module 8
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Key Concepts and Skills
- Understand:
- The payback rule and its shortcomings
- Accounting rates of return and their problems
- The internal rate of return and its strengths and weaknesses
- The net present value rule and why it is the best decision criteria
- The modified internal rate of return
- The profitability index and its relation to NPV
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Chapter Outline
8.1 Net Present Value
8.2 The Payback Rule
8.3 The Average Accounting Return
8.4 The Internal Rate of Return
8.5 The Profitability Index
8.6 The Practice of Capital Budgeting
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Capital Budgeting
- Analysis of potential projects
- Long-term decisions
- Large expenditures
- Difficult/impossible to reverse
- Determines firm’s strategic direction
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Good Decision Criteria
- All cash flows considered?
- TVM considered?
- Risk-adjusted?
- Ability to rank projects?
- Indicates added value to the firm?
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Net Present Value
How much value is created from undertaking an investment?
Step 1: Estimate the expected future cash flows.
Step 2: Estimate the required return for projects of this risk level.
Step 3: Find the present value of the cash flows and subtract the initial investment to arrive at the Net Present Value.
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Net Present Value
Sum of the PVs of all cash flows
8-*
Initial cost often is CF0 and is an outflow.
NPV =
∑
n
t = 1
CFt
(1 + R)t
- CF0
NOTE: t=0
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
NPV =
∑
n
t = 0
CFt
(1 + R)t
8.*
NPV – Decision Rule
- If NPV is positive, accept the project
- NPV > 0 means:
- Project is expected to add value to the firm
- Will increase the wealth of the owners
- NPV is a direct measure of how well this project will meet the goal of increasing shareholder wealth.
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Sample Project Data
- You are looking at a new project and have estimated the following cash flows, net income and book value data:
- Year 0: CF = -165,000
- Year 1: CF = 63,120 NI = 13,620
- Year 2: CF = 70,800 NI = 3,300
- Year 3: CF = 91,080 NI = 29,100
- Average book value = $72,000
- Your required return for assets of this risk is 12%.
- This project will be the example for all problem exhibits in this chapter.
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Computing NPV for the Project
- Using the formula:
NPV = -165,000/(1.12)0 + 63,120/(1.12)1 + 70,800/(1.12)2 + 91,080/(1.12)3 = 12,627.41
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
NPV
| Year | 0 | 1 | 2 | 3 |
| Cash Flows | -165000 | 63120 | 70800 | 91080 |
| Required Return | 0.12 | |||
| NPV - WRONG | $11,274.48 | |||
| NPV - RIGHT | $12,627.41 | |||
| IRR | 16% | 16.13% | ||
| Default Format |
NPV (2)
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(C3,B8:B10) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| CALCULATOR | |||
| CF | |||
| CF0 | (165,000.00) | ||
| C01 | 63,120.00 | ||
| F01 | 1.00 | ||
| C02 | 70,800.00 | ||
| F02 | 1.00 | ||
| C03 | 91,080.00 | ||
| F03 | 1.00 | ||
| NPV | |||
| I | 12.00 | ||
| CPT | 12,627.41 |
IRR_a
| Capital Budgeting Project | IRR | |
| Required Return = | 12% | |
| IRR | ||
| Year | CF | |
| 0.00 | (165,000.00) | |
| 1.00 | 63,120.00 | |
| 2.00 | 70,800.00 | |
| 3.00 | 91,080.00 | |
| EXCEL | =IRR(B7:B10) | 16.13% |
| CALCULATOR | ||
| CF | ||
| CF0 | (165,000.00) | |
| C01 | 63,120.00 | |
| F01 | 1.00 | |
| C02 | 70,800.00 | |
| F02 | 1.00 | |
| C03 | 91,080.00 | |
| F03 | 1.00 | |
| IRR | ||
| CPT | 16.13 |
IRR_b
| Capital Budgeting Project | IRR | |
| Required Return = | 12% | |
| IRR | ||
| Year | CF | |
| 0.00 | (165,000.00) | |
| 1.00 | 63,120.00 | |
| 2.00 | 70,800.00 | |
| 3.00 | 91,080.00 | |
| EXCEL | =IRR(B7:B10) | 16.13% |
| CALCULATOR | ||
| CF | ||
| CF0 | (165,000.00) | |
| C01 | 63,120.00 | |
| F01 | 1.00 | |
| C02 | 70,800.00 | |
| F02 | 1.00 | |
| C03 | 91,080.00 | |
| F03 | 1.00 | |
| IRR | ||
| CPT | 16.13 |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | $ (90,000) | |
| 1 | $ 132,000 | |
| 2 | $ 100,000 | |
