A. Payback Period
The payback period is defined as the number of years required
to recover a project's cost. The payback period provides an indication of a project's risk and liquidity, because it shows
how long the invested capital will be "at risk." Payback period is more
of a technique than a specific formula. The payback period is the calculated
as the number of years required to "payback" the cost of the project.
Decision Rule:
- Accept project if payback period < maximum
acceptable payback period.
- Reject project if payback period > maximum
acceptable payback period.
Example: XYZ Corporation is considering the following project. It is the policy of XYZ for projects to have a payback period of 4 years or less. Evaluate the project based on the payback method.
Should XYZ accept the project?
Year |
0 |
1 |
2 |
3 |
4 |
5 |
Cash Flow |
-10000 |
5000 |
2000 |
4000 |
1000 |
1000 |
The cost of the project is $10,000. The payback period
is the number of years it takes for the project's cash flows (positive) to payback the cost of the project. After year one, the project has paid back $5000 of the $10000 cost.
After year two, the project has paid back $7000 of the $10000 cost. After
year three, the project has paid a total of $11000. The project's payback period
lies between 2 to 3 years. To payback the $10000 we only need $3000 of the $4000
that the project is expected to generate in year three. If we assume that the
cash flows are paid evenly over the period, the payback period is 2.75 years (payback = year before full recovery + unrecovered
cost at start of year/cash flow for year = 2 + 3000/4000). The project should
be accepted since its payback period is less than the maximum acceptable payback period.
Calculating the payback period is easy if the positive cash flows are annuities. The payback period in this case is simply the cost divided by the annual cash flow. For example (11-1 on
page 529), if the cost of a project is $52,125 and the project is expected to generate annual cash flows of $12,000 per year
for eight years, the payback period is 4.34 years (Payback period = 52125/12000).
Advantages:
- Easy to calculate and understand
- Provides and
indication of a project's risk and liquidity
Disadvantages:
- Ignores time value of money - to correct for
this disadvantage the discounted payback period can be used. The discounted payback period is an improvement
over the regular payback method because the present value (discounted) of the project's cash flows is used to calculate the
payback period. The discounted payback method considers the time value of money.
- Does not consider cash flows occurring after
the payback period
B. Net Present Value
The net present value (NPV) method discounts all cash flows
at the project's cost of capital (required rate of return) and then sums those cash flows. NPV gives a direct measure of the
benefit in dollars of undertaking the project. NPV can be considered a measure
of the project's profitability in dollars. NPV is also the amount of value ("value
added") the project will add to the firm. The project is accepted if the NPV
is positive. Positive NPV projects add value to the firm and increases shareholder's
wealth.
Decision Rule:
- Accept project if
NPV > 0.
- Reject project
if NPV < 0.
Example: Assume that you convince XYZ Corporation that
they should judge the project on a decision rule that considers time value of money, all the project's cash flows, and the
project's required rate of return. XYZ tells you that the project has equivalent
risk to the company and the company's WACC is 10%. Calculate the project's NPV
and then make a recommendation concerning the acceptance or rejection of the project.
Year |
0 |
1 |
2 |
3 |
4 |
5 |
Cash Flow |
-10000 |
5000 |
2000 |
4000 |
1000 |
1000 |
Project should be accepted because it will add value ($507.54) to the
company.
Advantages:
- Considers time value of money
- Considers all cash flows
- NPV is the value the project
will add to the firm
- Considered to
be the best decision criteria
Disadvantages:
- NPV will be erroneous
if cash flow estimates are incorrect (requires accurate cash flow estimations)
- NPV is a dollar return but percent
returns are easier to communicate and understand
C. Internal Rate of Return
The internal rate of return (IRR) is defined as the discount
rate which forces a project's NPV to equal zero. The IRR is the project's expected rate of return (same as a bond's yield
to maturity). The project is accepted if the IRR (expected return) is greater
than the cost of capital (required return).
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Decision Rule:
- Accept project if
IRR > k.
- Reject project
if IRR < k.
Advantages:
- Considers time value
of money
- Considers all cash
flows
- IRR is the
expected rate of return for the project
- IRR is a percent
return that is considered easier to communicate and understand
Disadvantages:
- IRR will be erroneous
if cash flow estimates are incorrect (requires accurate cash flow estimations)
- Multiple IRRs are possible for nonnormal cash flow streams. A normal cash flow stream is one where there the project's cost (negative cash flow)
is followed by positive cash flows. In other words, there is only one sign change (negative cash flows
followed by positive cash flows). A nonnormal cash flow stream is one in which there are multiple sign changes (negative
cash flows followed by positive and negative cash flows). A nonnormal cash flow
stream will result in multiple IRRs but DOES NOT affect the NPV calculation.
- Reinvestment rate assumption
- Both NPV and IRR have an implied reinvestment rate assumption. For the NPV
calculation, it is assumed that all of the project's cash flows are reinvested at the project's required rate of return (k). For the IRR calculation, it is assumed that all of the project's cash flows are
reinvested at the project's expected rate of return (IRR). For a
project that has the same level of risk as the firm, the NPV method assumes that cash flows will be reinvested at the firm's
cost of capital, while the IRR method assumes reinvestment at the project's IRR. Reinvestment at the cost of capital is generally
a better assumption in that it is closer to reality. The reinvestment rate assumption
can cause conflicting results when evaluating mutually exclusive projects (next discussion).
For a given project, the NPV and IRR will give the same
accept/reject decision. In other words, if the NPV > 0, then IRR > k; or
if the NPV = 0, then IRR = k; or if NPV<0, then IRR<k.
The modified IRR (MIRR) corrects for some of the problems
involved with IRR. MIRR is discussed further in the textbook but will not on
the test.