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CHAPTER 7 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA

By Peter Hamilton,2014-08-11 23:10
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CHAPTER 7 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA

    CHAPTER 7: NET PRESENT VALUE AND OTHER INVESTMENT

    CRITERIA

A. OVERVIEW

    Motivation How do we evaluate long-term projects? How do we choose among various

    long-term investment projects? What criteria would you use?

    Definition Capital budgeting refers to the process of evaluating and selecting long-term investment projects that achieve the goal of maximizing owners’ wealth.

    Definition A capital expenditure is an outlay of funds that is expected to produce benefits over a period of time longer than one year.

     An operating expenditure is an outlay of funds that is expected to

    produce benefits over a period of time shorter than one year.

Motives: affects the way we identify cash flows

     Expansion

     Replacement

     Renewal

     Others

Process of capital budgeting

     Generate proposal

     Review and analysis

     Make decision

     Implement

     Follow-up

B. TERMINOLOGY

     Types of projects:

     Independent : Cash flows are unrelated

     Accepting one project does not eliminate others

Example Purchase a computer network and install air-conditioning in the building

     Mutually exclusive: Competing projects (substitutes)

     Accepting one project would eliminate others

Example Acquire a firm (backward integration) vs. contract out the production to the

    backward linkage, choose among from other suppliers

Funding constraint:

     Unlimited funds : No funding constraint (no capital rationing)

     Can accept any independent projects that meet the decision criteria

     Implication Can use accept/reject approach to make

    investment decision

     Capital rationing: Constrained by amount of funds available

     Firm must ration its funds to allocate among projects that maximize share value

     Implication Use the ranking approach to help select

     the best projects

C. COMPONENTS OF CASH FLOW

    1. Initial investment / incremental cost / incremental investment

     Relevant cash outflows now to embark on a capital budgeting project

    2. Operating cash inflows

     The incremental after-tax cash inflows resulting from a project during

    its life

    3. Terminal cash flow

     The after-tax non-operating cash flow at the final year of the project

    (liquidation of the project)

D. APPROACH 1: PAYBACK PERIOD

    Definition: The length of time in years it takes for a project’s yearly incremental after-tax cash flows to recover the incremental investment in the project

Formula: Incremental investment Payback period Constant cash flow

    Decision rule: A project should be accepted if its payback period is less than a specified cutoff period.

    Note: If cash flow is a mixed stream, payback period is the year when cash flow just recovers the incremental investment.

    Example The incremental investment is $25,000. If cash flow is a constant amount of $5,000 per year. The payback period is 5.

    Example If cash flow is $5,000 for the first year, $6,000 for the second year, $3,000 for the third year, and $4,000 for subsequent years, then the payback period is between 5 to 6 years.

    Example Consider the following two projects. Which one would you choose, using the payback period approach?

     Year 0 1 2 3

    Project A -2000 1500 300 200

    Project B -2000 200 300 1500

    Example Consider the following two projects. The cutoff period is 2 years. Which one would you choose?

     Year 0 1 2 3

    Project A -2000 1000 1000 5000

Project B -2000 1000 1000 3000

Summary:

     Easy to communicate / calculate

     A quick measure of “risk exposure”

     No mention of CF after the payback period

     Ignore the time value of money

E. APPROACH 2: DISCOUNTED PAYBACK PERIOD

    Definition: The length of time in years it takes for a project’s discounted yearly incremental after-tax cash flows to recover the incremental investment in the project

    Decision rule: A project should be accepted if its discounted payback period is less than a specified cutoff period.

    Example Consider the following two projects. The cutoff period is 2 years. Which one would you choose, using the discounted payback period approach with a discount rate of 10%?

     Year 0 1 2 3

    Project A -2000 500 1500 1000

    Project B -2000 1500 500 1000

F. APPROACH 3: BOOK RATE OF RETURN

    Definition: Book rate of return is the accounting income divided by book value. Also called accounting rate of return.

Formula:

    Book income Book rate of return Book assets

Decision rule: Accept the project if book rate of return > required return

    Example (p. 219). A company invests $90,000 in a machine, which will increase cash flow by $50,000 a year for 3 years. Allowance for depreciation is $30,000 a year. Find the book rate of return.

Book value Book value

    (begin) Net income (end) Return

    90 50-30=20 60 22.2

    60 50-30=20 30 33.3

    30 50-30=20 0 66.7

G. APPROACH 4: NET PRESENT VALUE

    Definition: Net Present Value (NPV) is the present value of the sum of discounted cash flows minus initial investment.

