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Decision Criteria

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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 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.

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