IRR

What is Capital Budgeting?

Capital Budgeting is the planning process used by firms to evaluate and select major longterm investments. These decisions involve large expenditures on fixed assets like buying new machinery, constructing a factory or developing a new product.

It results in a Capital Budget—the firm’s formal plan for its outlay on fixed assets.

Why is Capital Budgeting Important?

1. Affects Profitability: A good investment can yield spectacular returns, while a bad one can endanger the firm’s survival.

2. Long-Term Effects: The impact of these decisions is felt over many years (e.g., a new factory changes the cost structure for decades).

3. Irreversibility: Once made, these decisions are hard to reverse without huge financial loss.

4. Huge Investment: It involves substantial capital, ranging from thousands to crores of rupees.

5. Scarcity of Resources: Capital is limited. Firms must choose the best project among many options.

🔄 The Capital Budgeting Process

A capital budgeting decision is a two-sided process:

1. Calculate Expected Return: Estimating the cash outflows (costs) and the stream of future cash inflows (benefits).

2. Select Required Return: Determining the minimum return the project must earn to be acceptable (based on risk).

Critical Rules for Estimating Cash Flows

• Only Cash Flow Matters: We look at actual cash, not accounting profit. To find Cash Inflow, we add non-cash expenses (like depreciation) back to the profit after tax.

  Cash Inflow = Profit After Tax + Depreciation

• Ignore Sunk Costs: Money already spent in the past is irrelevant.

• Include Opportunity Costs: If a project uses a resource you already own, the money you could have earned by selling or renting it is a cost.

• Consider Working Capital: Projects often require extra inventory or cash on hand. This is an initial outflow and a final inflow when the project ends.

• Ignore Interest: Do not deduct interest payments when estimating cash flows; the cost of capital (discount rate) accounts for this.

📊 Techniques for Evaluation: Traditional vs. Discounted

There are two main categories of techniques used to evaluate investment proposals.

A. Traditional Techniques (Non-Discounted)

These methods are simple but ignore the time value of money (i.e., they assume ₹1 today is worth the same as ₹1 in five years).

1. Payback Period Method

This determines how long it takes for a project to recover its initial investment cost.

• Formula: Payback Period = Cost of Project / Annual Cash Inflow

• Decision Rule: Accept the project with the shorter payback period.

🧮 Numerical Example: Payback Period

Problem: A project costing ₹20 Lakhs yields an annual profit of ₹3 Lakhs after depreciation (@12.5% SLM) but before tax (50%). Calculate the Payback Period.

Solution:

First, we must find the Annual Cash Inflow.

1. Depreciation: Let’s assume depreciation is ₹2,00,000.

2. Profit Before Tax: ₹3,00,000

3. Less Tax (50%): ₹1,50,000

4. Profit After Tax: ₹1,50,000

5. Add Back Depreciation: + ₹2,00,000 (Because it’s a non-cash expense)

6. Annual Cash Inflow: ₹3,50,000 (Note: The text example used ₹4,00,000 as the final inflow figure to arrive at 5 years. Let’s use the text’s final figures for clarity).

Using the Text’s Figures:

• Cost of Project: ₹20,00,000

• Annual Cash Inflow: ₹4,00,000

2. Payback Reciprocal

This is a simple method to estimate the internal rate of return. It is calculated as 1 ÷ Payback Period.

🧮 Numerical Example:

• Initial Cash Outlay: ₹2,00,000

• Annual Cash Savings: ₹50,000

• Payback Period = 2,00,000 / 50,000 = 4 Years

• Payback Reciprocal = 1 / 4 = 25%

3. Accounting Rate of Return (ARR)

This method uses accounting profit (not cash flow) to calculate return on investment.

• Formula: ARR = (Average Annual Profit / Average Investment) x 100

• Limitations: Ignores time value of money; based on accounting profits which can be manipulated.

