrange the equation as follows:
Present value = Future Value – Interest earned
$10,000 = $13,383 – $3,383
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Present Value Tables
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Table Used to calculate the value today of
• Present Value of $1 (Appendix B, Table B-1)
One future amount(a lump sum)
• Present Value of Annuity of $1 (Appendix B, Table B-2)
A series of equal future amounts (annuities)
Present Value of a Lump Sum
How much would I have to invest today (in the present time) to have $13,383 five years in the future if I invested at 6%?
Present value = Future value × PV factor for i = 6%, n = 5
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Present Value of a Lump Sum
How much would I have to invest today (in the present time) to have $13,383 five years in the future if I invested at 6%?
Present value = Future value × PV factor for i = 6%, n = 5
= $13,383 × 0.747
= $9,997
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Present Value of an Annuity
How much would I have to invest today (in the present time) to receive $2,000 at the end of each year for five years if I invested at 6%?
Present value = Amount of each cash inflow × Annuity PV factor for i = 6%, n = 5
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Present Value of an Annuity
How much would I have to invest today (in the present time) to receive $2,000 at the end of each year for five years if I invested at 6%?
Present value = Amount of each cash inflow × Annuity PV factor for i = 6%, n = 5
= $2,000 × 4.212
= $8,424
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Verification of Present Value of an Annuity Calculation
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Present Value Summary—Lotto Example
Let’s assume you have just won the lottery after purchasing one $5 lottery ticket. The state offers you the following three payout options for your after-tax prize money:Option 1: $1,000,000 nowOption 2: $150,000 at the end of each year for the next 10 years ($1,500,000 total)Option 3: $2,000,000 at the end of 10 years
Which alternative should you take?
(Assume an 8% interest rate.)
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Present Value Summary—Lotto Example
Option 1: Present value = $1,000,000
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Present Value Summary—Lotto Example
Option 1: Present value = $1,000,000
Option 2:
Present value = Amount of each cash inflow × Annuity PV factor for i = 8%, n = 10
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Present Value Summary—Lotto Example
Option 1: Present value = $1,000,000
Option 2:
Present value = Amount of each cash inflow × Annuity PV factor for i = 8%, n = 10
= $150,000 × 6.710
= $1,006,500
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Present Value Summary—Lotto Example
Option 1: Present value = $1,000,000
Option 2:
Present value = Amount of each cash inflow × Annuity PV factor for i = 8%, n = 10
= $150,000 × 6.710
= $1,006,500
Option 3:
Present value = Principal × PV factor for i = 8%, n = 10
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Present Value Summary—Lotto Example
Option 1: Present value = $1,000,000
Option 2:
Present value = Amount of each cash inflow × Annuity PV factor for i = 8%, n = 10
= $150,000 × 6.710
= $1,006,500
Option 3:
Present value = Principal × PV factor for i = 8%, n = 10
= $2,000,000 × 0.463
= $926,000
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Present Value of Lottery Payout Options
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Calculate the present value of the following future cash flows, rounding all calculations
to the nearest dollar:
11.$5,000 received in three years with interest of 10%.
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Calculate the present value of the following future cash flows, rounding all calculations
to the nearest dollar:
11.$5,000 received in three years with interest of 10%.
This is an example of a lump sum payment:
Present value = Principal × PV factor for i = 10%, n = 3
= $5,000 × 0.751
= $3,755
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Calculate the present value of the following future cash flows, rounding all calculations
to the nearest dollar:
12.$5,000 received in each of the following three years with interest of 10%.
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Calculate the present value of the following future cash flows, rounding all calculations
to the nearest dollar:
12.$5,000 received in each of the following three years with interest of 10%.
This is an example of an annuity:
Present value = Amount of each cash inflow × Annuity PV factor for i = 10%, n = 3= $5,000 × 2.487= $12,435
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Calculate the present value of the following future cash flows, rounding all calculations
to the nearest dollar:
13.Payments of $2,000, $3,000, and $4,000 received in years 1, 2, and 3, respectively, with interest of 7%.
Although this example has three payments, they are not equal payments. Therefore, this is not an annuity, but a series of lump sums.
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Year 1: Present value = Principal × PV factor for i = 7%, n = 1
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Year 1: Present value = Principal × PV factor for i = 7%, n = 1
= $2,000 × 0.935
= $1,870
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Year 1: Present value = Principal × PV factor for i = 7%, n = 1
= $2,000 × 0.935
= $1,870
Year 2: Present value = Principal × PV factor for i = 7%, n = 2
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Year 1: Present value = Principal × PV factor for i = 7%, n = 1
= $2,000 × 0.935
= $1,870
Year 2: Present value = Principal × PV factor for i = 7%, n = 2
= $3,000 × 0.873
= $2,619
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Year 1: Present value = Principal × PV factor for i = 7%, n = 1
= $2,000 × 0.935
= $1,870
Year 2: Present value = Principal × PV factor for i = 7%, n = 2
= $3,000 × 0.873
= $2,619
Year 3: Present value = Principal × PV factor for i = 7%, n = 3
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Year 1: Present value = Principal × PV factor for i = 7%, n = 1
= $2,000 × 0.935
= $1,870
Year 2: Present value = Principal × PV factor for i = 7%, n = 2
= $3,000 × 0.873
= $2,619
Year 3: Present value = Principal × PV factor for i = 7%, n = 3
= $4,000 × 0.816
= $3,264
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Year 1: Present value = Principal × PV factor for i = 7%, n = 1
= $2,000 × 0.935
= $1,870
Year 2: Present value = Principal × PV factor for i = 7%, n = 2
= $3,000 × 0.873
= $2,619
Year 3: Present value = Principal × PV factor for i = 7%, n = 3
= $4,000 × 0.816
= $3,264
The total present value is $7,753 ($1,870 + $2,619 + $3,264).
