Project viability and cash flow projection methods

Welcome to Capital Project Evaluation!

In this chapter, we explore how businesses decide which big projects are worth their time and money. Imagine you are given £10,000 to invest in either a coffee shop or a tech startup. How do you choose? In the world of CB1, we use specific mathematical tools to answer this. Don't worry if this seems tricky at first; we will break down each method step-by-step!

1. The Basics: Cash Flow vs. Profit

Before we dive into the methods, remember one golden rule in project evaluation: Cash is King. Most of these methods focus on net cash flows (the actual money moving in and out) rather than accounting profits. This is because you can't pay your bills with "accrued profit"—you need actual cash in the bank!

Quick Review: Net Cash Flow = Cash Inflows minus Cash Outflows.

2. Payback Period (PBP)

The Payback Period is the simplest method. It asks one question: "How long will it take to get my initial investment back?"

How to calculate it:

You simply add up the cash inflows year by year until they equal the initial cost.
Example: You spend £100 today. You get £50 in Year 1 and £50 in Year 2. Your PBP is 2 years.

Decision Rule:

Accept the project if the PBP is less than a pre-determined target set by the company.

Pros and Cons:

+ Pros: Very simple to understand; focuses on liquidity (getting cash back fast).
- Cons: It ignores the Time Value of Money and, more importantly, it ignores any cash flows that happen after the payback date. If a project makes £1 million in Year 10, PBP won't care!

Memory Aid: Think of PBP as "Patience Breaks Poverty"—how much patience do you have before you are back in the black?

3. Discounted Payback Period (DPBP)

This is a "leveled-up" version of the PBP. It solves the problem of the Time Value of Money by discounting the cash flows before adding them up.

Step-by-Step Process:
1. List the annual cash flows.
2. Discount each cash flow to its Present Value (PV) using the company's required rate of return.
3. Add these PVs cumulatively until the initial investment is recovered.

Key Takeaway: The DPBP will always be longer than the standard PBP because money in the future is worth less than money today.

4. Net Present Value (NPV)

The NPV is the "Gold Standard" of project evaluation. It tells us the total value a project adds to the company in today's money.

The Formula:

\( NPV = \sum_{t=1}^{n} \frac{C_t}{(1+r)^t} - I \)

Where:
\( C_t \) = Cash flow at time \( t \)
\( r \) = Discount rate (cost of capital)
\( I \) = Initial Investment

Decision Rule:

If NPV > 0: Accept the project (it adds value).
If NPV < 0: Reject the project (it destroys value).
If NPV = 0: You are indifferent (you break even exactly).

Analogy:

Imagine someone offers you £110 in a year's time if you give them £100 today. If the bank interest rate is 10%, that £110 is only worth £100 today. Your NPV is £0. If the bank rate was only 5%, the deal is much better, and your NPV would be positive!

Common Mistake to Avoid: Never use accounting profit in an NPV calculation. Only use cash flows!

5. Internal Rate of Return (IRR)

The IRR is the "break-even" interest rate. It is the specific discount rate that makes the NPV of a project exactly zero.

Decision Rule:

Accept the project if the IRR is greater than the Cost of Capital.
Example: If a project's IRR is 15% and it costs you 10% to borrow the money, you make a 5% "profit" in rate terms.

How to find it (Interpolation):

Since the IRR formula is hard to solve directly, we usually find one NPV that is positive and one that is negative, then use this formula:
\( IRR \approx L + \frac{NPV_L}{NPV_L - NPV_H} \times (H - L) \)

Where \( L \) is the lower discount rate and \( H \) is the higher discount rate.

Did you know? A project can sometimes have multiple IRRs if the cash flows change from positive to negative more than once. This is one reason why NPV is often considered more reliable than IRR.

6. Accounting Rate of Return (ARR)

Unlike the other methods, the ARR uses accounting profits instead of cash flows. It expresses the average annual profit as a percentage of the investment.

The Formula:

\( ARR = \frac{\text{Average Annual Accounting Profit}}{\text{Average Investment}} \times 100\% \)

Note: Average Investment is usually calculated as \( \frac{\text{Initial Outlay} + \text{Residual Value}}{2} \).

Key Takeaway:

The ARR is popular with managers because it links directly to the company's published financial statements, but actuaries dislike it because it ignores the timing of cash flows.

7. Summary Comparison: Which Method is Best?

When comparing projects, you might find that NPV and IRR give different rankings. In these cases, NPV is always the preferred method because it measures the absolute increase in shareholder wealth.

Quick Summary Table:
1. PBP: Good for liquidity, ignores time value.
2. NPV: The best for wealth maximization, uses cash flows.
3. IRR: Easy to understand as a percentage, but can be misleading.
4. ARR: Uses profit, ignores time value, easy for non-finance managers.

Don't feel overwhelmed! The best way to master these is to practice calculating one of each. Once you see how the numbers move, the logic becomes second nature. You've got this!

Welcome to the Core of Project Appraisal!

Hi there! Welcome to one of the most practical and important chapters in your CB1 journey. In the previous chapters, you might have learned about different ways to value a business or a project. But how do we get the numbers that go into those calculations? That is exactly what we are going to cover today.

Estimating cash flows is like being a detective. You need to look at a project and decide which pieces of money moving in and out actually "count." Get this right, and your Net Present Value (NPV) calculations will be solid. Get it wrong, and you might recommend a project that actually loses money!

Don't worry if this seems a bit technical at first. We will break it down step-by-step, using simple logic and real-world examples.

