PM - Decision Making Techniques

Cost-Volume-Profit Analysis

DIFFERENT TECHNIQUES:

Cost-volume-profit analysis is used to determine how changes in costs and volume affect a company's
operating income and net income.

There are a number of techniques that can be used to understand how changes in cost and volume impact on
profits:

1) Break-even point. This tells us the volume of sales at which we make a zero profit. To make a zero profit,
we just need to ensure that:

Total contribution = Fixed costs

Contribution = Sales revenue - Variable costs

Contribution per unit = Sales price per unit - Variable costs per unit

The break-even formula can be defined as:

Fixed costs
Break-even volume =
Contribution per unit

Break-even volume Fixed costs

Break-even revenue = x =
Selling price per unit Contribution to sales ratio (see below)

Fixed costs
Break-even for multi-product =
Weighted average contribution per unit
 Total contribution
Weighted average contribution per unit =
Total volume sold

2) Margin of safety. This tells us how far our sales volume can fall before we start incurring a loss. The larger
the margin of safety, the better, this means that sales would have to drop some way before we start making
a loss. It is calculated as follows:

Margin of safety (volume) = Budgeted sales volume - Break-even sales volume

Margin of safety (volume)

Margin of safety (as a %) = x 100%
Budgeted sales volume

3) Contribution to sales ratio. This ratio tells us how much of our revenue is converted to contribution to
cover our fixed costs. The higher the c/s ratio, the better, as this means that we are generating a higher
contribution per $ of revenue.

Contribution per unit

Contribution to sales ratio =
Selling price per unit

Total contribution
Weighted average C/S ratio =
Total revenue

4) We can extend the break-even calculations to find a target profit or target revenue:

Fixed costs + target profit

Target profit (volume) =
Contribution per unit

Fixed costs + target profit

Target revenue = Target profit (volume) x Selling price per unit =
Contribution to sales ratio

Fixed costs + target profit

Target revenue for multi-products =
Weighted average c/s ratio
5) Break-even chart:

6) Profit-volume chart. This chart plots the profits made at different sales volumes:

7) Profit-volume chart for multiple products. The chart we have just plotted is only relevant in single-
product scenarios, so we now need to look at the situation with regards to multiple products:
- We need to rank the products based on their c/s ratio;
- Then we decide which product to make first, which to make second, and so on;
- We then calculate the total profit made at each output level and chart this on the graph to find the break-
even point.
LIMITATIONS:

The methods discussed have the following limitations:

1) All of the methods assume that fixed costs are constant at all output volumes and that there are not stepped
fixed costs;
2) The methods assume that variable costs and selling prices do not change as output and sales volumes
change;
3) We are assuming that the efficiency and productivity are also constant at all output levels, and that there is
no learning curve effect or price-demand relationships;
4) We are assuming that whatever we produce, we sell, so there are no changes in our inventory levels;
5) There is an assumption that fixed and variable costs can be split and that there are no semi-variable costs
within the business.
 PM - Decision Making Techniques
Make or Buy and Other Short Term Decisions

MAKE OR BUY DECISION:

When we consider the issues surrounding short-term decision making, we need to assess:

1) Resources available to us. Where there are restrictions, we can use limiting factor analysis or linear
programming;
2) Whether there are options available to us when resources are scarce. We need to consider the cost of
buying the product in and we also need to think about the quality of the product being made for us;
3) Continuity of supply and lead times. If we are considering outsourcing production we need to ensure that we
can meet customer demand;
4) Whether we will be tied to a supplier for a fixed period of time and what is the minimum contract term or
minimum purchase quantity;
5) Whether the supplier has the appropriate skill set to replicate the product that we are currently making in-
house. Or does the supplier have specialist skills that we don’t currently have in-house or don’t wish to
focus our time on;
6) Other factors specific to the company such as confidentiality, ethical considerations or union involvement if
work is outsourced.

We need to remember a few key features of relevant costing:

- Fixed costs are ignored unless they change as a result of the decision;
- We only consider future cash flows;
- We only consider changes in those cash flows as a result of the decision we are making;

So we are only interested in future incremental cash flows.

Where there is spare capacity it will make sense to make products in-house as the variable cost of making will
usually be lower than the cost of buying a ready made product. If, however, the cost of buying-in is lower than
the variable costs of manufacture we would opt to buy-in as this will increase our contribution per unit and our
overall profit.
Where there is no spare capacity and we are not meeting demand we then need to consider which products we
should make in-house and which we should buy-in by looking at what is cheaper to do and the amount of fixed
costs we might save by buying in the products in rather than making them.

SHUT-DOWN DECISION:

Here we need to look at the cost savings associated with the closure and also at the lost revenue resulting from
that closure.

The basic principle is that we need to calculate the lost contribution (sales minus variable costs) resulting from
the closure and compare this to the fixed costs we would save through the closure:

Contribution lost > Fixed cost saved Keep the operation running

Contribution lost < Fixed cost saved Close the operation

Note: We should also ensure we cover any costs of redundancies, any potential legal action resulting from the
closure, any retraining of existing employees and compensation to customers awaiting products that they will
now not receive.

ONE-OFF CONTRACTS:

The incremental future cash flows associated with the contract, such as increased labour costs, increased fixed
costs, increased overheads and so on need to be combined to find the total relevant cost of the contract.

Minimum price = Total of future incremental cash flows

Contract price < Relevant costs Decline the contract

Contract price > Relevant costs Accept the contract

Note: There may be other factors that mean a company would take on the contract despite the potential loss.

JOINT PRODUCTS:

A joint product happens when two or more products are made from the same processing operation that are
roughly equal in terms of selling price.