| 3 | $ (150,000) | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
Computing NPV for the Project
Using the TI BAII+ CF Worksheet
Display You Enter
CF, 2nd,CLR WORK
C00 -165000 Enter, Down
C01 63120 Enter, Down
F01 1 Enter, Down
C02 70800 Enter, Down
F02 1 Enter, Down
C03 91080 Enter, Down
F03 1 Enter, NPV
I 12 Enter, Down
NPV CPT
12,627.41
8-*
Cash Flows:
CF0 = -165000
CF1 = 63120
CF2 = 70800
CF3 = 91080
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Calculating NPVs with Excel
- NPV function: =NPV(rate,CF01:CFnn)
- First parameter = required return entered as a decimal (5% = .05)
- Second parameter = range of cash flows beginning with year 1
- After computing NPV, subtract the initial investment (CF0)
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
NPV
| Year | 0 | 1 | 2 | 3 |
| Cash Flows | -165000 | 63120 | 70800 | 91080 |
| Required Return | 0.12 | |||
| NPV - WRONG | $11,274.48 | |||
| NPV - RIGHT | $12,627.41 | |||
| IRR | 16% | 16.13% | ||
| Default Format |
NPV (2)
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| CALCULATOR | |||
| CF | |||
| CF0 | (165,000.00) | ||
| C01 | 63,120.00 | ||
| F01 | 1.00 | ||
| C02 | 70,800.00 | ||
| F02 | 1.00 | ||
| C03 | 91,080.00 | ||
| F03 | 1.00 | ||
| NPV | |||
| I | 12.00 | ||
| CPT | 12,627.41 |
IRR_a
| Capital Budgeting Project | IRR | |
| Required Return = | 12% | |
| IRR | ||
| Year | CF | |
| 0.00 | (165,000.00) | |
| 1.00 | 63,120.00 | |
| 2.00 | 70,800.00 | |
| 3.00 | 91,080.00 | |
| EXCEL | =IRR(B7:B10) | 16.13% |
| CALCULATOR | ||
| CF | ||
| CF0 | (165,000.00) | |
| C01 | 63,120.00 | |
| F01 | 1.00 | |
| C02 | 70,800.00 | |
| F02 | 1.00 | |
| C03 | 91,080.00 | |
| F03 | 1.00 | |
| IRR | ||
| CPT | 16.13 |
IRR_b
| Capital Budgeting Project | IRR | |
| Required Return = | 12% | |
| IRR | ||
| Year | CF | |
| 0.00 | (165,000.00) | |
| 1.00 | 63,120.00 | |
| 2.00 | 70,800.00 | |
| 3.00 | 91,080.00 | |
| EXCEL | =IRR(B7:B10) | 16.13% |
| CALCULATOR | ||
| CF | ||
| CF0 | (165,000.00) | |
| C01 | 63,120.00 | |
| F01 | 1.00 | |
| C02 | 70,800.00 | |
| F02 | 1.00 | |
| C03 | 91,080.00 | |
| F03 | 1.00 | |
| IRR | ||
| CPT | 16.13 |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | $ (90,000) | |
| 1 | $ 132,000 | |
| 2 | $ 100,000 | |
| 3 | $ (150,000) | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ||||||||
| 0 | -60 | ||||||||
| 1 | 155 | ||||||||
| 2 | -100 | ||||||||
| Method 1: Discounting Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 155 | |||||||
| 2 | -100 | 0 | |||||||
| IRR= | 19.74% | ||||||||
| Method 2: Reinvestment Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -60 | |||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 86 | 19.87% | |||||
| IRR= | 19.72% | ||||||||
| Method 3: Combination Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 186 | ||||||
| IRR= | 19.87% | ||||||||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
Net Present Value
Sum of the PVs of all cash flows.
8-*
<< CALCULATOR
<< EXCEL
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Rationale for the NPV Method
- NPV = PV inflows – Cost
NPV=0 → Project’s inflows are “exactly sufficient to repay the invested capital and provide the required rate of return”
- NPV = net gain in shareholder wealth
- Rule: Accept project if NPV > 0
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
NPV Method
- Meets all desirable criteria
- Considers all CFs
- Considers TVM
- Adjusts for risk
- Can rank mutually exclusive projects
- Directly related to increase in VF
- Dominant method; always prevails
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Payback Period
- How long does it take to recover the initial cost of a project?
- Computation
- Estimate the cash flows
- Subtract the future cash flows from the initial cost until initial investment is recovered
- A “break-even” type measure
- Decision Rule – Accept if the payback period is less than some preset limit
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Computing Payback for the Project
- Do we accept or reject the project?
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Decision Criteria Test
Payback
- Does the payback rule:
- Account for the time value of money?
- Account for the risk of the cash flows?
- Provide an indication about the increase in value?
