Business | Decision-making techniques

Welcome to Decision-Making Techniques!

Hello future business leader! This chapter is incredibly important because it moves us beyond guesswork and into data-driven strategy. Every successful business makes critical choices about expansion, investments, and product development.

You are about to learn the powerful quantitative tools that managers use to weigh the pros and cons of different options and choose the path that offers the best return. Don't worry if some of the formulas look challenging at first—we will break them down step-by-step!

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I. Decision Trees: Mapping Uncertainty

Decision trees are visual tools that help managers structure and analyze sequences of decisions under conditions of risk (where probabilities are known).

What is a Decision Tree?

Imagine you have three options for your Saturday: study, work, or go out. But you don't know if it will rain. A decision tree maps out all these potential outcomes and their associated chances.

In business, a decision tree calculates the Expected Monetary Value (EMV) of different strategic options.

Key Components of a Decision Tree

• Decision Node (Square \(\Box\)): Represents a point where a choice must be made (e.g., launch product A or product B).
• Chance Node (Circle \(\bigcirc\)): Represents a point where outcomes are uncertain, and probabilities apply (e.g., success or failure).
• Branches: Lines connecting nodes, representing different courses of action or possible outcomes.
• Probabilities (P): The likelihood of an outcome occurring, written as a decimal (e.g., 0.6 for a 60% chance).
• Expected Values (EMV): The financial result expected from a path.

Calculating Expected Monetary Value (EMV)

The EMV helps us determine the weighted average of potential outcomes. It is the core calculation for decision trees.

Formula for EMV:
EMV = \(\sum (Probability \times Expected \ Outcome)\)

Step-by-Step EMV Calculation Process

1. Start from the Right: Begin at the end of the tree (the outcomes).
2. Calculate EMV at each Chance Node (\(\bigcirc\)): Multiply the financial value of each outcome by its probability, then add the results together.
3. Work Backwards to the Decision Node (\(\Box\)): When you reach a square (decision) node, select the path with the highest EMV.
4. Include Costs: Don't forget to subtract any initial costs (like investment or research costs) associated with a specific path *after* calculating the gross EMV.

Analogy: Think of a raffle ticket. If the prize is \$100 and you have a 1 in 10 chance (P=0.1) of winning, the EMV of holding that ticket is 0.1 x \$100 = \$10.

Advantages and Disadvantages of Decision Trees

Advantages (Pros):

• Forces managers to consider all possible outcomes systematically.
• Incorporates risk (probabilities) into the decision-making process.
• Easy to understand visually.

Disadvantages (Cons):

• Relies heavily on accurate probability estimates, which are often subjective guesses.
• Focuses only on financial outcomes and ignores qualitative factors (e.g., staff morale, reputation).
• Can become very complex if too many options are included.

Quick Review: Decision Trees

Decision Trees calculate EMV by multiplying Probability by Outcome. The square node means you choose; the circle node means chance determines the result.

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II. Investment Appraisal Techniques

Investment appraisal refers to the quantitative techniques used to evaluate the financial feasibility of long-term capital projects, such as buying new machinery, building a new factory, or launching a massive new product line.

These techniques help a business answer the question: "Which project offers the best value for money over the long term?"

Key Concept: Net Cash Flow
This is the money coming into the business from the project (inflows) minus the money leaving the business (outflows) for a specific period.

1. Payback Period (PP)

The Payback Period measures how long it takes for a project to generate enough net cash flow to recover the initial investment cost. It focuses on speed and liquidity (how quickly cash is returned).

Calculation Method

Scenario A: Equal Annual Cash Flows
If cash flows are the same each year, the calculation is simple:

PP = \(\frac{Initial \ Investment}{Annual \ Net \ Cash \ Flow}\)

Scenario B: Unequal Annual Cash Flows (More Common)

1. Calculate the cumulative cash flow year by year until the initial investment is recovered.
2. Identify the year the payback occurs (e.g., between Year 3 and Year 4).
3. Calculate the remaining fraction of the year:
   Fraction = \(\frac{Cash \ needed \ to \ payback}{Cash \ inflow \ in \ the \ following \ year}\)

Example: If \$50,000 is needed at the start of Year 3, and Year 3 brings in \$100,000, the extra time needed is \(\frac{\$50,000}{\$100,000} = 0.5\) years (or 6 months).

Decision Rule

Businesses usually set a maximum acceptable payback period (e.g., 3 years). Choose the project with the shortest payback period.