So we need to find the incremental revenue that would be generated by the higher selling price of the product
going through more production processes and compare this to the incremental costs of those production
processes.

Incremental revenue > Incremental costs Go ahead with the further processing

Incremental revenue < Incremental costs Sell the products off at the split-off point
 without further processing.

Note: Here we are not interested in the cost of the joint product at the time of split-off as these costs are
effectively sunk costs (not relevant costs).
 PM - Decision Making Techniques
Dealing with Risk and Uncertainty in Decision Making

RISK VS UNCERTAINTY:

Risk ≠ Uncertainty

Risk is a quantifiable measure and involves known possibilities and known or estimable probabilities.

With uncertainty , either the probabilities are unknown, and (or) also some of the possibilities are unknown.

The key difference boils down to whether or not you have any experience of the event, because experience builds
a knowledge of possibilities and probabilities.

PAY-OFF TABLES:

Pay-off tables can help us to make decisions when we are faced with risk.

Example: The table below shows the contribution that would arise depending on the decision of the sandwich
shop owner (across the top) and the risky variable (down the left hand side):
If the shop owner was risk neutral, he would choose the option which, on average, will earn him the highest return.
In other words, he will make his choice based on expected values. However, he may not be risk neutral.
He could be risk averse or risk seeking.

A risk averse decision maker is a pessimist and assumes that poor outcomes will occur following their decision.
They make a decision that will make that poor outcome the best it can possibly be, which is known as the
“maximin” approach.

A risk seeking decision maker is an optimist. He assumes good outcomes will follow from his decisions, therefore
focusing on the upside. He will choose the option that gives him the maximum possible return and
ignore the downside possibility attached to the decision, which is known as the “maximax” approach.

A risk averse individual may seek to choose the option that minimises the size of the error they make in hindsight.
This involves constructing a table of opportunity costs, which uses the payoff table as a starting point:

This approach of minimising a maximum possible regret is known as “minimax regret”, and is a form of risk
aversion.

If the shop owner was offered a perfect information about what the street demand will be, the value of the decision
with perfect information would be calculated as follows:

Remember: No information is perfect in the real world.

Sometimes, we may face more than one risky variable. For example, suppose we are unsure about what sales
and fixed costs might be. If we wanted to calculate, as a risk neutral decision maker, what expected profits are,
given that contribution per unit is $4, we would do it as follows:

Note: Joint probability tables are useful things that tell us more than simply expected values.
DECISION TREES:

A decision tree is a visual representation of a set of interrelated decisions that shows the reader a path from one
decision to the next.

Imagine that the shop owner is considering opening another sandwich shop. The decision tree could look as follows
(assuming that he is risk neutral):

- Decision trees are read from left to right;

- We calculate decision trees from right to left;
- A square node means a decision needs to be made;
- A circular node is down to chance.

Note: In your exam questions, there may be a choice - to do market research or not. If the path with research is
higher than without research, then this additional value can be attributed to the imperfect information generated
by the research itself. This approach can help us to determine the maximum we would be prepared to pay for that
information.

SENSITIVITY ANALYSIS:

Imagine that a sandwich shop owner is considering launching a new line of yogurts to sell as desserts. The
following information is available:
1) Sales price sensitivity. Sales revenue would have to increase by $250 to eliminate the profit:

Required decrease in sales $250

Sales price sensitivity = = = 12.5%
Total sales $2000

Note: The shop owner is 12.5 % sensitive to his estimate of the sales price.

2) Variable cost sensitivity. Variable cost would have to increase by $250 to eliminate the profit:

Required increase in VC $250

Variable cost sensitivity = = = 20%
Total VC $1250

Note: The shop owner is 20% sensitive to his original estimate of variabl cost.

3) Sales volume sensitivity. A reduction in sales volume affects both sales revenue and variable cost. In
other words, it affects contribution:

Decrease in contribution $250

Sales volume sensitivity = = = 33%
Total contribution $750

Note: The shop owner is 33% sensitive to sales volume.

4) Fixed costs sensitivity. Fixed costs would need to increase by $250 from the current $500 to eliminate the
profit entirely:

Required increase in FC $250

Fixed cost sensitivity = = = 50%
Total FC $500
Note: The shop owner is 50% sensitive to his estimate of fixed costs.

The decision maker should focus on those variables with a low percentage when refining their estimates and
considering their final decision.

The sensitivity analysis has the following drawbacks:

- It is not an “optimising technique” (i.e., it doesn't provide any specific answer as to whether or not we should
continue);
- It doesn’t include any consideration for how likely the decision is to be wrong;
- It only looks at one variable changing at a time, which is unrealistic.
SIMULATIONS AND SCENARIO PLANNING:

In the above example, the shop owner used a “point estimate” for each of the variables. However, if he had the
experience or could do sufficient research, he could produce a more detailed probability distribution. Here is
an example of a normal distribution that might better represent the potential volume of sales:

The standard deviation (σ) is used to quantify the amount of variation around the average. It is calculated using
the following formula:

- EV is the expected value;

- p is probability;
- x is a possible outcome.

The shop owner could combine the probability distributions to come up with a probability distribution of profit. It
might look like this:

Note: Although this is not an optimising technique, in that it doesn’t give a “yes” or “no” answer, it still gives a more
realistic picture of what the future might hold.
Often, organisations will consider a series of plausible future events to map out how they might affect the
business and how the business could plan in advance to respond. For example, an airline might consider what
happens if fuel prices increase by 30 %.

There must be sufficient skill and experience in the organisation to consider which variables to focus on first, but
this can be a useful tool to help organisations plan in advance.