- Permit project ranking?
- Should we consider the payback rule for our primary decision rule?
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Advantages and Disadvantages of Payback
- Advantages
- Easy to understand
- Adjusts for uncertainty of later cash flows
- Biased towards liquidity
- Disadvantages
- Ignores the time value of money
- Requires an arbitrary cutoff point
- Ignores cash flows beyond the cutoff date
- Biased against long-term projects, such as research and development, and new projects
8-*
ASKS THE WRONG QUESTION!
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Average Accounting Return
- Many different definitions for average accounting return (AAR)
- In this book:
- Note: Average book value depends on how the asset is depreciated.
- Requires a target cutoff rate
- Decision Rule: Accept the project if the AAR is greater than target rate.
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Computing AAR for the Project
- Sample Project Data:
- Year 0: CF = -165,000
- Year 1: CF = 63,120 NI = 13,620
- Year 2: CF = 70,800 NI = 3,300
- Year 3: CF = 91,080 NI = 29,100
- Average book value = $72,000
- Required average accounting return = 25%
- Average Net Income:
($13,620 + 3,300 + 29,100) / 3 = $15,340
- AAR = $15,340 / 72,000 = .213 = 21.3%
- Do we accept or reject the project?
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Decision Criteria Test - AAR
- Does the AAR rule account for the time value of money?
- Does the AAR rule account for the risk of the cash flows?
- Does the AAR rule provide an indication about the increase in value?
- Should we consider the AAR rule for our primary decision criteria?
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Advantages and Disadvantages
of AAR
- Advantages
- Easy to calculate
- Needed information usually available
- Disadvantages
- Not a true rate of return
- Time value of money ignored
- Uses an arbitrary benchmark cutoff rate
- Based on accounting net income and book values, not cash flows and market values
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Internal Rate of Return
- Most important alternative to NPV
- Widely used in practice
- Intuitively appealing
- Based entirely on the estimated cash flows
- Independent of interest rates
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
IRR: Definition and
Decision Rule
- Definition:
- IRR = discount rate that makes the NPV = 0
- Decision Rule:
- Accept the project if the IRR is greater than the required return
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
NPV vs. IRR
8-*
IRR: Enter NPV = 0, solve for IRR.
NPV: Enter r, solve for NPV
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Computing IRR for the Project
- Without a financial calculator or Excel, this becomes a trial-and-error process
- Calculator
- Enter the cash flows as for NPV
- Press IRR and then CPT
- IRR = 16.13% > 12% required return
- Do we accept or reject the project?
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Computing IRR for the Project
Using the TI BAII+ CF Worksheet
Display You Enter
CF, 2nd, CLR WORK
C00 165000 Enter, Down
C01 63120 Enter, Down
F01 1 Enter, Down
C02 70800 Enter, Down
F02 1 Enter, Down
C03 91080 Enter, Down
F03 1 Enter, IRR
IRR CPT
16.1322
8-*
Cash Flows:
CF0 = -165000
CF1 = 63120
CF2 = 70800
CF3 = 91080
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Calculating IRR with Excel
- Start with the cash flows as you did to solve for NPV
- Use the IRR function
- Enter the range of cash flows, beginning with the initial cash flow (Cash flow 0)
- You can enter a guess, but it is not necessary
- The default format is a whole percent
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Calculating IRR with Excel
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ||||||||
| 0 | -60 | ||||||||
| 1 | 155 | ||||||||
| 2 | -100 | ||||||||
| Method 1: Discounting Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 155 | |||||||
| 2 | -100 | 0 | |||||||
| IRR= | 19.74% | ||||||||
| Method 2: Reinvestment Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -60 | |||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 86 | 19.87% | |||||
| IRR= | 19.72% | ||||||||
| Method 3: Combination Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 186 | ||||||
| IRR= | 19.87% | ||||||||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ||||||||
| 0 | -60 | ||||||||
| 1 | 155 | ||||||||
| 2 | -100 | ||||||||
| Method 1: Discounting Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 155 | |||||||
| 2 | -100 | 0 | |||||||
| IRR= | 19.74% | ||||||||
| Method 2: Reinvestment Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -60 | |||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 86 | 19.87% | |||||
| IRR= | 19.72% | ||||||||
| Method 3: Combination Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 186 | ||||||
| IRR= | 19.87% | ||||||||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
NPV Profile For The Project
8-*
IRR = 16.13%
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Decision Criteria Test
IRR
- Does the IRR rule:
- Account for the time value of money?
- Account for the risk of the cash flows?
- Provide an indication about the increase in value?
- Permit project ranking?
- Should we consider the IRR rule for our primary decision criteria?
