When making any economic analysis projected into the future, there is always an element of uncertainty associated with the alternatives being studied, and it is precisely this lack of certainty that makes decision-making quite difficult.
In order to facilitate decision-making within the company, a sensitivity analysis can be carried out, which will indicate the variables that most affect the economic result of a project and which are the variables that have little impact on the final result.
In an individual project, sensitivity must be made with respect to the most uncertain parameter; for example, if you have an uncertainty regarding the sale price of the item you plan to manufacture, it is important to determine how sensitive the Internal Rate of Return (IRR) or Net Present Value (NPV) is with respect to the sale price. If you have two or more alternatives, it is important to determine the conditions under which one alternative is better than another.
Evaluation criteria
Projects must take into account all the aspects that go into determining decisions that affect the economic resources of the company.
You could see this phenomenon with a simple example; if a factory is currently supposed to produce a certain item manually. The production of each employee is five (5) units a day and they are paid $ 1,000 a day.
The possibility of acquiring a machine that can produce up to 100 units per day is presented, which costs $ 600,000 and has an annual operating cost of $ 30,000. For the first year and each subsequent year, the cost of operation increases by 15%, it requires a single operator and it is estimated that a daily salary of approximately $ 2,500 may be paid.
Determine to what extent manual work is profitable, which will be called plan A and at what time is profitable the purchase of the machine that can be put to work to its maximum capacity, which will be named plan B, assuming a Rate Opportunity Interest Rate (TIO) of 30%.
If an analysis of the problem is carried out, the cost of an item in plan A would be: 100/5 = 200 and the total cost would be given by the quantities produced, that is, 200X.
In the case of plan B, the cost of labor per unit of production would be given by 2,500 / 100 = 25 and the total cost by 25X.
But in this the value of the Equivalent Annual Uniform Cost (CAUE) of the production must be added, which in the example would be:
CAUE: 600,000 / a10¬30% + 30,000 /(0.15- 0.3) (a10¬30%) - 300,000 / S10¬30% + 25X
CAUE = 232,747 + 25X
The equilibrium point between the two plans is obtained when the Total Cost of A equals the Total Cost of B. that is:
200X = 232,747 + 25X
X = 1,330 units
Sensitivity analysis is an important part of presenting new financial projects within the company
If a graph is constructed that relates the costs with the numbers of units produced, it is necessary to:
1. For plan A:
|
PLAN A |
|
|
X |
COST A |
|
500 |
100,000 |
|
1330 |
266,000 |
|
2000 |
400,000 |
2. For plan B:
|
PLAN B |
|
|
X |
COST B |
|
500 |
245,247 |
|
1330 |
266,000 |
|
2000 |
282,747 |
3. By joining the cost results in a graph, we have:
In the graph, it is observed that, for an annual production of less than 1,330 units, Plan A is better, and from then on, Plan B is better. Making a decision, based on 1,330 units, is highly risky, because any error in the production estimate (determined by sales) can change the decision from one plan to another; however, for a production greater than 2,000 units or less than 1,000 units, it will be very successful since it practically becomes insensitive to production errors.
The maximum variation or error K that can be committed, without changing the decision, will be:
K = Xe - X / X
Where Xe = Balance point of the number of units produced.
X = Estimated annual production.
If K tends to zero, the sensitivity of the decision will be very high and if K is large the sensitivity will be low. Naturally, the subjective concept, which depends on the good judgment of the financial analyst.
In the example, the sensitivity index K is calculated:
K = 1330 - 2000/2000
K = - 0.335
K = - 33.5%
This means that a decrease of 33.5% is not enough to change the decision. If a production of 1,200 units is assumed, it would be necessary to:
K = 1330 - 1200/1200
K = 0.11
K = 11%
This means that an increase in production of 11% that would be equivalent to 1,200 * 0.11 = 132 units does not change the decision.
