CHAPTER 7: NET PRESENT VALUE AND OTHER INVESTMENT
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
Process of capital budgeting
• Generate proposal
• Review and analysis
• Make decision
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
• 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
• 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
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
• 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.
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.
n ？，NPV；CF(1;T)*PVIF;IC？,ttk ，(a；1t！；
Decision rule: Accept the project if NPV > 0.
• Use opportunity cost of capital (expected rate of return of the best alternative
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 NPV；CF(1;T)*PVIF;IC；0 ？att,k，(a；t1！；
Decision rule: Accept project if IRR is higher than the opportunity cost of capital
• 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
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 ANPV；project 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
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