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
IRR - Advantages
- Preferred by executives
- Intuitively appealing
- Easy to communicate the value of a project
- If the IRR is high enough, may not need to estimate a required return
- Considers all cash flows
- Considers time value of money
- Provides indication of risk
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
IRR - Disadvantages
- Can produce multiple answers
- Cannot rank mutually exclusive projects
- Reinvestment assumption flawed
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Summary of Decisions for the Project
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
| Summary | |
| Net Present Value | Accept |
| Payback Period | ??? |
| Average Accounting Return | ??? |
| Internal Rate of Return | Accept |
8.*
NPV vs. IRR
- NPV and IRR will generally give the same decision
- Exceptions
- Non-conventional cash flows
- Cash flow sign changes more than once
- Mutually exclusive projects
- Initial investments are substantially different
- Timing of cash flows is substantially different
- Will not reliably rank projects
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
IRR & Non-Conventional
Cash Flows
- “Non-conventional”
- Cash flows change sign more than once
- Most common:
- Initial cost (negative CF)
- A stream of positive CFs
- Negative cash flow to close project.
- For example, nuclear power plant or strip mine.
- More than one IRR ….
- Which one do you use to make your decision?
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Multiple IRRs
- Descartes Rule of Signs
- Polynomial of degree n→n roots
- When you solve for IRR you are solving for the root of an equation
- 1 real root per sign change
- Rest = imaginary (i2 = -1)
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Non-Conventional Cash Flows
- Suppose an investment will cost $90,000 initially and will generate the following cash flows:
- Year 1: 132,000
- Year 2: 100,000
- Year 3: -150,000
- The required return is 15%.
- Should we accept or reject the project?
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Non-Conventional Cash Flows
Summary of Decision Rules
- NPV > 0 at 15% required return, so you should Accept
- IRR =10.11% (using a financial calculator), which would tell you to Reject
- Recognize the non-conventional cash flows and look at the NPV profile
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
NPV
| Year | 0 | 1 | 2 | 3 |
| Cash Flows | -165000 | 63120 | 70800 | 91080 |
| Required Return | 0.12 | |||
| NPV - WRONG | $11,274.48 | |||
| NPV - RIGHT | $12,627.41 | |||
| IRR | 16% | 16.13% | ||
| Default Format |
NPV (2)
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR_a
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ||||||||
| 0 | -60 | ||||||||
| 1 | 155 | ||||||||
| 2 | -100 | ||||||||
| Method 1: Discounting Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 155 | |||||||
| 2 | -100 | 0 | |||||||
| IRR= | 19.74% | ||||||||
| Method 2: Reinvestment Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -60 | |||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 86 | 19.87% | |||||
| IRR= | 19.72% | ||||||||
| Method 3: Combination Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 186 | ||||||
| IRR= | 19.87% | ||||||||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
NPV Profile
8-*
IRR = 10.11% and 42.66%
When you cross the x-axis more than once, there will be more than one return that solves the equation
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Independent versus Mutually Exclusive Projects
- Independent
- The cash flows of one project are unaffected by the acceptance of the other.
- Mutually Exclusive
- The acceptance of one project precludes accepting the other.
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Reinvestment Rate Assumption
- IRR assumes reinvestment at IRR
- NPV assumes reinvestment at the firm’s weighted average cost of capital (opportunity cost of capital)
- More realistic
- NPV method is best
- NPV should be used to choose between mutually exclusive projects
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Example of Mutually Exclusive Projects
8-*
The required return for both projects is 10%.
Which project should you accept and why?
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
| Period | Project A | Project B |
| 0 | -500 | -400 |
| 1 | 325 | 325 |
| 2 | 325 | 200 |
| IRR | 19.43% | 22.17% |
| NPV | 64.05 | 60.74 |
8.*
NPV Profiles
8-*
IRR for A = 19.43%
IRR for B = 22.17%
Crossover Point = 11.8%
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Two Reasons NPV Profiles Cross
- Size (scale) differences.
- Smaller project frees up funds sooner for investment.
- The higher the opportunity cost, the more valuable these funds, so high discount rate favors small projects.
- Timing differences.
- Project with faster payback provides more CF in early years for reinvestment.
- If discount rate is high, early CF especially good
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Conflicts Between NPV and IRR
- NPV directly measures the increase in value to the firm
- Whenever there is a conflict between NPV and another decision rule, always use NPV
- IRR is unreliable in the following situations:
- Non-conventional cash flows
- Mutually exclusive projects
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Modified Internal Rate of Return (MIRR)
- Controls for some problems with IRR
- Three Methods:
1.Discounting Approach = Discount future outflows to present and add to CF0
2. Reinvestment Approach = Compound all CFs except the first one forward to end
3. Combination Approach – Discount outflows to present; compound inflows to end
- MIRR will be unique number for each method
- Discount (finance) /compound (reinvestment) rate externally supplied
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
MIRR Method 1
Discounting Approach
8-*
Step 1: Discount future outflows (negative cash flows) to present and add to CF0
Step 2: Zero out negative cash flows which have been added to CF0.