1. The Fundamental Golden Rule: The Incremental Principle

The most important thing to remember is the Incremental Principle. When evaluating a project, we only care about the change in cash flows that happens specifically because we took on the project.

Ask yourself: "If I don't do this project, does this cash flow still happen?"
- If the answer is Yes, ignore it.
- If the answer is No, include it.

Sunk Costs (The "Let It Go" Costs)

A Sunk Cost is money that has already been spent and cannot be recovered, regardless of whether the project goes ahead.
Example: You spent \$10,000 last year on a feasibility study to see if a new juice bar would work. Whether you open the juice bar today or not, that \$10,000 is gone.
Common Mistake: Students often try to include sunk costs to "recoup" them. In CB1, we ignore them! We only look forward, never backward.

Opportunity Costs (The "Road Not Taken")

An Opportunity Cost is the value of the next best alternative that you give up to do this project. Even if no physical cash leaves your pocket today, it is a real cost.
Example: If you use a warehouse you already own for a new project, you can't rent it out to someone else. The lost rent is a cash outflow for the project.

Side Effects and Externalities

Sometimes a new project affects your existing business. This is often called Cannibalization or Erosion.
Example: If Apple releases a new iPhone, sales of the older iPhone might drop. We must subtract those lost sales from the new project’s cash flows.

Quick Summary: Only include Incremental flows. Ignore Sunk Costs. Include Opportunity Costs and Side Effects.

2. Dealing with Inflation

Inflation is the general increase in prices over time. In CB1, you must be very careful to be consistent. There are two ways to handle this:

1. Nominal Approach: Use "Nominal Cash Flows" (the actual dollars you expect to see in the future, including inflation) and discount them using a "Nominal Discount Rate."
2. Real Approach: Use "Real Cash Flows" (expressed in today's purchasing power) and discount them using a "Real Discount Rate."

The Golden Rule of Consistency: Never mix and match!
- Nominal Flows + Nominal Rate = Correct.
- Real Flows + Real Rate = Correct.
- Nominal Flows + Real Rate = Disaster!

The Fisher Equation

You can convert between real and nominal rates using this formula:
\( (1 + i) = (1 + r) \times (1 + h) \)
Where:
\( i \) = nominal interest rate
\( r \) = real interest rate
\( h \) = expected inflation rate

Memory Aid: Think of Nominal as "Name only" (the number on the bill) and Real as "Real power" (what it can actually buy).

3. Taxation and Capital Allowances

Tax is a real cash outflow. However, the government often gives businesses a "discount" on their taxes to encourage investment in equipment. This is done through Capital Allowances (sometimes called Tax-allowed Depreciation).

The Tax Shield

Depreciation itself is not a cash flow (it's just an accounting entry). However, because depreciation reduces your taxable profit, you pay less tax. This saving is called a Tax Shield.

The cash flow effect of a capital allowance is:
\( Tax\ Saving = Capital\ Allowance \times Tax\ Rate \)

Tax Timing

In many exam questions, tax is not paid in the same year the profit is earned. It is often paid one year later.
Example: If a project earns profit in Year 1, the tax cash outflow might occur in Year 2. Always read the question carefully to see if tax is paid "in the same year" or "in arrears."

Key Takeaway: Depreciation is NOT a cash flow, but the Tax Saving resulting from it IS a cash flow.

4. Working Capital

When you start a project, you often need to tie up money in Working Capital (like buying inventory or having cash in the till). This is a cash outflow at the start of the project.

As the project grows, you might need more working capital (an additional outflow). At the end of the project, you usually recover all that working capital (a cash inflow), as you sell off the last of the stock and collect your final payments.

Quick Review Box: Working Capital Tips
- Initial investment = Outflow (Year 0).
- Increase in working capital = Outflow.
- Decrease in working capital = Inflow.
- Recovery at the end = Inflow (usually in the final year).

5. Step-by-Step: How to Estimate Project Cash Flows

When you face a complex problem, follow these steps to stay organized:

1. Identify the Initial Investment: This includes the cost of the asset, delivery, and setup, plus any initial working capital.
2. Forecast Operating Cash Flows:
- Calculate Revenues (Price x Volume).
- Subtract Operating Costs (Variable and Fixed).
- Note: Do NOT subtract interest payments here! Interest is handled by the discount rate.
3. Calculate Tax: Apply the tax rate to the operating profit, making sure to subtract capital allowances first to find the taxable amount.
4. Identify Terminal Cash Flows: At the end of the project, add back any scrap value (salvage value) of the equipment and the recovery of working capital.

6. Common Mistakes to Avoid

Don't worry if this seems tricky at first, many students make these mistakes! Just keep an eye out for them:

- Including Interest Payments: In project appraisal, we use the discount rate (like WACC) to account for the cost of financing. If you subtract interest payments as a cash flow AND use a discount rate, you are double-counting the cost of money.
- Forgetting the Terminal Value: Many students forget to "clean up" at the end of the project by adding back the scrap value and working capital recovery.
- Miscalculating the Tax Shield: Remember that you only get the tax saving on the allowable depreciation, not the total cost of the asset all at once (unless it's a 100% first-year allowance).

Final Summary

- Cash flows must be incremental.
- Sunk costs are ignored; Opportunity costs are included.
- Be consistent with Inflation (Nominal vs. Real).
- Working capital is invested at the start and recovered at the end.
- Tax is a cash flow, and Capital Allowances provide a Tax Shield.

You’ve got this! Practice setting up these cash flows in a table format (Year 0, Year 1, Year 2...) to keep your work clear and easy to follow.