Net Present Value (NPV) with Inflation and Taxation: A Simple Explanation

What is NPV with Inflation and Taxation?

Net Present Value (NPV) measures the profitability of an investment by discounting future cash flows to their present value. In the ACCA FM exam, you’ll adjust cash flows for inflation (rising costs/prices) and taxation (e.g., tax on profits, tax relief on capital costs) to assess real-world viability.

Let’s explore NPV for a project investment.

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Key Components of NPV Calculation

To calculate NPV with inflation and tax:

1. Nominal Cash Flows: Adjust real cash flows for inflation.
2. Tax Impact: Account for tax on profits and tax relief (e.g., capital allowances).
3. Discounting: Use the nominal discount rate (adjusted for inflation) to find present value.

Formulae

• Nominal Cash Flow = Real Cash Flow × (1 + Inflation Rate)^n (n = year)
• Tax on Profits = Taxable Profit × Tax Rate
• NPV = Sum of Discounted Cash Flows - Initial Investment

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Numeric Example

A company invests $100,000 in a machine:

• Life: 3 years
• Real Cash Inflows: $50,000/year (before inflation)
• Inflation Rate: 5% per year
• Tax Rate: 20% (payable in the year profits arise)
• Nominal Discount Rate: 10% (includes inflation)
• Capital Allowance: 100% in Year 1 (tax relief on $100,000)

Step 1: Calculate Nominal Cash Flows

• Year 1: $50,000 × 1.05 = $52,500
• Year 2: $50,000 × (1.05)^2 = $50,000 × 1.1025 = $55,125
• Year 3: $50,000 × (1.05)^3 = $50,000 × 1.157625 = $57,881

Step 2: Adjust for Tax and Capital Allowance

• Taxable Profit: Nominal Cash Flow (no other costs assumed)
• Tax: 20% of nominal cash flows
  • Year 1: $52,500 × 20% = $10,500
  • Year 2: $55,125 × 20% = $11,025
  • Year 3: $57,881 × 20% = $11,576
• Tax Relief (Year 1): $100,000 × 20% = $20,000 (capital allowance)

Step 3: Net Cash Flows and NPV

Year	Nominal CF	Tax	Tax Relief	Net CF	Discount Factor (10%)	Present Value
0	-$100,000	-	-	-$100,000	1.000	-$100,000
1	$52,500	-$10,500	$20,000	$62,000	0.909	$56,358
2	$55,125	-$11,025	-	$44,100	0.826	$36,427
3	$57,881	-$11,576	-	$46,305	0.751	$34,775

• NPV = -$100,000 + $56,358 + $36,427 + $34,775 = $27,560

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What Does This Mean?

• NPV ($27,560): Positive, so the project is viable (returns exceed costs).
• Inflation: Increases cash inflows but erodes real value.
• Taxation: Reduces cash flows, offset by Year 1 relief.

Management might ask: Is 10% the right discount rate? Could inflation rise further?

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Why It Matters for ACCA FM

NPV with inflation and tax tests your ability to:

• Adjust cash flows for economic factors (inflation).
• Incorporate tax effects in investment decisions.
• Use discounting to evaluate project profitability.

Practice with multi-year projects or varying rates to pass in FM!

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