Allowing for inflation and taxation in DCF

Financial Management (FM) · ACCA · 5 min read

Introduction: Bringing Real-World Factors into Investment Appraisal

Welcome to one of the most practical parts of the Financial Management (FM) syllabus! Up until now, you might have practiced Net Present Value (NPV) in a "perfect world" where prices stay the same and the taxman doesn't exist. In reality, prices rise over time (inflation) and companies must pay a portion of their profits to the government (taxation).

If we ignore these two factors, our project calculations will be inaccurate, and we might end up making the wrong investment decisions. Don't worry if this seems a bit heavy at first—we will break it down step-by-step!

Part 1: Dealing with Inflation

Inflation is the tendency for the prices of goods and services to rise over time. This means a dollar today will buy more than a dollar next year. In FM, we need to make sure our cash flows and our discount rate are speaking the same "language" regarding inflation.

Real vs. Nominal (Money) Rates

There are two ways to look at interest rates and cash flows:
1. Real: This ignores inflation. It’s the "underlying" value.
2. Nominal (or Money): This includes inflation. It’s the actual amount of cash that will change hands.

The Analogy: Imagine you have \$100 and a loaf of bread costs \$1. You can buy 100 loaves. If inflation is 10%, next year that bread costs \$1.10. To still buy 100 loaves, you need \$110. The 10% extra you need is the inflation, while the 100 loaves represent your real purchasing power.

The Fisher Equation

To move between real and nominal rates, we use the Fisher Equation (found in your exam formula sheet):
$ (1 + i) = (1 + r) \times (1 + h) $

Where:
$ i $ = Nominal (Money) rate
$ r $ = Real rate
$ h $ = Inflation rate

Which approach should you use?

The golden rule is consistency. You have two choices for your NPV calculation:
1. The Nominal Approach (Most Common): Use nominal cash flows (inflated) and discount them using the nominal rate.
2. The Real Approach: Use real cash flows (today's prices) and discount them using the real rate. (Note: This is only used if all cash flows inflate at the same rate, which is rare in exams!)

Step-by-Step: Inflating Cash Flows

If an exam question says "Sales are \$10,000 in today's prices" and inflation is 5%, you must inflate them year by year:
\n- Year 1: $ \$10,000 \times (1.05)^1 = \$10,500 $
\n- Year 2: $ \$10,000 \times (1.05)^2 = \$11,025 $
\n- Year 3: $ \$10,000 \times (1.05)^3 = \$11,576 $

Quick Review: Always check if the question gives you "current prices" (needs inflating) or "nominal prices" (already inflated). If different items (like sales and costs) have different inflation rates, you must use the nominal approach.

Key Takeaway: Always match your cash flows to your discount rate. If you have inflated cash flows, use the money (nominal) rate!

Part 2: Dealing with Taxation

Tax is a cash outflow. It reduces the net benefit of a project. In the FM exam, we focus on two main tax impacts: Tax on Operating Profits and Tax-Allowable Depreciation.

1. Tax on Operating Profits

When a project makes a profit, the company pays corporate tax.
Important: In exams, tax is often paid one year after the profit is earned. This is known as a one-year lag.
- Profit in Year 1 $ \rightarrow $ Tax paid in Year 2
- Profit in Year 2 $ \rightarrow $ Tax paid in Year 3

2. Tax-Allowable Depreciation (TAD) / Capital Allowances

The taxman does not allow "accounting depreciation" as an expense for tax purposes. Instead, they give us Tax-Allowable Depreciation (TAD). Think of TAD as a "Tax Shield" or a "Discount Coupon" that reduces your tax bill.

The TAD Process:

1. Calculate the TAD (usually 25% on a reducing balance basis).
2. Multiply the TAD by the tax rate (e.g., 30%) to find the Tax Saving.
3. This Tax Saving is a cash inflow (because it's money you didn't have to pay to the government).

