Part 119: Financial Tools

  • Also known as “Constrained Optimization Techniques”
  • On the PMP Exam, questions with the word “programming” may refer to Constrained Optimization Techniques
    • Payback Period for an investment
      • How many months or years until we generate revenue that is equal to the investment
      • For example, if we invest $1,000,000 up front, and we generate revenues of $100,000 each year, it would take us 10 years to recover the $1,000,000.  Thus, the Payback Period is 10 years (assuming no inflation)
    • Return on Investment
      • The percentage of money an investment generates
      • For example, if we invest $1,000,000 up front, and generate revenues of $100,000 each year, our Return on Investment is 10%.  $100,000 is 10% of $1,000,000.
    • Internal Rate of Return
      • The Internal Rate of Return (IRR) tells us how profitable an investment will be
      • Its calculated from
      • Every corporation has cash that it can either invest or leave in the bank to collect interest.
      • Just because an investment is expected to produce more money than the interest that the bank is paying doesn’t mean that the corporation will invest in it.  That is because new investments have risks.  So, the corporation only invests in projects that meet its minimum acceptable rate of return.
      • With any investment, there is an amount of money going in at the beginning (the negative cash flow), and then a whole bunch of money being paid off (the positive cash flow).
      • In the IRR, we add up all the positive and negative cash flows and make them equal to 0.  Then we try to figure out what the value of “r” should be.  “r” is our Internal Rate of Return.
      • For example, if we build an office building, we put up the money for the construction costs and then the tenants pay us rent.
      • Let’s say our cash flow looks like this following table.  In real life, the cash flow will be more complicated (our office building would have maintenance & taxes)

YEAR 1-$1,000,000 investment/construction cost
YEAR 2$260,000 lease payment
YEAR 3$270,000 lease payment
YEAR 4$270,000 lease payment
YEAR 5$350,000 lease payment
  • What is our IRR?  We can use the equation.This is complicated math.  In a normal math equation, we find a solution.  In this equation, we pretend that the answer is 0 and then try to figure out what value of “r” will get us zero.  It’s more complicated because r is present in every term of the equation, so it’s a lot harder to solve (r shows up multiple times in the equation).  In real life, you can use a computer to solve for “r”.  On the PMP exam, you won’t be given a math question this complicated.  You might get a bunch of IRR values and asked to choose the best one.Also, due to the math involved, it’s important to remember that multiple values of “r” may solve the equation.  Mathematically, they are all correct.  But for our purposes, we’re looking for a value of “r” that is between 0 and 1.00.  Typical values of “r” are between 0.01 (1%) and 0.20 (20%).In this equation, the values of “r” that are mathematically correct are r=-1.67, and r=0.06.  Only 0.06 is valid.  That means that our internal rate of return is 6%.A negative value of “r” means that our project costs more than it will bring in.Discounted Cash Flow
    • Present Value (PV)
      • Also known as the time value of money
      • Due to inflation, money decreases in value over time (goods and services get more expensive)
      • When given a sum of money in the future, the Present Value is how much that sum is worth now
      • Calculated from


PV = Present Value
FV = Future Value
i = Interest Rate
t = Time

For example, if the interest rate is 8% per year, and we have an investment that is expected to return $1000 in two years, its present value is:

  • Net Present Value
    • The same as the Present Value, except that it considers the sum of the Present Value of multiple inflows and outflows that take place in the future
    • Example, if the interest rate is 8% per year, and you have the following
      $200,000 investment at the beginning of the project
      $100,000 investment at one year in the project
      $80,000 return at two years in the project
      $80,000 return at three years in the project
      $80,000 return at four years in the project

      We would calculate the present value for each value (outflows are negative)