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### Chapter 7

What’s next?

- Capital Budgeting: involves making decisions about real asset investments.
- Chapter 7: Net Present Value and Other Investment Criteria
- Chapter 8: Estimating cash flows for a potential investment.
- Chapter 12: Estimating a required rate of return for a potential investment = opportunity cost of capital. (need chapters 10 & 11 to help us with chapter 12)

Net Present Value & Other Investment Criteria

Topic Overview

- Project Types
- Capital Budgeting Decision Criteria
- Net Present Value (NPV)
- Payback Period
- Internal Rate of Return (IRR)
- Profitability Index (PI)
- Equivalent Annual Cost and Equivalent Annual Annuity
- Capital Rationing

Learning Objectives

- Understand how to calculate and use capital budgeting decision techniques: Payback, NPV, IRR, & PI.
- Understand the advantages and disadvantages of each technique.
- Understand which project to select when there is a ranking conflict between NPV and IRR.

Think about this as we cover Chapter 7 Investment Criteria.

- Which of the following investment opportunities would you prefer?
- #1) Give me $1 now and I’ll give you $2 at the end of class.
- #2) Give me $100 now and I’ll give you $150 at the end of class.

Project Types

- Independent Projects – don’t affect acceptance of other projects
- Mutually Exclusive Projects – interact with other projects or accomplish the same objective
- Normal Projects -only one sign change in sequence of cash flows
- Non-normal Projects - multiple sign changes in cash flow series.

Our Case Study

- We want to help Marge Simpson, Inc. analyze the following business opportunities by using the following cash flow information. Assume Marge's opportunity cost of capital is 12%.

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

Net Present Value

NPV = PV - required investment

Net Present Value

Terminology

C = Cash Flow

t = time period of the investment

r = “opportunity cost of capital”

- The Cash Flow could be positive or negative at any time period.

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.

Marge’s NPVs: r = 12%

- Calculator Steps. Falafel-Full: CF0 = -20,000, C01 = 15,000, F01 = 2, C02 = 13,000, F02 = 1, C03 = 3,000. NPV: I = 12, CPT NPV = 16,510
- Pretzel: CF0 = -20,000, C01 = 2,000, F01=1, C02 = 2,500, F02=1, C03 = 3,000, F03=1, C04 = 50,000. NPV: I = 12, CPT NPV = 17,690

Excel and NPV: Why Microsoft deserves its legal troubles.

- Excel’s NPV function is goofed up. =NPV(r, range of cash flows)
- Assumes first cash flow in range occurs at t = 1.
- See spreadsheet.
- Solution to this spreadsheet problem: exclude initial cost (t = 0 cash flow) from NPV cell range and add initial cost (if already negative) to the NPV function.

Marge’s NPV Decision

- If projects are independent, Marge should select both.
- Both have positive NPV.
- If the projects are mutually exclusive, select How ‘Bout A Pretzel?
- Pretzel NPV > Falafel NPV.

Payback Period (PB)

- Measures how long it takes to recovers a project’s cost.
- Easy to calculate and a good measure of a project’s risk and liquidity.
- Decision Rule: Accept if PB < some maximum period of time.

Marge’s Payback (Assume Marge’s max is 2 years)

- Falafel PB = less than 2 years
- Pretzel PB = less than 4 years
- Marge should choose Falafel using Payback Period.

Problems with Payback

- Ignores time value of money!
- Ignores cash flows beyond payback period.
- Not a good investment decision technique.

Internal Rate of Return (IRR)

- Internal Rate of Return is a project’s expected rate of return on its investment.
- IRR is the interest rate where the PV of the project’s cash flows equals its cost.
- In other words, the IRR is the rate where a project’s NPV = 0.
- ∑CFt/(1 + IRR)t = Cost
- Decision Rule: Accept if IRR > r (opportunity cost of capital).
- Non-normal projects have multiple IRRs. Don’t use IRR to decide on non-normal projects.

Marge’s IRRs

- Best to use calculator. Calculator Steps.
- Falafel-Full: CF0 = -20,000, C01 = 15,000, F01 = 2, C02 = 13,000, F02 = 1, C03 = 3,000. Press IRR, then CPT: IRR = 54.7%
- Pretzel: CF0 = -20,000, C01 = 2,000, F01=1, C02 = 2,500, F02=1, C03 = 3,000, F03=1, C04 = 50,000. Press IRR, then CPT: IRR = 33.3%
- r = 12%. If independent projects: select both, IRRs > 12%. Mutually exclusive: select Falafel; higher IRR.

Comparison of NPV & IRR

- For normal independent projects, all three methods give same accept/reject decision.
- NPV > 0 yields IRR > r in order to lower NPV to 0.
- However, these methods can rank mutually exclusive projects differently.
- What to do, then?

NPV Profiles

- A graph which shows a project’s NPV at different interest rates (opportunity cost of capital).
- Can illustrate ranking conflicts between NPV and IRR.
- Below is a table of NPVs for Marge’s projects.