Step-by-Step: The TAD "Balancing" Act

When you sell the asset at the end of the project (the "scrap value"), you must do a final calculation:
- If your Tax Value (Written Down Value) is higher than the Scrap Value, you get a Balancing Allowance (extra tax saving).
- If your Tax Value is lower than the Scrap Value, you have a Balancing Charge (extra tax to pay).

Memory Aid: "TAD is my friend." It feels like an expense, but it actually creates cash inflows by saving you tax!

Key Takeaway: Tax is an outflow (usually lagged by a year), but Tax-Allowable Depreciation creates a tax saving, which is an inflow.

Part 3: Putting It All Together (The Pro-Forma)

When you tackle a full NPV question with inflation and tax, follow this structure in your spreadsheet:

NPV Layout Example:

Year 0 | Year 1 | Year 2 | Year 3 | Year 4
Initial Investment: (Cost at T0)
Inflated Sales: (Inflated by $ h $)
Inflated Costs: (Inflated by $ h $)
Net Cash Flow: (Sales - Costs)
Tax on Profit: (Usually 1-year lag)
Tax Benefit of TAD: (Usually 1-year lag)
Scrap Value: (At the end of the project)
Total Cash Flows: (Sum of all above)
Discount Factor: (Using Nominal Rate $ i $)
Present Value: (Total Cash Flow $ \times $ Discount Factor)

Common Pitfall to Avoid: Never subtract accounting depreciation from your cash flows in NPV. We only care about the tax saving from the TAD, not the depreciation amount itself. NPV is for cash, and depreciation is not cash!

Final Quick Tips for Success

- Read the timing carefully: Does tax start in Year 1 or Year 2?
- Working Capital: If working capital is mentioned, remember it usually inflates too! (We cover this in a separate section, but keep it in the back of your mind).
- Don't Panic: If you get stuck on a tax calculation, make a reasonable assumption, state it, and move on. You can still get most of the marks for the rest of your NPV table!

Summary: Inflation makes future cash flows bigger (nominal) or requires a special discount rate (real). Taxation reduces your net cash flow but offers savings through Capital Allowances. Master the Fisher Equation and the TAD table, and you will be well on your way to passing the FM exam!

Quick check

Can you answer these now?

Open each question to check the key ideas from this chapter.

What is the difference between a real interest rate and a nominal (money) interest rate?

A real interest rate ignores inflation and represents underlying purchasing power, whereas a nominal rate includes inflation and represents the actual cash that will change hands.

What formula is used to convert between real and nominal interest rates?

The Fisher Equation: $ (1 + i) = (1 + r) \times (1 + h) $, where $ i $ is the nominal rate, $ r $ is the real rate, and $ h $ is the inflation rate.

What are the two consistent approaches for calculating NPV when inflation is present?

The Nominal Approach (inflated cash flows discounted at the nominal rate) and the Real Approach (real cash flows discounted at the real rate).

How do you calculate the nominal cash flow for a specific year if given a price in 'today's terms'?

Use the formula: $ \text{Nominal Cash Flow} = \text{Current Price} \times (1 + h)^n $, where $ h $ is the inflation rate and $ n $ is the number of years.

What is a 'one-year lag' in the context of corporate taxation?

It means the tax on a specific year's profit is paid one year later; for example, tax on Year 1 profit is a cash outflow in Year 2.

How does Tax-Allowable Depreciation (TAD) affect a project's cash flows?

TAD creates a 'tax shield' by reducing taxable profit, resulting in a cash inflow (tax saving) equal to $ \text{TAD Amount} \times \text{Tax Rate} $.

What is a Balancing Allowance versus a Balancing Charge at the end of an asset's life?

A Balancing Allowance is an extra tax saving when the asset's tax value (WDV) is higher than the scrap value; a Balancing Charge is extra tax to pay when the scrap value exceeds the WDV.

Why must accounting depreciation be excluded from the NPV calculation pro-forma?

Accounting depreciation is a non-cash bookkeeping entry; NPV is strictly concerned with the timing and amount of actual cash movements.

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