FIN 300

Investment Decision Criteria
Lecture 8

Topics Covered



  • Net Present Value (NPV)
  • Internal Rate of Return (IRR)
  • Profitability Index (PI)
  • Average Accounting Return (AAR)

Net Present Value


  • The sum of all discounted cash flows
  • Includes initial investment
  • Everything is discounted to PV terms and summed:

    $ NPV = \sum_{t=0}^{T} \dfrac{CF_t}{(1+R)^t} $

  • Accept project if $NPV>0$
Example

Suppose a project required an initial investment of $\$200$ with the following cash flows in years 1, 2, and 3: $\$$160, $\$$150, $\$$140. $R=8\%$. What is the project's NPV?

$ NPV = CF_0 + \dfrac{CF_1}{(1+R)}+ \dfrac{CF_2}{(1+R)^2}+ \dfrac{CF_3}{(1+R)^3} $

$ NPV = - \$200 + \dfrac{\$160}{(1+0.08)}+ \dfrac{\$150}{(1+0.08)^2}+ \dfrac{\$140}{(1+0.08)^3} $

$ NPV = \$187.88 $

NPV > 0 ; Accept the project.
Example
Same as previous, except $R=10\%$

$ NPV = - \$200 + \dfrac{\$160}{(1+0.10)}+ \dfrac{\$150}{(1+0.10)^2}+ \dfrac{\$140}{(1+0.10)^3} $

$ NPV = \$174.60 $


What rate of return would bring NPV down to zero?

Internal Rate of Return

  • Sometimes we do not know the discount rate
  • We usually know (estimate) cash flows and timing
  • This information gives us an implied return
  • Accept projects with $IRR>R$

IRR
$\sum_{t=0}^{T} \dfrac{CF_t}{(1+IRR)^t} = 0$

IRR is the discount rate that makes $NPV=0$
Example

Suppose a project required an initial investment of $\$200$ with the following cash flows in years 1, 2, and 3: $\$$160, $\$$150, $\$$140. What is the project's IRR?

$ 0 = CF_0 + \dfrac{CF_1}{(1+IRR)}+ \dfrac{CF_2}{(1+IRR)^2}+ \dfrac{CF_3}{(1+IRR)^3} $

Using a financial calculator:

$IRR=.57=57\%$
(Accept this project if $R<57\%$)
Shortcomings of the IRR

  • Multiple IRRs with unconventional cash flows
      Modifiedd IRR (MIRR) is an attempt to workaround this

  • IRR is not a good measure with mutually exclusive projects

  • We can always use NPV if we know R

Profitability Index

  • Also known as Benefit/Cost Ratio
  • Sum of future discounted cash flows divided by the initial cost
  • Accounts for time value of money
  • Accept a project if $PI>1$

Profitability Index (PI)
$PI = \dfrac{\sum_{t=1}^{T} \dfrac{CF_t}{(1+R)^t}}{|CF_0|}$
Example

Suppose a project required an initial investment of $\$200$ with the following cash flows in years 1, 2, and 3: $\$$160, $\$$150, $\$$140. $R=8\%$. What is the project's PI?

$ \sum_{t=1}^{T} \dfrac{CF_t}{(1+R)^t} = \dfrac{\$160}{(1+0.08)}+ \dfrac{\$150}{(1+0.08)^2}+ \dfrac{\$140}{(1+0.08)^3} $ $=\$387.88$

$|CF_0| = \$200$

$PI= \dfrac{\$387.88}{\$200}$$=1.94$

Average Accounting Return

  • A simple method to give a rate of return to a project
  • There are variations of this measure
  • Ratio of average net income to average book value


$\text{Average Accounting Return} = \dfrac{\text{Average Net Income}}{\text{Average Book Value}}$
Example
Over the past 5 years, average net income has been $\$1,260$. The average book value has been $\$10,000$. What is the average accounting return?

$AAC=\dfrac{\$1,260}{10,000}$$=0.126$$=12.6\%$

Summary



  • Net Present Value (NPV)
  • Internal Rate of Return (IRR)
  • Profitability Index (PI)
  • Average Accounting Return (AAR)