Determining NPV/IRR Conflict Range

- For each year, subtract one project’s cash flows from the other.
- If there is a change of signs of these cash flow differences, a ranking conflict exists.
- Find IRR of these cash flow differences to find rate where the two projects have the same NPV = crossover rate.
- At a cost of capital less than this crossover rate, a ranking conflict between NPV and IRR exists.

Marge’s crossover rate

- At a cost of capital less than 14.1%, Pretzel has higher NPV but lower IRR = Ranking Conflict.
- At cost of capital greater than 14.1%, Falafel has the higher NPV and IRR.
- Why? Cash flow timing differences in this case.
- Other cause: initial cost differences, but not here.

Reconciling NPV/IRR Ranking Conflicts

- Shareholder Wealth Maximization:
- Want to add more value to the firm than less.
- Result: Choose project with highest NPV when NPV/IRR ranking conflict exists for mutually exclusive projects.
- Also, IRR has the multiple IRR problem for non-normal projectslike the following.

Acme, Inc. Rocket-Powered Roller Blade Project

- Acme is considering the following project which would market these roller blades to coyotes trying to catch road runners. Acme expects a cash inflow in the year 1, but an outflow in the 2nd (last) year of the project due to liability claims from injured cartoon coyotes. Acme’s opportunity cost of capital is 13%.

Year 0 1 2

Cash Flow (5) 30 (30)

NPV = -1.95 IRR = 26.8%

Rocket-Powered Roller Blade NPV Profile

- At Acme’s 13% opportunity cost of capital, the project has a negative NPV even though the IRRs is greater than 13%.
- Because of this conflict, don’t use IRR to make decisions for non-normal projects! (or look for a first IRR that is less than cost of capital)

Comparing Projects with unequal lives

- To replace the Budweiser sign that the ferret dropped in the frog pond, Louie the Lizard is evaluating two new signs. Louie must purchase and care for a replacement sign indefinitely. Here are the annual costs for the two replacement signs.
- Which sign should Louie choose given an opportunity cost of capital of 11%?

YearFrying FrogsLizards Leaping over Frogs

0 4,000 6,000

1 1,000 900

2 1,000 700

3 700

4 700

Equivalent Annual Cost

Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine.

Louie The Lizard’s Decision, r = 11%

YearFrying FrogsLizards Leaping over Frogs

0 4,000 6,000

1 1,000 900

2 1,000 700

3 700

4 700

- Frying Frogs (FF) PV of costs = 5713
- Lizards Leaping (LL) PV of costs = 8352
- FF EAC: 5713=PV, 11=I/Y, 2=N, 0=FV, CPT PMT = 3336
- LL EAC: 8352=PV, 11=I/Y, 4=N, 0=FV, CPT PMT = 2692
- Louie should choose the Lizards Leaping over Frogs sign because of its lower cost on an annual basis.

Comparing Projects (NPV>0) with unequal lives: Equivalent Annual Annuity

- Burns Power is considering the following mutually exclusive projects in order to increase power consumption in Springfield indefinitely. Which project should be selected if Burns Power’s opportunity cost of capital is 10%?

Year 0 1 2 3

Sun-Blocker (50) 60 60

Fog-Maker (30) 40 40 40

Find NPV and Equivalent Annual Annuity

- NPV of Sun-Blocker = $54.1 m
- NPV of Fog-Maker = $69.5 m
- Sun-Blocker EAA: -54.1=PV, 10=I/Y, 2=N, 0=FV, CPT PMT = $31.2m
- Fog-Maker EAA: -69.5=PV, 10=I/Y, 3=N, 0=FV, CPT PMT = $27.9m
- Burns should choose the Sun-Blocker because it would add the most value on an annual basis.

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.

Investment Timing: #31, pg 207 of textbook

- Can purchase a scanner today for $400 that would provide $60 in annual benefits for 10 years. However, scanner prices are expected to decrease 20% per year.
- Should you purchase the scanner today or wait if your discount rate is 10%?
- PV of annual benefits: 60=PMT, 10=N, 10=I/Y, 0=FV, CPT PV = $369
- NPV = $369 – Expected Scanner Cost

Investment Timing Example (cont.): r = 10%

- Year Cost PV Benefits NPV at Purchase NPV Today
- 0 400 369 -31 -31
- 1 320 369 49 45
- 2 256 369 113 93
- 3 205 369 164 123
- 4 164 369 205 140
- 5 131 369 238 148
- 6 105 369 264 149
- 7 84 369 285 146
- To maximize value, you should wait 6 years to buy the scanner.

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.

Profitability Index (PI)

- The ratio of the net present value of a project’s cash flows to its cost.
- PI = NPV/Cost
- Decision Rule: Accept if PI > 0
- PI can be used to rank projects under capital rationing conditions. Accept highest PI projects under the capital constraint to maximize NPV.
- CAUTION: PI can rank mutually exclusive projects that have different initial costs differently than NPV.

Summary of Capital Budgeting Methods

- Want a method the uses the time value of money with all project cash flows: NPV, PI, IRR.
- IRR can give erroneous decision for non-normal projects.
- Overall, NPV is the best and preferred method.
- However, under capital rationing (budget restraint), ranking projects by PI can be useful in helping to maximize NPV under capital constraint.

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