Step 3: Compute IRR normally
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||
| R = | 20% | ||
| Yr | CF | ||
| 0 | -60 | ||
| 1 | 155 | ||
| 2 | -100 | ||
| Method 1: Discounting Approach | |||
| R = | 20% | ||
| Yr | CF | ADJ | MCF |
| 0 | -60 | -69.4444444444 | -129.4444444444 |
| 1 | 155 | 155 | |
| 2 | -100 | 0 | |
| IRR= | 19.74% | ||
| Method 2: Reinvestment Approach | |||
| R = | 20% | ||
| Yr | CF | ADJ | MCF |
| 0 | -60 | -60 | |
| 1 | 155 | 0 | |
| 2 | -100 | 186 | 86 |
| IRR= | 19.72% | ||
| Method 3: Combination Approach | |||
| R = | 20% | ||
| Yr | CF | ADJ | MCF |
| 0 | -60 | -69.4444444444 | -129.4444444444 |
| 1 | 155 | 0 | |
| 2 | -100 | 186 | 186 |
| IRR= | 19.87% | ||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ||||||||
| 0 | -60 | ||||||||
| 1 | 155 | ||||||||
| 2 | -100 | ||||||||
| Method 1: Discounting Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 155 | |||||||
| 2 | -100 | 0 | |||||||
| IRR= | 19.74% | ||||||||
| Method 2: Reinvestment Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -60 | |||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 86 | 19.87% | |||||
| IRR= | 19.72% | ||||||||
| Method 3: Combination Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 186 | ||||||
| IRR= | 19.87% | ||||||||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
MIRR Method 2
Reinvestment Approach
8-*
Step 1: Compound ALL cash flows (except CF0) to end of project’s life
Step 2: Zero out all cash flows which have been
added to the last year of the project’s life.
Step 3: Compute IRR normally
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||
| R = | 20% | ||
| Yr | CF | ||
| 0 | -60 | ||
| 1 | 155 | ||
| 2 | -100 | ||
| Method 1: Discounting Approach | |||
| R = | 20% | ||
| Yr | CF | ADJ | MCF |
| 0 | -60 | -69.4444444444 | -129.4444444444 |
| 1 | 155 | 155 | |
| 2 | -100 | 0 | |
| IRR= | 19.74% | ||
| Method 2: Reinvestment Approach | |||
| R = | 20% | ||
| Yr | CF | ADJ | MCF |
| 0 | -60 | -60 | |
| 1 | 155 | 0 | |
| 2 | -100 | 186 | 86 |
| IRR= | 19.72% | ||
| Method 3: Combination Approach | |||
| R = | 20% | ||
| Yr | CF | ADJ | MCF |
| 0 | -60 | -69.4444444444 | -129.4444444444 |
| 1 | 155 | 0 | |
| 2 | -100 | 186 | 186 |
| IRR= | 19.87% | ||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ||||||||
| 0 | -60 | ||||||||
| 1 | 155 | ||||||||
| 2 | -100 | ||||||||
| Method 1: Discounting Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 155 | |||||||
| 2 | -100 | 0 | |||||||
| IRR= | 19.74% | ||||||||
| Method 2: Reinvestment Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -60 | |||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 86 | 19.87% | |||||
| IRR= | 19.72% | ||||||||
| Method 3: Combination Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 186 | ||||||
| IRR= | 19.87% | ||||||||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
MIRR Method 3
Combination Approach
8-*
Step 1: Discount all outflows (except CF0) to
present and add to CF0.
