Managerial Fin
Copyright © 2015 by The McGraw-Hill Companies, Inc. All rights reserved
Chapter 8
Net Present Value and Other Investment Criteria
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Topics Covered
8.1 Net Present Value
8.2 The Internal Rate of Return Rule
8.3 The Profitability Index
8.4 The Payback Rule
8.5 More Mutually Exclusive Projects
8.6 A Last Look
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2
Net Present Value
Net Present Value - Present value of cash flows minus initial investments
Opportunity Cost of Capital - Expected rate of return given up by investing in a project
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4
Net Present Value
Example
Q: Suppose we can invest $50 today & receive $60 later today. What is our increase in value?
Initial Investment
Added Value
$50
$10
A: Profit = −$50 + $60
= $10
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6
Net Present Value
Example
Suppose we can invest $50 today and receive $60 in one year. What is our increase in value given a 10% expected return?
This is the definition of NPV
Initial Investment
Added Value
$50
$4.55
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8
Valuing an Office Building
Step 1: Forecast cash flows
Cost of building = C0 = 350,000
Sale price in Year 1 = C1 = 400,000
Step 2: Estimate opportunity cost of capital
If equally risky investments in the capital market
offer a return of 7%, then
Cost of capital = r = 7%
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Valuing an Office Building
Step 3: Discount future cash flows
Step 4: Go ahead if PV of payoff exceeds investment
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Risk and Present Value
Higher risk projects require a higher rate of return
Higher required rates of return cause lower PVs
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Risk and Present Value
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Risk and Present Value
New NPV = 357,143 − 350,000 = $7,143
Higher risk = Lower value
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Net Present Value
NPV = PV - required investment
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11
Net Present Value
C0 = Initial cash flow (often negative)
C1 = Cash flow at time 1
C2 = Cash flow at time 2
Ct = Cash flow at time t
t = Time period of the investment
r = Opportunity cost of capital
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11
Net Present Value
Net Present Value Rule
Managers increase shareholders’ wealth by accepting all projects that are worth more than they cost
Therefore, they should accept all projects with a positive net present value
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13
Net Present Value
Example
You have the opportunity to purchase an office building. You have a tenant lined up that will generate $25,000 per year in cash flows for three years. At the end of three years you anticipate selling the building for $450,000. How much would you be willing to pay for the building?
Assume a 7% opportunity cost of capital.
$$$$$$$$$$
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14
Example - continued
Net Present Value
$25,000
$25,000
$25,000
$450,000
$475,000
0 1 2 3
Present Value
23,364
21,836
387,741
$432,942
$$$$
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16
Net Present Value
Example - continued
If the building is being offered for sale at a price of $375,000, would you buy the building? What is the added value generated by your purchase and management of the building?
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17
Invest
Sell
Rent
Rent
Rent
Net Present Value
Example - continued
If the building is being offered for sale at a price of $375,000, would you buy the building and what is the added value generated by your purchase and management of the building?
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18
Internal Rate of Return
Internal Rate of Return (IRR) - Discount rate at which NPV = 0
Rate of Return Rule - Invest in any project offering a rate of return that is higher than the opportunity cost of capital
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Internal Rate of Return
Example
You can purchase a building for $350,000. At the end of the year you will sell the building for $400,000. What is the rate of return on this investment?
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21
Internal Rate of Return
IRR = 14.29%
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24
Discount rate (%)
NPV (,000s)
Internal Rate of Return
Example
You can purchase a building for $375,000. The investment will generate $25,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?
IRR = 12.56%
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23
Internal Rate of Return
IRR=12.56%
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24
Discount rate (%)
NPV (,000s)
Internal Rate of Return
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23
Internal Rate of Return
Calculating the IRR can be a laborious task. Fortunately, financial calculators can perform this function easily. Note the previous example.
HP-10B EL-733A BAII Plus
-375,000 CFj -375,000 CFi CF
25,000 CFj 25,000 CFfi 2nd {CLR Work}
25,000 CFj 25,000 CFi -375,000 ENTER
475,000 CFj 475,000 CFi 25,000 ENTER
{IRR/YR} IRR 25,000 ENTER
475,000 ENTER
IRR CPT
All produce IRR=12.56
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26
Internal Rate of Return
Example
You have two proposals to choice between. The initial proposal (H) has a cash flow that is different than the revised proposal (I). Using IRR, which do you prefer?
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Internal Rate of Return
50
40
30
20
10
0
-10
-20
NPV $, 1,000s
Discount rate, %
8 10 12 14 16
Revised proposal
Initial proposal
IRR= 14.29%
IRR= 12.56%
IRR= 11.72%
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Internal Rate of Return
Example
You have two proposals to choose between. The initial proposal has a cash flow that is different than the revised proposal. Using IRR, which do you prefer?
| Project | C0 | C1 | C2 | C3 | IRR | NPV@7% |
| Initial Proposal | -350 | 400 | 14.29% | $ 23,832 | ||
| Revised Proposal | -375 | 25 | 25 | 475 | 12.56% | $ 57,942 |
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Internal Rate of Return
Pitfall 3 - Mutually Exclusive Projects
IRR sometimes ignores the magnitude of the project
The following two projects illustrate that problem
Pitfall 1 - Lending or Borrowing?
