Capital budgeting (or investment appraisal) is the planning process used to determine whether a firm's long term investments such as new machinery, replacement machinery, new plants, new products, and research development projects are worth pursuing. It is budget for major capital, or investment, expenditures.
Many formal methods are used in capital budgeting, including the techniques such as
· Accounting rate of return
· Net present value
· Profitability index
· Internal rate of return
· Modified internal rate of return
· Equivalent annuity
These methods use the incremental cash flows from each potential investment, or project Techniques based on accounting earnings and accounting rules are sometimes used - though economists consider this to be improper - such as the accounting rate of return, and "return on investment." Simplified and hybrid methods are used as well, such as payback period and discounted payback period.
I. Net Present Value (NPV) or net present worth (NPW) is defined as the sum of the present values (PVs) of the individual cash flows. In the case when all future cash flows are incoming (such as coupons and principal of a bond) and the only outflow of cash is the purchase price, the NPV is simply the PV of future cash flows minus the purchase price (which is its own PV). NPV is a central tool in discounted cash flow (DCF) analysis, and is a standard method for using the time value of money to appraise long-term projects. Used for capital budgeting, and widely throughout economics, finance, and accounting, it measures the excess or shortfall of cash flows, in present value terms, once financing charges are met.
Formula
Each cash inflow/outflow is discounted back to its present value (PV). Then they are summed. Therefore NPV is the sum of all terms,
where
t - the time of the cash flow
i - the discount rate (the rate of return that could be earned on an investment in the financial markets with similar risk.)
Rt - the net cash flow (the amount of cash, inflow minus outflow) at time t (for educational purposes, R0 is commonly placed to the left of the sum to emphasize its role as (minus) the investment.
The result of this formula if multiplied with the Annual Net cash in-flows and reduced by Initial Cash outlay will be the present value but in case where the cash flows are not equal in amount then the previous formula will be used to determine the present value of each cash flow separately. Any cash flow within 12 months will not be discounted for NPV purpose.
What NPV Means
NPV is an indicator of how much value an investment or project adds to the firm. With a particular project, if Rt is a positive value, the project is in the status of discounted cash inflow in the time of t. If Rt is a negative value, the project is in the status of discounted cash outflow in the time of t. Appropriately risked projects with a positive NPV could be accepted. This does not necessarily mean that they should be undertaken since NPV at the cost of capital may not account for opportunity cost, i.e. comparison with other available investments. In financial theory, if there is a choice between two mutually exclusive alternatives, the one yielding the higher no-no should be selected.
If... / It means... / Then...NPV > 0 / the investment would add value to the firm / the project may be accepted
NPV < 0 / the investment would subtract value from the firm / the project should be rejected
NPV = 0 / the investment would neither gain nor lose value for the firm / We should be indifferent in the decision whether to accept or reject the project. This project adds no monetary value. Decision should be based on other criteria, e.g. strategic positioning or other factors not explicitly included in the calculation.
Example
A corporation must decide whether to introduce a new product line. The new product will have startup costs, operational costs, and incoming cash flows over six years. This project will have an immediate (t=0) cash outflow of $100,000 (which might include machinery, and employee training costs). Other cash outflows for years 1-6 are expected to be $5,000 per year. Cash inflows are expected to be $30,000 each for years 1-6. All cash flows are after-tax, and there are no cash flows expected after year 6. The required rate of return is 10%. The present value (PV) can be calculated for each year:
Year / Cashflow / Present ValueT=0 / / -$100,000
T=1 / / $22,727
T=2 / / $20,661
T=3 / / $18,783
T=4 / / $17,075
T=5 / / $15,523
T=6 / / $14,112
The sum of all these present values is the net present value, which equals $8,881.52. Since the NPV is greater than zero, it would be better to invest in the project than to do nothing, and the corporation should invest in this project if there is no mutualy exclusive alternative with a higher NPV.
Discount rate is an interest rate a central bank charges depository institutions that borrow reserves from it.
The term discount rate has two meanings:
· the same as interest rate; the term "discount" does not refer to the common meaning of the word, but to the meaning in computations of present value, e.g. net present value or discounted cash flow
· the annual effective discount rate, which is the annual interest divided by the capital including that interest; this rate is lower than the interest rate; it corresponds to using the value after a year as the nominal value, and seeing the initial value as the nominal value minus a discount; it is used for Treasury Bills and similar financial instruments
Annual effective discount rate
The annual effective discount rate is the annual interest divided by the capital including that interest, which is the interest rate divided by 100% plus the interest rate. It is the annual discount factor to be applied to the future cash flow, to find the discount, subtracted from a future value to find the value one year earlier.
For example, suppose there is a government bond that sells for $95 and pays $100 in a year's time. The discount rate according to the given definition is
The interest rate is calculated using 95 as its base:
For every annual effective interest rate, there is a corresponding annual effective discount rate, given by the following formula:
or inversely,
where the approximations apply for small i and d; in fact i - d = id.
Payback period in capital budgeting refers to the period of time required for the return on an investment to "repay" the sum of the original investment. For example, a $1000 investment which returned $500 per year would have a two year payback period. The time value of money is not taken into account. Payback period intuitively measures how long something takes to "pay for itself." All else being equal, shorter payback periods are preferable to longer payback periods.