Step 2: Compound all cash inflows to end of
project’s life
Step 3: Compute IRR normally
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||
| R = | 20% | ||
| Yr | CF | ||
| 0 | -60 | ||
| 1 | 155 | ||
| 2 | -100 | ||
| Method 1: Discounting Approach | |||
| R = | 20% | ||
| Yr | CF | ADJ | MCF |
| 0 | -60 | -69.4444444444 | -129.4444444444 |
| 1 | 155 | 155 | |
| 2 | -100 | 0 | |
| IRR= | 19.74% | ||
| Method 2: Reinvestment Approach | |||
| R = | 20% | ||
| Yr | CF | ADJ | MCF |
| 0 | -60 | -60 | |
| 1 | 155 | 0 | |
| 2 | -100 | 186 | 86 |
| IRR= | 19.72% | ||
| Method 3: Combination Approach | |||
| R = | 20% | ||
| Yr | CF | ADJ | MCF |
| 0 | -60 | -69.4444444444 | -129.4444444444 |
| 1 | 155 | 0 | |
| 2 | -100 | 186 | 186 |
| IRR= | 19.87% | ||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ||||||||
| 0 | -60 | ||||||||
| 1 | 155 | ||||||||
| 2 | -100 | ||||||||
| Method 1: Discounting Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 155 | |||||||
| 2 | -100 | 0 | |||||||
| IRR= | 19.74% | ||||||||
| Method 2: Reinvestment Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -60 | |||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 86 | 19.87% | |||||
| IRR= | 19.72% | ||||||||
| Method 3: Combination Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 186 | ||||||
| IRR= | 19.87% | ||||||||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
MIRR in Excel
- Excel = Method 3
- MIRR = discount rate which causes the PV of a project’s terminal value (TV) to equal the PV of costs (outflows)
- MIRR assumes CFs reinvested at WACC
- Function: =MIRR(Range, FR, RR)
FR = Finance rate (discount)
RR = Reinvestment rate (compound)
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ||||||||
| 0 | -60 | ||||||||
| 1 | 155 | ||||||||
| 2 | -100 | ||||||||
| Method 1: Discounting Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 155 | |||||||
| 2 | -100 | 0 | |||||||
| IRR= | 19.74% | ||||||||
| Method 2: Reinvestment Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -60 | |||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 86 | 19.87% | |||||
| IRR= | 19.72% | ||||||||
| Method 3: Combination Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 186 | ||||||
| IRR= | 19.87% | ||||||||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
MIRR
First, find PV and TV
(FR = RR = 20%)
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
155.0
-100.0
0
1
2
20%
- 60.00
20%
TV inflows
-129.444
PV outflows
186
-69.444
186
Second: Find discount rate that equates PV and TV
8-*
MIRR = 19.87%
186.0
0
1
2
-129.444
TV inflows
PV outflows
MIRR = 19.87%
$129.444 =
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
$186.0
(1+MIRR)2
- Formula:
R = (186 / 129.444)1/2 – 1 = .1987 = 19.87%
- Calculator – the sign convention matters!!!
2 N
-129.444 PV
0 PMT
186 FV
CPT I/Y = 19.87%
- Excel: =RATE(2,0,-129.444,186) = 0.1987
=MIRR(Range, FR, RR) 19.87%
8-*
Second: Find discount rate that equates PV and TV
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
MIRR versus IRR
- MIRR correctly assumes reinvestment at opportunity cost = WACC
- MIRR avoids the multiple IRR problem
- Managers like rate of return comparisons, and MIRR is better for this than IRR
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
Profitability Index
- Measures the benefit per unit cost, based on the time value of money
- A profitability index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value
- Can be very useful in situations of capital rationing
- Decision Rule: If PI > 1.0 Accept
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Profitability Index
- For conventional CF Projects:
PV(Cash Inflows)
Absolute Value of Initial Investment
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Advantages and Disadvantages of Profitability Index
- Advantages
- Closely related to NPV, generally leading to identical decisions
- Considers all CFs
- Considers TVM
- Easy to understand and communicate
- Useful in capital rationing
- Disadvantages
- May lead to incorrect decisions in comparisons of mutually exclusive investments (can conflict with NPV)
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Profitability Index
Example of Conflict with NPV
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ||||||||
| 0 | -60 | ||||||||
| 1 | 155 | ||||||||
| 2 | -100 | ||||||||
| Method 1: Discounting Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 155 | |||||||
| 2 | -100 | 0 | |||||||
| IRR= | 19.74% | ||||||||
| Method 2: Reinvestment Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -60 | |||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 86 | 19.87% | |||||
| IRR= | 19.72% | ||||||||
| Method 3: Combination Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 186 | ||||||
| IRR= | 19.87% | ||||||||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
Capital Budgeting in Practice
- Consider all investment criteria when making decisions
- NPV and IRR are the most commonly used primary investment criteria
- Payback is a commonly used secondary investment criteria
- All provide valuable information
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Summary
Calculate ALL -- each has value
Method What it measures Metric
NPV $ increase in VF $$
Payback Liquidity Years
AAR Acct return (ROA) %
IRR E(R), risk %
PI If rationed Ratio
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
NPV Summary
Net present value =
- Difference between market value (PV of inflows) and cost
- Accept if NPV > 0
- No serious flaws
- Preferred decision criterion
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
IRR Summary
Internal rate of return =
- Discount rate that makes NPV = 0
- Accept if IRR > required return
- Same decision as NPV with conventional cash flows
- Unreliable with:
- Non-conventional cash flows
- Mutually exclusive projects
- MIRR = better alternative
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Payback Summary
Payback period =
- Length of time until initial investment is recovered
- Accept if payback < some specified target
- Doesn’t account for time value of money
- Ignores cash flows after payback
- Arbitrary cutoff period
- Asks the wrong question
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
AAR Summary
Average Accounting Return=
- Average net income/Average book value
- Accept if AAR > Some specified target
- Needed data usually readily available
- Not a true rate of return
- Time value of money ignored
- Arbitrary benchmark
- Based on accounting data not cash flows
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
Profitability Index Summary
Profitability Index =
- Benefit-cost ratio
- Accept investment if PI > 1
- Cannot be used to rank mutually exclusive projects
- May be used to rank projects in the presence of capital rationing
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Quick Quiz
- Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9% and required payback is 4 years.