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Learning Objective 4
Use discounted cash Use discounted cash flow methods to make flow methods to make
capital investment capital investment decisionsdecisions
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Expected Cash Inflowsfor Two Projects
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Net Present Value
• Measures the net difference between– The present value of the investment’s net
cash inflows– The investment’s cost (cash outflows)
• Use minimum required rate of return– Discount rate– Hurdle rate
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NPV with Equal Periodic Net Cash Inflows—Laptop Project
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NPV with Equal Periodic Net Cash Inflows—Laptop Project
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NPV with Equal Periodic Net Cash Inflows—Laptop Project
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Decision Rule forNet Present Value (NPV)
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DECISION RULE: Net Present Value (NPV)
If the NPV is positive: If the NPV is negative:
Invest Do not invest
NPV with Unequal Periodic Net Cash Inflows—Desktop Project
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Laptop Project versusDesktop Project
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NPV of a Project with Residual Value
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Smart Touch LearningCapital Investment Options
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Profitability Index—Laptop and Desktop Projects
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Internal Rate of Return (IRR)
NPV = Present value of net cash inflows − Initial investment
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Internal Rate of Return (IRR)
NPV = Present value of net cash inflows − Initial investment
If:
NPV = 0
then:
Initial investment = Present value of net cash inflows
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IRR with Equal Periodic Net Cash Inflows—Step 1
1. Initial investment = PV of net cash inflows
Initial investment = Amount of cash inflow × Annuity PV factor (i = ?, n = given)
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IRR With Equal Periodic Net Cash Inflows—Step 2
1. Initial investment = PV of net of net cash inflows
Initial investment = Amount of cash inflow × Annuity PV factor (i = ?, n = given)
2. $1,000,000 = $305,450 × Annuity PV factor (i =?, n = 5)
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IRR with Equal Periodic Net Cash Inflows—Step 3
1. Initial investment = PV of net of net cash inflows
Initial investment = Amount of cash inflow × Annuity PV factor (i = ?, n = given)
2. $1,000,000 = $305,450 × Annuity PV factor (i =?, n = 5)
3. Annuity PV factor (i = ?, n = 5) = Initial investment / Amount of cash inflow
= $1,000,000 / $305,450
= 3.274
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IRR with Equal Periodic Net Cash Inflows—Step 4
1. Initial investment = PV of net of net cash inflows
Initial investment = Amount of cash inflow × Annuity PV factor (i = ?, n = given)
2. $1,000,000 = $305,450 × Annuity PV factor (i =?, n = 5)
3. Annuity PV factor (i = ?, n = 5) = Initial investment / Amount of cash inflow
= $1,000,000 / $305,450
= 3.274
4. Find the interest rate that corresponds to this Annuity PV factor.
Scan the row corresponding to the project’s expected life (5 years).
Choose the column(s) with the number closest to the Annuity PV factor you calculated in step 3.
The 3.274 annuity factor is in the 16% column. Therefore, the IRR of the laptop project is 16%.
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Proof That NPV = 0 When the Discount Rate = IRR
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Decision Rule for Internal Rate of Return (IRR)
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DECISION RULE: Internal Rate of Return (IRR)
If the IRR meets or exceedsthe required rate of return:
If the IRR is less thanthe required rate of return:
Invest Do not invest
IRR for Smart TouchLearning’s B2B Portal
Annuity PV factor (i = ?, n = 6) = Initial investment / Amount of cash inflow
= $240,000 / $60,000
= 4.000
Find the interest rate that corresponds to this Annuity PV factor.
Scan the row corresponding to the project’s expected life (6 years).
Choose the column(s) with the number closest to the Annuity PV factor you calculated.
The IRR is between 12% and 14%.
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IRR with Unequal PeriodicNet Cash Flows
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Comparison of Capital Investment Analysis Methods
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Laptop Computer Project and Desktop Computer Project
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Capital Investment AnalysisUsing Excel
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Decision Tree for Capital Rationing
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Cornell Company is considering a project with an initial investment of $596,500 that is expected to produce cash inflows of $125,000 for nine years. Cornell’s required rate of return is 12%.
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15. What is the IRR of the project?
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15. What is the IRR of the project?
Annuity PV factor (i = ?, n = 9) = Initial investment / Amount of cash inflow
= $596,500 / $125,000
= 4.772
The IRR is 15%, which is the factor determined below in the n = 9 row of Table B-2.
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16. Is this an acceptable project for Cornell?
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16. Is this an acceptable project for Cornell?
Unless negative qualitative factors exist, Cornell should accept the project because the IRR of 15% is more than the required rate of 12%. Also, the net present value is positive; $69,500.
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