With some cash, the NPV of the project increases as the discount rate increases
This is contrary to the normal relationship between PV and discount rates
Pitfall 2 - Multiple Rates of Return
Certain cash flows can generate NPV = 0 at two different discount rates
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Profitability Index
Profitability Index
Ratio of net present value to initial investment
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Profitability Index
| Cash Flows | |||||
| Project | C0 | C1 | C2 | NPV @ 10% | Profitability Index |
| C | -10 | 30 | 5 | 21.40 | 2.1 |
| D | -5 | 5 | 20 | 16.07 | 3.2 |
| E | -5 | 5 | 15 | 11.94 | 2.4 |
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Capital Rationing
Capital Rationing - Limit set on the amount of funds available for investment
Soft Rationing - Limits on available funds imposed by management
Hard Rationing - Limits on available funds imposed by the unavailability of funds in the capital market
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48
Payback Method
Payback Period - Time until cash flows recover the initial investment of the project
The payback rule specifies that a project be accepted if its payback period is less than the specified cutoff period
The following example will demonstrate the absurdity of this statement
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28
Payback Method
| Cash Flows | |||||
| Project | C0 | C1 | C2 | Payback | NPV @ 10% |
| F | -2,000 | +1,000 | +10,000 | 2 | +7,249 |
| G | -2,000 | +1,000 | 0 | 2 | -264 |
| H | -2,000 | +2,000 | 0 | 2 | -347 |
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32
Project Interactions
When you need to choose between mutually exclusive projects, the decision rule is simple:
Calculate the NPV of each project
From those options that have a positive NPV, choose the one whose NPV is highest
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35
Mutually Exclusive Projects
Example
Select one of the two following projects, based on highest NPV
Assume a 7% discount rate
| System | C0 | C1 | C2 | C3 | NPV |
| Faster | -800 | 350 | 350 | 350 | +118.5 |
| Slower | -700 | 300 | 300 | 300 | +87.3 |
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Investment Timing
Sometimes you have the ability to defer an investment and select a time that is more ideal at which to make the investment decision
A common example involves a tree farm
You may defer the harvesting of trees
By doing so, you defer the receipt of the cash flow, yet increase the cash flow
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Investment Timing
Example
You may purchase a computer anytime within the next five years. While the computer will save your company money, the cost of computers continues to decline. If your cost of capital is 10% and given the data listed below, when should you purchase the computer?
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39
Investment Timing
Example
You may purchase a computer anytime within the next five years. While the computer will save your company money, the cost of computers continues to decline. If your cost of capital is 10% and given the data listed below, when should you purchase the computer?
| Time | Cost | PV Savings | NPV at Purchase | NPV Today |
| 0 | 50 | 70 | 20 | 20.0 |
| 1 | 45 | 70 | 25 | 22.7 |
| 2 | 40 | 70 | 30 | 24.8 |
| 3 | 36 | 70 | 34 | Date to purchase 25.5 |
| 4 | 33 | 70 | 37 | 25.3 |
| 5 | 31 | 70 | 39 | 24.2 |
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40
Equivalent Annual Annuity
Equivalent Annual Annuity - The cash flow per period with the same present value as the cost of buying and operating a machine
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42
Equivalent Annual Annuity
Example
Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual annuity method.
| Costs ($ thousands) | |||||||
| Year: | 0 | 1 | 2 | 3 | PV @ 6% | EAA | |
| Machine I | -15 | -4 | -4 | -4 | -25.69 | -9.61 | |
| Machine J | -10 | -6 | -6 | -21.00 | -11.45 |
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45
Equivalent Annual Annuity
Example (with a twist)
Select one of the two following projects, based on highest “equivalent annual annuity” (r = 9%).
| Project | C0 | C1 | C2 | C3 | C4 | NPV | EAA |
| A | -15 | 4.9 | 5.2 | 5.9 | 6.2 | ||
| B | -20 | 8.1 | 8.7 | 10.4 |
2.82
2.78
.87
1.10
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47
Capital Budgeting Techniques
| Criterion | Definition | Investment Rule | Comments |
| Net present value (NPV) | Present value of cash inflows minus present value of cash outflows | Accept project if NPV is positive. For mutually exclusive projects, choose the one with the highest (positive) NPV. | The “gold standard” of investment criteria. Only criterion necessarily consistent with maximizing the value of the firm. Provides appropriate rule for choosing among mutually exclusive investments. Only pitfall involves capital rationing, when one cannot accept all positive NPV projects. |
| Internal rate of return (IRR) | The discount rate at which project NPR equals zero | Accept project if IRR is greater than opportunity cost of capital. | If used properly, results in same accept-reject decision as NPV in the absence of project interactions. However, beware of the following pitfalls: IRR cannot rank mutually exclusive projects—the project with higher IRR may have lower NPV. The simple IRR rule cannot be used in cases of multiple IRRs or an upward-sloping NPV profile. |
| Profitability index | Ratio of net present value to initial investment | Accept project if profitability index is greater than 0. In case of capital rationing, accept projects with highest profitability index. | Results in same accept-reject decision as NPV in the absence of project interactions. Useful for ranking projects in case of capital rationing, but misleading in the presence of interactions. Cannot rank mutually exclusive projects. |
| Payback period | Time until the sum of project cash flows equals the initial investment | Accept project if payback period is less than some specified number of years. | A quick and dirty rule of thumb, with several critical pitfalls. Ignores cash flows beyond the acceptable payback period. Ignores discounting. Tends to improperly reject long-lived projects. |
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Capital Budgeting Techniques
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55
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Calculating IRR by using a spreadsheet
YearCash FlowFormula
0(375,000.00) IRR = 12.56%=IRR(B4:B7)
125,000.00
225,000.00
3475,000.00
Sheet1
| Calculating IRR by using a spreadsheet | |||||
| Year | Cash Flow | Formula | |||
| 0 | (375,000.00) | IRR = | 12.56% | =IRR(B4:B7) | |
| 1 | 25,000.00 | ||||
| 2 | 25,000.00 | ||||
| 3 | 475,000.00 |
Sheet2
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