Evaluation of Payback Period

• Pro: Simple to calculate and understand; excellent measure of risk (quicker payback = less time for things to go wrong).
• Con: Ignores all cash flows that occur after the payback period is reached.
• Con: Ignores the overall profitability of the project.

2. Accounting Rate of Return (ARR)

The ARR (sometimes called the Return on Capital Employed, ROCE) calculates the average annual profit generated by the project as a percentage of the initial investment. It focuses on profitability.

Crucial Preliminary Step: Finding Average Annual Profit

ARR uses profit, not just cash flow. To find profit, we must account for depreciation (the loss in value of an asset over time).

Profit = Net Cash Flow – Depreciation

Average Annual Profit = \(\frac{Total \ Net \ Profit \ over \ the \ project's \ life}{Number \ of \ years}\)

ARR Formula

ARR = \(\frac{Average \ Annual \ Profit}{Initial \ Investment} \times 100\)

Did you know? Unlike Payback and NPV, ARR is the only method that uses profit figures from the Income Statement, rather than pure cash flows.

Decision Rule

Choose the project with the highest ARR, provided it exceeds the company’s target rate of return.

Evaluation of ARR

• Pro: Uses the entire life of the project (unlike Payback).
• Pro: Easy to compare with other business targets (e.g., existing ROCE).
• Con: Ignores cash timing. It treats profit earned in Year 1 the same as profit earned in Year 10.
• Con: It is based on accounting profit, which can be manipulated by different depreciation methods.

3. Net Present Value (NPV)

The Net Present Value (NPV) is considered the most sophisticated and powerful technique. It recognizes that money received today is worth more than the same amount of money received in the future. This is the concept of the Time Value of Money (TVM).

Understanding the Time Value of Money (TVM)

Why is money today worth more?

1. Inflation: Money loses purchasing power over time.
2. Opportunity Cost: If you have the money today, you could invest it and earn interest or returns (the opportunity you lose by waiting).

To use NPV, we must "discount" future cash flows back to their value today (their Present Value).

The Discount Factor

The discount factor (DF) is used to convert future money into present money. It depends on the company's cost of capital (the cost of financing the project, often represented as an interest rate).

Present Value (PV) = Future Cash Flow \(\times\) Discount Factor

The discount factor for a given interest rate (r) and year (n) is calculated as: DF = \(\frac{1}{(1+r)^n}\)

The NPV Calculation

NPV is the sum of all Present Values of the project's cash flows, minus the initial cost.

NPV = \(\sum (PV \ of \ all \ future \ cash \ flows) - Initial \ Outlay\)

Step-by-Step NPV Process

1. Identify the net cash flows for each year of the project.
2. Find the appropriate Discount Factor (usually provided in tables or specified by the question) for each year.
3. Calculate the Present Value (PV) for each year (Cash Flow x DF).
4. Sum up all the PVs.
5. Subtract the initial investment (which is already at Present Value, usually occurring in Year 0).

Decision Rule

• If NPV is Positive (\(NPV > 0\)): The project is financially worthwhile, as it yields a return greater than the cost of capital. ACCEPT.
• If NPV is Negative (\(NPV < 0\)): The project will destroy wealth. REJECT.

Evaluation of NPV

• Pro: The most comprehensive technique as it considers profitability, timing, and the cost of capital.
• Pro: Provides a clear measure of how much value (wealth) the project will add to the business.
• Con: Complex to calculate, especially without tables or software.
• Con: The result is highly sensitive to the discount rate chosen (if the discount rate is wrong, the NPV will be wrong).

Memory Aid: Remember the difference between the three: Payback = Period (Time); ARR = Accounting Profit (Percentage); NPV = Now (Present Value).

III. Using Appraisal Techniques Together

It is crucial to remember that managers rarely rely on just one technique. They use all three to gain a complete picture:

• Payback tells them the risk and liquidity.
• ARR tells them the overall accounting profitability.
• NPV tells them the true economic value.

Sometimes, the techniques conflict. A project might have a fast payback but a low NPV. In such cases, the business needs to decide whether short-term stability (Payback) or long-term wealth creation (NPV) is more important.

Common Mistake to Avoid

Students often forget that the initial investment (Year 0 cash flow) is treated as a negative value (outflow) and is not discounted in the NPV calculation, as it happens "today."

Well done! Mastering these decision-making techniques is vital for success in this course and in the real business world. Keep practicing the formulas!