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25.2 Evaluate the Payback and Accounting Rate of Return in Capital Investment Decisions

Payback Period​

Payback period measures the time required to recover the initial investment in cash terms. It is simple and focuses on liquidity but ignores the time value of money and cash flows after payback.

Formula (Equal Cash Flows): Payback Period = Initial Investment ÷ Annual Cash Inflow

Formula (Unequal Cash Flows):

  • Accumulate cash inflows until they equal the initial investment

Example:

  • Initial investment: €150,000
  • Annual cash inflow: €50,000
  • Payback: €150,000 ÷ €50,000 = 3 years

Example (Unequal):

  • Initial investment: €200,000
  • Year 1: €60,000
  • Year 2: €70,000 (cumulative €130,000)
  • Year 3: €80,000 (cumulative €210,000)
  • Payback: 2 + (€70,000 needed / €80,000 in Year 3) = 2.875 years

Advantages:

  • Simple to calculate
  • Focuses on liquidity and risk (faster payback = lower risk)
  • Useful when cash is tight

Disadvantages:

  • Ignores time value of money
  • Ignores cash flows after payback
  • Bias towards short-term projects

Discounted Payback Period​

Discounted payback accounts for time value of money by discounting cash flows before computing payback.

Steps:

  1. Discount each cash inflow to present value
  2. Accumulate discounted cash flows
  3. Determine when cumulative discounted inflows = initial investment

Example:

  • Initial investment: €200,000
  • Discount rate: 8%
  • Cash inflows: €60,000, €70,000, €80,000, €90,000
  • Discount each inflow: Year 1 PV = €60,000 / (1.08)^1 = €55,556
  • Accumulate PVs until payback achieved

Accounting Rate of Return (ARR)​

ARR (also called return on average investment) measures the average accounting profit relative to the investment.

Formula: ARR = Average Annual Accounting Profit ÷ Initial Investment

or ARR = Average Annual Accounting Profit ÷ Average Investment

Example:

  • Initial investment: €100,000
  • Useful life: 5 years
  • Salvage value: €10,000
  • Average investment: (Initial + Salvage) / 2 = (€100,000 + €10,000) ÷ 2 = €55,000
  • Annual accounting profit: €15,000
  • ARR = €15,000 ÷ €55,000 = 27.27%

Advantages:

  • Uses accounting data (easy to understand)
  • Considers entire life of project

Disadvantages:

  • Ignores time value of money
  • Uses accounting profit, not cash flows
  • Depends on depreciation method

Comparison: Payback vs. ARR​

MethodFocusProsCons
PaybackLiquidity, riskSimple, highlights riskIgnores time value & later cash flows
Discounted PaybackLiquidity with time valueImproves paybackStill ignores cash flows after payback
ARRAccounting profitabilityUses entire lifeIgnores cash flows & time value

Luxembourg Compliance Note​

Banks and investors in Luxembourg may ask for payback and ARR metrics, but they also expect NPV/IRR for major investments. ARR must align with Luxembourg GAAP/IFRS depreciation and tax rules.

Think It Through​

In what situations might payback still be a useful decision metric despite its limitations? How could ARR be misleading?