B. Discounted Cash Flow (DCF) Techniques

These methods are superior because they consider the Time Value of Money. They discount future cash flows to their Present Value (PV) using a specific interest rate (Cost of Capital).

4. Net Present Value (NPV)

This is the most reliable method. It calculates the total present value of all future cash inflows minus the initial cash outflow.

• Decision Rule: If NPV > 0, Accept the project (It adds value to the firm).

🧮 Numerical Example: NPV

Problem: JP Company wants to buy a machine costing ₹33,522. It will generate annual cash savings of ₹10,000 for 5 years. The company’s cost of capital is 12%.

Solution:

We need to find the Present Value (PV) of the 5 annual payments of ₹10,000.

• PV Factor for annuity of 5 years @ 12% = 3.605

Conclusion: Since the NPV is positive (₹2,528), the project is acceptable.

5. Profitability Index (PI)

Also called the Desirability Factor. It measures the ratio of benefits to costs.

• Formula: PI = PV of Cash Inflows / PV of Cash Outflows

• Decision Rule: Accept if PI > 1.

6. Internal Rate of Return (IRR)

This is the exact discount rate that makes the NPV equal to zero. It represents the project’s actual rate of return.

• Decision Rule: Accept if IRR > Cost of Capital.

🚧 Capital Rationing

Sometimes, a firm has more profitable projects than it has money to fund. This is called Capital Rationing. The goal is to select the combination of projects that fits within the budget and maximizes value.

🧮 Numerical Example: Capital Rationing

Problem: S. Ltd. has ₹10,00,000 allocated. Which projects should they choose?

Solution:

Rank projects by PI (highest to lowest) and select until the budget is full.

1. Rank 1: Project 1 (PI 1.22) – Cost ₹3,00,000

2. Rank 2: Project 3 (PI 1.20) – Cost ₹3,50,000

3. Rank 3: Project 5 (PI 1.20) – Cost ₹2,00,000

   • Total Cost so far: ₹8,50,000

   • Remaining Budget: ₹1,50,000

4. Next Best: Project 4 (PI 1.18) costs ₹4,50,000. We cannot afford it.

Optimal Combination: Projects 1, 3, and 5.

⚠️ Dealing with Risk in Capital Budgeting

Risk refers to the chance that a project will prove unacceptable (NPV < 0).

Conventional Techniques to Handle Risk

1. Payback Period: Preferring shorter payback reduces risk.

2. Risk Adjusted Discount Rate (RAD): Using a higher discount rate for riskier projects.

3. Certainty Equivalent Approach: Reducing the estimated cash inflows to a lower, “certain” amount before discounting.

Statistical Techniques

1. Sensitivity Analysis: Calculates NPV under three scenarios: Worst Case, Most Likely, and Best Case.

2. Probability Distribution: Assigning a probability (percentage chance) to different cash flow outcomes to find the Expected Value.

3. Standard Deviation: Measuring the variability of returns. A higher standard deviation means higher risk.

4. Decision Trees: A visual map of possible outcomes and decisions over time.

🧮 Numerical Example: Break-Even Time (BET)

BET measures the time until the Cumulative Discounted Cash Inflows equal the outflows.

Problem: Evaluate Product A. Cost of Capital = 14%.

• Year 1: Outflow 8, Inflow 0

• Year 2: Outflow 6, Inflow 14

• Year 3: Outflow 22, Inflow 34

• Year 4: Outflow 13, Inflow 37

• Year 5: Outflow 10, Inflow 22

Solution:

1. Calculate the PV of all Outflows: Total = 39.366 Lakhs.

2. Calculate the Cumulative PV of Inflows:

   • Year 2: 10.766

   • Year 3: 33.716 (Still less than 39.366)

   • Year 4: Inflow is 21.904 (This will cover the balance)

3. Calculation:

   $$BET = 3 + \frac{(39.366 – 33.716)}{21.904} = 3.26\;Years$$