- What is the payback period?
- What is the NPV?
- What is the IRR?
- Should we accept the project?
- What decision rule should be the primary decision method?
- When is the IRR rule unreliable?
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Quick Quiz Solution
8-*
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ||||||||
| 0 | -60 | ||||||||
| 1 | 155 | ||||||||
| 2 | -100 | ||||||||
| Method 1: Discounting Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 155 | |||||||
| 2 | -100 | 0 | |||||||
| IRR= | 19.74% | ||||||||
| Method 2: Reinvestment Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -60 | |||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 86 | 19.87% | |||||
| IRR= | 19.72% | ||||||||
| Method 3: Combination Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 186 | ||||||
| IRR= | 19.87% | ||||||||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
NPV
| Capital Budgeting Project | NPV | ||
| Required Return = | 12% | ||
| Year | CF | Formula | Disc CFs |
| 0 | (165,000.00) | =(-165000)/(1.12)^0 = | (165,000.00) |
| 1 | 63,120.00 | =(63120)/(1.12)^1 = | 56,357.14 |
| 2 | 70,800.00 | =(70800)/(1.12)^2 = | 56,441.33 |
| 3 | 91,080.00 | =(91080)/(1.12)^3 = | 64,828.94 |
| 12,627.41 | |||
| EXCEL | =NPV(D2,B5:B7) | 177,627.41 | |
| NPV + CF0 | 12,627.41 | ||
| EXCEL | =IRR(B4,B7) | 16.13% |
IRR
| IRR | ||
| Year | CF | |
| 0 | (165,000.00) | |
| 1 | 63,120.00 | |
| 2 | 70,800.00 | |
| 3 | 91,080.00 | |
| EXCEL | =IRR(B3:B6) | 16.13% |
NCCF
| Non-conventional Cash Flows | ||
| I = | 15% | |
| YR | CF | |
| 0 | -$90,000 | |
| 1 | $132,000 | |
| 2 | $100,000 | |
| 3 | -$150,000 | |
| NPV | $1,769.54 | > 0 |
| IRR-1 | 10.11% | < 15% |
| IRR-2 | 42.66% | > 15% |
MIRR
| MIRR | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ||||||||
| 0 | -60 | ||||||||
| 1 | 155 | ||||||||
| 2 | -100 | ||||||||
| Method 1: Discounting Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 155 | |||||||
| 2 | -100 | 0 | |||||||
| IRR= | 19.74% | ||||||||
| Method 2: Reinvestment Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -60 | |||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 86 | 19.87% | |||||
| IRR= | 19.72% | ||||||||
| Method 3: Combination Approach | |||||||||
| R = | 20% | ||||||||
| Yr | CF | ADJ | MCF | ||||||
| 0 | -60 | -69.4444444444 | -129.4444444444 | ||||||
| 1 | 155 | 0 | |||||||
| 2 | -100 | 186 | 186 | ||||||
| IRR= | 19.87% | ||||||||
| Excel: | 19.87% |
PI
| PI vs NPV | ||
| A | B | |
| CF(0) | (10,000.00) | (100,000.00) |
| PV(CIF) | 15,000.00 | 125,000.00 |
| PI | 1.50 | 1.25 |
| NPV | 5,000.00 | 25,000.00 |
QUIZ
| A/1 | B | C | D | E | F |
| 2 | Quick Quiz | Chapter 8 | |||
| 3 | r = | 9% | |||
| 4 | Req. PB = | 4 yrs | |||
| 5 | |||||
| 6 | Cumulatve | Cumulative | |||
| 7 | t | CF | CFs | DCF | DCFs |
| 8 | 0 | (100,000.00) | (100,000.00) | (100,000.00) | (100,000.00) |
| 9 | 1 | 25,000.00 | (75,000.00) | 22,935.78 | (77,064.22) |
