Traditional Capital Budgeting Methods: Payback Period & ARR

Methods of capital budgeting are broadly classified into two categories:

1. Traditional (Non-Discounted) Methods: Ignore the Time Value of Money.
2. Modern (Discounted Cash Flow) Methods: Account for the Time Value of Money.

In this chapter, we master the two classic traditional techniques: the Payback Period (PBP) and the Accounting Rate of Return (ARR).

1. The Payback Period (PBP) Method

The Payback Period is the exact number of years and months required for a project to generate cumulative cash inflows equal to its original initial capital outlay.

It answers the simple question: “How long will it take to get our investment money back?”

Case A: When Annual Cash Inflows are CONSTANT (Even Cash Inflows)

When a machine generates the exact same Cash Flow After Tax (CFAT) every single year:

Payback Period = Initial Capital Investment / Annual Cash Inflow (CFAT)

Example:

• A new automated packaging machine costs ₹5,00,000.
• It generates an annual cash inflow of ₹1,25,000 each year for 6 years.
• Payback Period:

  Payback Period = ₹5,00,000 / ₹1,25,000 = 4.0 Years

Case B: When Annual Cash Inflows VARY (Uneven Cash Inflows)

In most real-world businesses, cash flows fluctuate each year. In this case, we compute Cumulative Cash Inflows:

Practical Solved Numerical Problem:

A project requires an initial cash outlay of ₹6,00,000. Its expected Cash Inflows After Tax (CFAT) over 5 years are:

Step-by-Step Calculation:

1. By the end of Year 3, the company has recovered ₹5,50,000.
2. Balance needed to reach the ₹6,00,000 initial outlay = ₹6,00,000 - ₹5,50,000 = ₹50,000.
3. During Year 4, the project generates ₹1,50,000.
4. Fraction of Year 4 needed:

   Fraction = Unrecovered Amount / Cash Inflow in Next Year = ₹50,000 / ₹1,50,000 = 0.33 Years (or 4 Months)

5. Exact Payback Period = 3 Years and 4 Months (3.33 Years).

Decision Rule for Payback Period:

• Independent Project: Accept if PBP is less than the maximum acceptable payback standard set by management.
• Mutually Exclusive Projects: Choose the project with the shortest payback period!

Evaluation of Payback Method:

• Merits: Extremely simple to understand and calculate; highly favored by small business owners; excellent measure of project liquidity and short-term capital recovery speed.
• Demerits:
  1. Completely ignores Time Value of Money: Treats ₹1,00,000 in Year 5 the same as ₹1,00,000 in Year 1!
  2. Ignores Cash Flows After the Payback Date: A project that recovers its money in 3 years and dies is preferred over a project that recovers in 3.5 years but generates massive profits for 20 more years!
  3. Ignores salvage value and economic life of the asset.

2. Accounting Rate of Return (ARR) Method

Unlike the payback method (which uses cash flows), the Accounting Rate of Return (ARR) is based on Accounting Net Profit After Tax as derived from financial accounts.

Formulas for ARR:

Standard Formula (Based on Average Investment):

ARR = (Average Annual Net Profit After Tax / Average Investment) × 100

Where:

Average Annual Profit = Total Profit After Tax over Project Life / Number of Years Average Investment = (Initial Outlay - Salvage Value) / 2 + Salvage Value + Additional Working Capital (If salvage value is zero, Average Investment = Initial Outlay / 2)

Solved Practical Numerical Problem on ARR:

An investment project costs ₹4,00,000 with an estimated economic life of 5 years and a scrap (salvage) value of ₹40,000. The annual net profits after depreciation and 30% tax are:

• Year 1: ₹40,000
• Year 2: ₹60,000
• Year 3: ₹70,000
• Year 4: ₹50,000
• Year 5: ₹30,000

Step 1: Calculate Average Annual Profit After Tax:

• Total Profit = ₹40,000 + ₹60,000 + ₹70,000 + ₹50,000 + ₹30,000 = ₹2,50,000
• Average Annual Profit = ₹2,50,000 / 5 = ₹50,000

Step 2: Calculate Average Investment:

Average Investment = (₹4,00,000 - ₹40,000) / 2 + ₹40,000 = (₹3,60,000 / 2) + ₹40,000 = ₹1,80,000 + ₹40,000 = ₹2,20,000

Step 3: Calculate ARR:

ARR = (₹50,000 / ₹2,20,000) × 100 = 22.73%

Decision Rule for ARR:

• Independent Project: Accept if ARR exceeds the minimum required accounting rate of return (e.g., benchmark rate of 15%).
• Mutually Exclusive Projects: Accept the project with the highest ARR!

Evaluation of ARR Method:

• Merits: Easy to calculate directly from standard P&L statements; considers earnings over the entire life of the project.
• Demerits: Uses accounting profit instead of cash flows (ignores non-cash distortion); completely ignores the time value of money!

3. Comparative Summary: Payback Period vs ARR

4. Summary & Quick Revision Checklist

• Payback Period: Time taken to recover original capital outlay; shorter payback is preferred.
• Payback Rule: Initial Investment / Annual CFAT (even) or Cumulative fraction (uneven).
• ARR Formula: (Average Profit After Tax / Average Investment) × 100.
• Critical Flaw of Both Methods: Neither accounts for the Time Value of Money!