**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).

_{}

**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
*n**ormal 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.