| 10 | 2 | 25,000.00 | (50,000.00) | 21,042.00 | (56,022.22) |
| 11 | 3 | 25,000.00 | (25,000.00) | 19,304.59 | (36,717.63) |
| 12 | 4 | 25,000.00 | 0.00 | 17,710.63 | (19,007.00) |
| 13 | 5 | 25,000.00 | 25,000.00 | 16,248.28 | (2,758.72) |
| 14 | (2,758.72) | ||||
| 15 | |||||
| 16 | Payback = | 4 years | |||
| 18 | |||||
| 19 | NPV = | ($2,758.72) | =NPV(E3,C9:C13)+C8 | ||
| 20 | IRR = | 7.93% | =IRR(C8:C13) |
Chapter 8
END
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
8.*
Capital Budgeting ProjectNPV
Required Return =12%
YearCFFormulaDisc CFs
0(165,000.00)=(-165000)/(1.12)^0 =(165,000.00)
163,120.00=(63120)/(1.12)^1 =56,357.14
270,800.00=(70800)/(1.12)^2 =56,441.33
391,080.00=(91080)/(1.12)^3 =64,828.94
12,627.41
å
=
+
=
n
0
t
t
t
)
R
1
(
CF
NPV
2
3
4
5
6
7
8
9
10
11
A B C D
Required Return = 12%
Year CF Formula Disc CFs
0(165,000.00) =(-165000)/(1.12)^0 = (165,000.00)
163,120.00 =(63120)/(1.12)^1 = 56,357.14
270,800.00 =(70800)/(1.12)^2 = 56,441.33
391,080.00 =(91080)/(1.12)^3 = 64,828.94
12,627.41
EXCEL =NPV(D2,B5:B7) 177,627.41
NPV + CF0 12,627.41
å
=
+
=
n
0
t
t
t
)
R
1
(
CF
NPV
0
n
1
t
t
t
CF
)
R
1
(
CF
NPV
-
+
=
å
=
Capital Budgeting Project
Year
CF
Cum. CFs
0
(165,000)
$
(165,000)
$
1
63,120
$
(101,880)
$
2
70,800
$
(31,080)
$
3
91,080
$
60,000
$
Payback =
year 2 +
+ (31080/91080)
Payback =
2.34
years
Value
Book
Average
Income
Net
Average
AAR
=
NPV
)
R
1
(
CF
n
0
t
t
t
=
+
å
=
0
)
IRR
1
(
CF
n
0
t
t
t
=
+
å
=
1
2
3
4
5
6
7
8
A B C
Year CF
0(165,000.00)
163,120.00
270,800.00
391,080.00
EXCEL =IRR(B3:B6) 16.13%
IRR
-20,000
-10,000
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
00.020.040.060.080.10.120.140.160.180.20.22
Discount Rate
NPV
0
)
IRR
1
(
CF
n
0
t
t
t
=
+
å
=
I = 15%
YRCF
0-$90,000
1$132,000
2$100,000
3-$150,000
NPV$1,769.54 > 0
IRR-110.11% < 15%
IRR-242.66% > 15%
($10,000.00)
($8,000.00)
($6,000.00)
($4,000.00)
($2,000.00)
$0.00
$2,000.00
$4,000.00
00.050.10.150.20.250.30.350.40.450.50.55
Discount Rate
NPV
($40.00)
($20.00)
$0.00
$20.00
$40.00
$60.00
$80.00
$100.00
$120.00
$140.00
$160.00
00.050.10.150.20.250.3
Discount Rate
NPV
A
B
Method 1: Discounting Approach
R =20%
YrCFADJMCF
0-60-69.444-129.44444
1155155
2-1000
IRR=19.74%
Method 2: Reinvestment Approach
R =20%
YrCFADJMCF
0-60 -60
1155 0
2-100186 86
IRR= 19.72%
Method 3: Combination Approach
R =20%
YrCFADJMCF
0-60-69.444-129.44444
11550
2-100186186
IRR=19.87%
0
n
1
t
t
t
CF
)
r
1
(
CF
PI
å
=
+
=
A B
CF(0) (10,000.00) (100,000.00)
PV(CIF) 15,000.00 125,000.00
PI 1.50 1.25
NPV 5,000.00 25,000.00
Quick Quiz
Chapter 8
r =9%
Req. PB =4 yrs
CumulatveCumulative
tCFCFsDCFDCFs
0(100,000.00)(100,000.00)(100,000.00)(100,000.00)
125,000.00(75,000.00)22,935.78(77,064.22)
225,000.00(50,000.00)21,042.00(56,022.22)
325,000.00(25,000.00)19,304.59(36,717.63)
425,000.000.0017,710.63(19,007.00)
525,000.0025,000.0016,248.28(2,758.72)
(2,758.72)
Payback =4 years
NPV =($2,758.72)=NPV(E3,C9:C13)+C8
IRR =7.93%=IRR(C8:C13)