Formula:

     n NPVCF(1;T)*PVIF;IC,ttk (a1t

Decision rule: Accept the project if NPV > 0.

Note:

     Use opportunity cost of capital (expected rate of return of the best alternative

    investment)

    Example (p.204-5) Real estate investment in an office building costs $50,000 for land and $300,000 for construction. You can sell the office building a year later for$400,000. Suppose the T-bill offers an interest rate of 7%. Would you invest in the real estate project?

    Example (p.207) A new computer system costs $100,000 to install and will last for 10 years. The new system will reduce the operating cost by $20,000 a year. The opportunity cost of capital is 12%. Would you buy the new system, using the NPV approach?

H. APPROACH 5: INTERNAL RATE OF RETURN (IRR)

Definition: Internal rate of return is the discount rate that causes NPV=0.

Formula (no closed-form):

    n Find k such that NPVCF(1;T)*PVIF;IC0 att,k(at1

Decision rule: Accept project if IRR is higher than the opportunity cost of capital

Note:

     Often use calculator

     Graphical approach

     Vary Ka (cost of capital) and find NPV

     Plot NPV (y-axis) against rate of return (cost of capital) Ka (x-axis)

     IRR = point cutting the x-axis

I. PITALLS OF THE IRR RULE

    1. Borrowing vs. lending

    Example. P. 217. Consider the following two projects:

     Year 0 1 IRR NPV10%

    Project J -100 150 50% +36.4

Project K +100 -150 50% -36.4

Project K +100 -150 @15% discount rate

     NPV = -30.4

     @20% discount rate

     NPV = -25.0

Which one would you choose?

2. Multiple rates of return

    Example. A project requires an initial investment of $22 million and produces an expected cash flow of $15 million in years 1 through 4. In year 5, the project requires another cost of $40 million. Opportunity cost of capital is 7% (Exercise: NPV = 0.7 million.) What is the IRR?

J. NPV vs. IRR

     Generate same accept / reject decision for projects

     Different in underlying assumptions

     NPV assumes project cash flows are reinvested at the cost of capital

     IRR assumes project cash flows are reinvested at IRR

     Different rankings of projects

     Differences in the magnitude and timing of cash flows

     Large inflows in early years result in high IRR

K. NOTES

    Note 1: Choosing between mutually exclusive projects with different useful life spans

    Motivation If projects are independent, the length of project life is not critical; but when projects are mutually exclusive (eliminate one for another), how do we compare a 10-year project with a 3-year project?

Method: Find the annualized net present value (ANPV)

     Definition The annualized net present value or equivalent annual cost

    is an annuity-equivalent amount of NPV over the project life

     Like PMT in your our calculation

Formula (ANPV): NPVproject j ANPVproject jPVIFA k%,nproject j

    Interpretation: ANPV gives the annual equal amount of “net cash flow” over the life

    of the project

    Example Two projects are presented. Both require an incremental cost of $8,000, but they have different expected cash flows. If the two projects are independent, which one would you recommend? What if they are mutually exclusive? Assume that these are CE cash flows and the risk-free rate of interest is 6%.

Year A B

1 3000 2000

    2 2000 2000

    3 1000 2000

    4 4000 2000

    5 2000

    6 2000

    7 2000

Note 2: Replacing an old machine

    Example: Suppose a machine costs an annual outflow of $12,000. If replaced, the NPV of the replacement would cost $25,000 for installation and a lower operating cost of $8,000 for the next 5 years. Should you replace the machine? (Use 6%.)

Note 3: Investment timing

    Motivation When would be the best time to acquire the project?

    Example (p.221) A project requires an initial investment of $50,000. The present value of the corresponding stream of cash flow is $70,000 at the time of project installation. Should the company postpone the project?

Note 4: Capital rationing

    Motivation What if you have a fixed budget to allocate among various independent project?

Formula (profitability index):

     NPVproject jProfitability index project jInitial investmentproject j

    Decision rule: Keep choosing projects with highest profitability index that falls within the budget limit.

    Example (p. 227) Consider the following projects. You have a budget limit of 10 million.

    Project PV Investment NPV P-index

    A 4 3 1 0.33

    B 6 5 1 0.20

    C 10 7 3 0.43

    D 8 6 2 0.33

    E 5 4 1 0.25

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