The time value of money is the value of money figuring in a given amount of interest earned over a given amount of time.
For example, 100 dollars of today's money invested for one year and earning 5 percent interest will be worth 105 dollars after one year. Therefore, 100 dollars paid now or 105 dollars paid exactly one year from now both have the same value to the recipient who assumes 5 percent interest; using time value of money terminology, 100 dollars invested for one year at 5 percent interest has a future value of 105 dollars.
Formula
Present value of a future sum
The present value formula is the core formula for the time value of money; each of the other formulae is derived from this formula. For example, the annuity formula is the sum of a series of present value calculations.
The present value (PV) formula has four variables, each of which can be solved for:
- PV is the value at time=0
- FV is the value at time=n
- i is the rate at which the amount will be compounded each period
- n is the number of periods (not necessarily an integer)
The cumulative present value of future cash flows can be calculated by summing the contributions of FVt, the value of cash flow at time=t
Note that this series can be summed for a given value of n, or when n is .
Payback Period Method for Capital Budgeting Decisions:
Objectives:
- Define and Explain payback period.
- Determine the payback period for an investment project.
- What are the advantages and disadvantages of Payback method?
Definition and Explanation:
The payback is another method to evaluate an investment project. The payback method focuses on the payback period. The payback period is the length of time that it takes for a project to recoup its initial cost out of the cash receipts that it generates. This period is some times referred to as" the time that it takes for an investment to pay for itself." The basic premise of the payback method is that the more quickly the cost of an investment can be recovered, the more desirable is the investment. The payback period is expressed in years. When the net annual cash inflow is the same every year, the following formula can be used to calculate the payback period.
Formula / Equation:
The formula or equation for the calculation of payback period is as follows:
Payback period = Investment required / Net annual cash inflow*
*If new equipment is replacing old equipment, this becomes incremental net annual cash inflow.
To illustrate the payback method, consider the following example:
Example:
York company needs a new milling machine. The company is considering two machines. Machine A and machine B. Machine A costs $15,000 and will reduce operating cost by $5,000 per year. Machine B costs only $12,000 but will also reduce operating costs by $5,000 per year.
Required:
· Calculate payback period.
· Which machine should be purchased according to payback method?
Calculation:
Machine A payback period = $15,000 / $5,000 = 3.0 years
Machine B payback period = $12,000 / $5,000 = 2.4 years
According to payback calculations, York company should purchase machine B, since it has a shorter payback period than machine A.
Evaluation of the Payback Period Method:
The payback method is not a true measure of the profitability of an investment. Rather, it simply tells the manager how many years will be required to recover the original investment. Unfortunately, a shorter payback period does not always mean that one investment is more desirable than another.
To illustrate, consider again the two machines used in the example above. since machine B has a shorter payback period than machine A, it appears that machine B is more desirable than machine A. But if we add one more piece of information, this illusion quickly disappears. Machine A has a project 10-years life, and machine B has a projected 5 years life. It would take two purchases of machine B to provide the same length of service as would be provided by a single purchase of machine A. Under these circumstances, machine A would be a much better investment than machine B, even though machine B has a shorter payback period. Unfortunately, the payback method has no inherent mechanism for highlighting differences in useful life between investments. Such differences can be very important, and relying on payback alone may result in incorrect decisions.
Another criticism of payback method is that it does not consider the time value of money. A cash inflow to be received several years in the future is weighed equally with a cash inflow to be received right now. To illustrate, assume that for an investment of $8,000 you can purchase either of the two following streams of cash inflows:
Stream 1 / $8,000 / $2,000 / $2,000 / $2,000 / $2,000
Stream 2 / $2,000 / $2,000 / $2,000 / $2,000 / $8,000
Which stream of cash inflows would you prefer to receive to receive in return for your $8,000 investment? Each stream has a payback period of four years. Therefore, if payback method alone were relied on in making the decision, you would be forced to say that the streams are equally desirable. However from the point of view of the time value of money, stream 2 is much more desirable than stream 1.
On the other hand, under certain conditions the payback method can be very useful. For one thing, it can help identify which investment proposals are in the "ballpark." That is, it can be used as a screening tool to help answer the question, "Should I consider this proposal further?" If a proposal does not provide a payback within some specified period, then there may be no need to consider it further. In addition, the payback period is often of great importance to new firms that are "cash poor." When a firm is cash poor, a project with a short payback period but a low rate of return might be preferred over another project with a high rate of return but a long payback period. The reason is that the company may simply need a faster return of its cash investment. And finally, the payback method is sometimes used in industries where products become obsolete very rapidly - such as consumer electronics. Since products may last only a year or two, the payback period on investments must be very short.
Extension of Payback Method:
The payback period is calculated by dividing the investment in a project by the net annual cash inflows that the project will generate. If equipment is replacing old equipment then any salvage to be received on disposal of the old equipment should be deducted from the cost of the new equipment, and only the incremental investment should be used in payback computation. In addition, any depreciation deducted in arriving at the project's net operating income must be added back to obtain the project's expected net annual cash inflow. To illustrate consider the following data: