Chapter: Capital Investment Appraisal

Hello everyone! Welcome to one of the most important topics in financial management: Capital Investment Appraisal. Don't let the fancy name scare you! This is all about how businesses make smart decisions on big, expensive, long-term projects.

Think about it: if a coffee shop owner wants to open a new branch, or a tech company wants to develop a new app, they need a way to figure out, "Is this project a good idea? Will it make us money in the long run?" That's exactly what we're going to learn in this chapter. It's the toolkit businesses use to peek into the future and make better choices. Let's get started!


1. What is a Capital Investment Decision?

A capital investment decision (also called capital budgeting) is the process of planning and deciding on long-term investments or projects.

These are not everyday decisions like buying more paper for the printer. These are the BIG ones:

  • Buying a new, expensive machine that will last for 10 years.
  • Building a whole new factory.
  • Launching a new product that requires a lot of research and development.
  • Expanding the business into a new country.

These decisions are crucial because they involve a lot of money, and the company is usually stuck with them for a long time. A bad decision can be very costly!

Factors to Consider When Making the Decision

Making a good decision isn't just about the numbers. Smart businesses look at both financial and non-financial factors.

Financial (Quantitative) Factors

These are the factors that we can measure in dollars and cents. They are all about the money.

  • Initial Investment Cost: How much money do we need to spend right now to start the project?
  • Expected Cash Inflows: How much extra cash will the project bring into the business each year?
  • Project Lifespan: How many years will the project be useful and generate cash?
  • Profitability: Will the project ultimately add to the company's profit?
Non-financial (Qualitative) Factors

These are the important things that are hard to put a number on, but can have a big impact on the business.

  • Example: A company is deciding whether to buy a cheaper machine that pollutes a lot, or a more expensive, eco-friendly one.
  • Company Image: Choosing the eco-friendly machine might improve how customers see the company.
  • Employee Morale: Investing in new, safer equipment can make employees happier and more productive.
  • Environmental Impact: How will the project affect the environment?
  • Social Responsibility: Does the project align with the company's ethical values?
  • Government Regulations: Does the project meet legal requirements?
Key Takeaway

Capital investment appraisal is the process of evaluating major projects. The final decision should be based on a mix of financial factors (the numbers) and non-financial factors (the wider impact).


2. The Tool Kit: Capital Investment Appraisal Methods

To help with the financial side of the decision, managers use several tools or methods. We'll look at two methods you need to be able to calculate, and two you just need to understand conceptually.

Methods to Calculate:

  1. Payback Period (PBP)
  2. Net Present Value (NPV)

Methods to Understand (Calculation NOT required for HKDSE):

  1. Internal Rate of Return (IRR)
  2. Accounting Rate of Return (ARR)

Method 1: The Payback Period (PBP) - "How Fast Do I Get My Money Back?"

The Payback Period is the simplest method. It just answers one question: "How long will it take for this project to earn back the money I initially invested?"

How to Calculate PBP (with EVEN cash flows)

When the project generates the same amount of cash each year, the calculation is super easy.

Example: A project costs $100,000 to start. It is expected to generate a cash inflow of $25,000 every year.

Formula:

$$ \text{Payback Period} = \frac{\text{Initial Investment}}{\text{Annual Cash Inflow}} $$

Calculation:

$$ \text{Payback Period} = \frac{\$100,000}{\$25,000 \text{ per year}} = 4 \text{ years} $$

It will take 4 years to get the initial investment back.

How to Calculate PBP (with UNEVEN cash flows)

Don't worry, this is also simple! We just need one extra step: calculating the cumulative cash flow (the running total).

Example: A project costs $50,000. The cash inflows are:
Year 1: $20,000
Year 2: $20,000
Year 3: $15,000
Year 4: $10,000

Step-by-step:

  1. Create a table with a 'Cumulative Cash Flow' column.
  2. Find out when the initial investment is recovered.

Year 0: Investment = -$50,000
Year 1: Inflow = $20,000. Cumulative = $20,000. (Still need $30,000)
Year 2: Inflow = $20,000. Cumulative = $20,000 + $20,000 = $40,000. (Still need $10,000)
Year 3: Inflow = $15,000. At the start of this year, we only needed $10,000 more to break even. This year, we get $15,000. So we will pay back the rest during Year 3.

The payback happens sometime in Year 3. To find out exactly when:

$$ \text{Payback Period} = 2 \text{ years} + \frac{\text{Amount still needed}}{\text{Cash flow in the next year}} $$ $$ = 2 \text{ years} + \frac{\$10,000}{\$15,000} = 2 + 0.67 = 2.67 \text{ years} $$

So, the payback period is 2.67 years.

The PBP Decision Rule
  • A company will usually have a maximum payback period they are willing to accept (e.g., 3 years). If the project's PBP is shorter than this, it might be accepted.
  • When comparing two projects, the one with the shorter payback period is usually preferred.
Usefulness and Limitations of PBP

Usefulness (Advantages):

  • Simple to calculate and understand. Great for quick checks.
  • Focuses on liquidity. It's good for businesses that need to get their cash back quickly.
  • Reduces risk. A quick payback means less time for things to go wrong.

Limitations (Disadvantages):

  • Ignores the time value of money. It treats a dollar received in Year 3 the same as a dollar received in Year 1. (We'll fix this with NPV!)
  • Ignores cash flows after the payback period. A project could make huge amounts of money in later years, but PBP wouldn't see this.

Method 2: Net Present Value (NPV) - "What's the Real Value in Today's Money?"

This method is a bit more advanced, but it's also much more powerful because it tackles the biggest weakness of the PBP method. It's based on one simple, but very important idea.

Prerequisite Concept: The Time Value of Money

The Time Value of Money means that money you have today is worth more than the same amount of money in the future. Why? Because you can invest the money you have today and it will grow (thanks to interest). If someone promises you $100 in one year, that's less valuable than getting $100 right now.

To compare money from different years, we need to bring all future money back to its value today. This process is called discounting.

Discounting is the opposite of earning interest. We use a discount rate (which is like an interest rate) to calculate the Present Value (PV) of a future cash flow.

How to Calculate NPV (Step-by-Step)

The Net Present Value (NPV) is simply the sum of the present values of all cash inflows minus the initial investment.

Example: A project costs $80,000. The expected cash inflows are:
Year 1: $30,000
Year 2: $40,000
Year 3: $50,000
The company's required rate of return (the discount rate) is 10%.

Step 1: Find the Present Value (PV) for each year's cash flow.
The formula to find the present value factor (PVF) is:

$$ \text{PVF} = \frac{1}{(1 + r)^n} $$

...where 'r' is the discount rate and 'n' is the number of years.

  • Year 1 PV: $$ \frac{\$30,000}{(1 + 0.10)^1} = \frac{\$30,000}{1.1} = \$27,273 $$
  • Year 2 PV: $$ \frac{\$40,000}{(1 + 0.10)^2} = \frac{\$40,000}{1.21} = \$33,058 $$
  • Year 3 PV: $$ \frac{\$50,000}{(1 + 0.10)^3} = \frac{\$50,000}{1.331} = \$37,566 $$

Step 2: Add up all the present values of the inflows.

$$ \text{Total PV of Inflows} = \$27,273 + \$33,058 + \$37,566 = \$97,897 $$

Step 3: Subtract the initial investment.

$$ \text{NPV} = \text{Total PV of Inflows} - \text{Initial Investment} $$ $$ \text{NPV} = \$97,897 - \$80,000 = \$17,897 $$
The NPV Decision Rule
  • If NPV is positive (> $0): The project is expected to earn more than the required rate of return. Accept the project.
  • If NPV is negative (< $0): The project is expected to earn less than the required rate of return. Reject the project.
  • If NPV is zero (= $0): The project is expected to earn exactly the required rate of return. The company is indifferent.
  • When comparing projects, choose the one with the highest positive NPV.
Usefulness and Limitations of NPV

Usefulness (Advantages):

  • Considers the time value of money. This is its biggest strength! It gives a more realistic view of profitability.
  • Considers all cash flows over the entire life of the project.
  • Provides a clear decision rule. Positive NPV is good, negative is bad. Simple.

Limitations (Disadvantages):

  • More complex to calculate than PBP.
  • Difficult to choose the correct discount rate. The final NPV is very sensitive to this choice.
  • It gives an absolute value ($), which can make it hard to compare projects of very different sizes.

Methods You Only Need to Understand (No Calculation Required!)

For your HKDSE exam, you just need to know what these two methods are. You do not need to calculate them.

Internal Rate of Return (IRR)
  • Concept: The IRR is the specific discount rate that makes the NPV of a project exactly equal to zero. You can think of it as the project's true rate of return.
  • Decision Rule: If the project's IRR is greater than the company's required rate of return, the project is accepted.
Accounting Rate of Return (ARR)
  • Concept: This method uses accounting profits from the Income Statement instead of cash flows. It calculates the average annual profit as a percentage of the investment.
  • Key Limitation: Its biggest weakness is that it uses profit, not cash flow, and it completely ignores the time value of money.

3. Final Showdown - Comparing the Methods

Let's summarise the key differences in a simple table. This is great for revision!

Method
Payback Period (PBP)

Considers Time Value of Money?
No

What it Measures
Time to recover investment (Liquidity)

Main Advantage
Simple and easy to understand

Main Disadvantage
Ignores cash flows after payback and time value of money


Method
Net Present Value (NPV)

Considers Time Value of Money?
Yes

What it Measures
Value added to the company in today's dollars (Profitability)

Main Advantage
Theoretically the best method; considers all cash flows and time value of money

Main Disadvantage
Can be complex to calculate and requires a pre-determined discount rate


Chapter Summary

Well done! You've learned the essential tools for making smart investment decisions.

Remember, no single method is perfect. In the real world, businesses often use a combination of these methods. They might use the Payback Period for a quick check on risk and liquidity, and then use NPV for a more detailed analysis of profitability. Finally, they will always consider the important non-financial factors before making a final decision.

Keep practicing the calculations for PBP and NPV, and you'll be an expert in no time!