Investment Selection Methods: Static and Dynamic
Static Methods to Select Investments
The easiest way to compare investments is to use static methods (that don’t depend on the time of the cash flows). These are approximations but they are very easy to calculate, so we will use them to make a first evaluation.
Methods:
- Payback
Used to find out when our investment will be recovered. The sooner, the better. To calculate the period, we will check the cash flows. When our investment is covered by those cash flows, we will consider the investment has been recovered.
Advantages:
- Very easy to calculate.
- Gives an initial idea to evaluate an investment.
Drawbacks:
- Doesn’t count the profitability of the investment.
- Cash flows after the recovery period are not considered.
- Total Cash Flow per Invested Monetary Unit
Another option is to find out the ratio between the invested capital (A) and the received cash flows (Q):
Formula: Profitability* = (Q1 + Q2 + … + QN) / A
*This is not real profitability
- >1 is a good investment (according to this method)
- <=1 is not a good investment
Drawbacks:
- Not using time.
- Not using interests.
- Mean Cash Flow per Invested Monetary Unit
Another option is to find out the ratio between the invested capital (A) and the mean of the received cash flows (Q) in n periods:
Formula: Q = (Q1 + Q2 + … + QN) / N
Rate Formula: Rate = Q / A
Main idea: To solve the ‘time’ problem. Now we are evaluating investments of different durations with more accurate criteria. Note that the rate refers to periods required to cover the investment.
Drawbacks:
- Not using interests.
Dynamic Methods to Select Investments
Net Present Value (NPV)
NPV tries to represent the value of an investment. It calculates the present value of all the cash flows using the desired interest rate (k).
Formula: Present Value (PV) of the future cash flows can be found as: PV = Qt / (1 + k)^t = Q1 / (1 + k) + Q2 / (1 + k)^2 + … + Qn / (1 + k)^n
And if we take into account the initial investment (A) at t = 0 (Q0), we can calculate the NET value of the PV (the NPV).
Formula NPV: NPV = Qt / (1 + k)^t = A + PV
- If NPV > 0, the investment is positive (generates benefits).
- If NPV = 0, it is the same as doing nothing, so we could consider not investing (we don’t risk our money).
- If NPV < 0, the investment is not giving us the interest we are asking of it, so we won’t invest in this project.
To calculate the desired rate we want, we use the following formula: k = i + g + (i * g)
Where:
- K = Desired interest we want to get from the investment
- G = Inflation rate
- I = The growth we want from our investment (excluding inflation rate)
Internal Rate of Return (IRR)
The IRR of an investment is the rate k that makes the NPV = 0. With the NPV, we were trying to find the present value of the entire investment using a specific k. Now, when calculating the IRR, we are finding the k (IRR) that makes the NPV = 0.
Formula: -A + Q1 / (1 + k)^1 + Q2 / (1 + k)^2 + … + Qn / (1 + k)^n = 0
In the formula above, the IRR will be k. When k is higher than the expected interest, we consider the investment to be a good one. It is very difficult to find an exact value of k, so we will replace it with different values to get an approximation:
- Try different values of k until NPV = 0.
- The value of k that makes NPV = 0 is the IRR.
If there is no inflation, the IRR would also be the real profitability of the investment. As this is not correct, we can find out the real profitability with:
rR (aka real profitability) = (ra (aka IRR) – g (aka inflation)) / (1 + g)
Time Value of Money (TVM)
- PV = Present Value
- FV = Future Cash Flow (aka Future Value)
- i = Interest rate (remember, if the interest is 15%, use 0.15)
- n = Number of interest periods
Formula 1: FV = PV * (1 + i)^n
Formula 2: PV = FV / (1 + i)^n = FV * (1 + i)^-n
CPM and PERT
CPM (Critical Path Method)
PERT (Program Evaluation and Review Technique)
Difference: With CPM, the time for performing the activities is determined; with PERT, the time for performing the activity is an estimation.
PERT
- Identify the specific activities and milestones.
- Determine the proper sequence of the activities.
- Construct a network diagram.
- Determine the critical path.