How to Value Goodwill

In the previous chapter, we learned how to fix past errors in partnership accounts after the books were closed. Now, we are going to look at the future of the firm. Specifically, we are going to talk about the invisible magic that makes a successful business worth far more than just the cash in its bank account and the furniture in its office.

Imagine two tea stalls side by side. Both have the exact same equipment, the same quality of tea leaves, and the same amount of capital invested. But Stall A has been there for twenty years. The owner knows everyone's name, the service is famously fast, and there is a line down the street every morning. Stall B opened yesterday and is empty.

If you wanted to buy Stall A, the owner wouldn't just charge you for the cost of the stove and the cups. They would charge you a premium for the loyal customer base, the brand name, and the guaranteed daily profits. That premium—the financial value of a business's good reputation—is called Goodwill.

In this chapter, we will learn exactly how accountants put a mathematical price tag on this invisible asset.

Why Do We Need to Value Goodwill?

If a partnership firm is just running normally day-to-day, it doesn't need to calculate the value of its goodwill. The reputation is just there, quietly bringing in customers.

We only need to calculate the exact mathematical value of goodwill when the structure of the partnership changes. In accounting, this is called the reconstitution of the firm.

Reconstitution happens during:

• Admission of a new partner: A new person is joining. They will get a share of future profits that the old partners worked hard for years to build. The new partner must pay the old partners for this privilege.
• Retirement or death of a partner: A partner is leaving. They helped build the firm's reputation, so they (or their family) deserve to be paid their share of the goodwill before they go.
• Change in the profit-sharing ratio: Even if no one leaves or joins, if the partners decide to change how they split profits, someone is gaining an advantage and someone is sacrificing. The gainer must compensate the sacrificer based on the firm's goodwill.

To make these compensations fair, we need a universally agreed-upon number. That is why we value goodwill.

Step Zero: Finding the "Normal" Business Profit

Before we can use any mathematical method to value goodwill, we need to look at the firm's past profits. Goodwill is based on the firm's ability to earn profits from its core business operations.

However, the Net Profit figure you see in a standard Profit & Loss Account often includes random, one-time events that have nothing to do with the firm's daily business.

For example, if a firm's factory caught fire and they lost ₹50,000, their Net Profit for that year will look very low. But that fire was a random tragedy, not a sign that the business is bad. If we use that artificially low profit to calculate goodwill, we will undervalue the firm.

Conversely, if the firm won a lottery or sold an old piece of land for a massive profit, their Net Profit will look artificially high. We cannot expect to sell land every year, so we must remove this one-time gain.

Before calculating goodwill, you must adjust the past years' profits to find the Normal Operating Profit.

How to Adjust Past Profits

Worked Example: Adjusting Profits

A firm's profits for the last three years were:

• 2021: ₹1,00,000 (includes an abnormal gain of ₹20,000 from selling old machinery)
• 2022: ₹80,000 (after charging an abnormal loss of ₹30,000 due to a warehouse fire)
• 2023: ₹1,10,000 (excludes ₹10,000 payable as an annual insurance premium)

Adjusted Normal Profits:

• 2021: ₹1,00,000 - ₹20,000 (abnormal gain) = ₹80,000
• 2022: ₹80,000 + ₹30,000 (abnormal loss) = ₹1,10,000
• 2023: ₹1,10,000 - ₹10,000 (forgotten normal expense) = ₹1,00,000

You will use these bolded numbers (80k, 110k, 100k) for all your goodwill calculations, completely ignoring the original unadjusted numbers.

Method 1: The Average Profit Method

This is the simplest and most common method. The logic is straightforward: a business's future profits will likely resemble its average past profits.

There is a crucial term used in this method (and the next one) that you must understand: Number of Years' Purchase.

There are two variations of this method: Simple Average and Weighted Average.

1A. Simple Average Profit Method

Use this when profits are relatively stable, fluctuating up and down without a clear, continuous trend.

Step 1: Calculate the Average Profit. Average Profit = Total of Adjusted Normal Profits / Number of Years

Step 2: Calculate Goodwill. Goodwill = Average Profit × Number of Years' Purchase

Worked Example: Using our adjusted profits from earlier (2021: ₹80,000; 2022: ₹1,10,000; 2023: ₹1,00,000). Calculate goodwill at 2 years' purchase of the average profit of the last 3 years.

• Total Profit = 80,000 + 1,10,000 + 1,00,000 = ₹2,90,000
• Average Profit = 2,90,000 / 3 = ₹96,667
• Goodwill = 96,667 × 2 = ₹1,93,334

1B. Weighted Average Profit Method

Use this method when profits show a clear, continuous rising trend (or a continuous falling trend).

If profits are growing every year, the most recent year is a much better indicator of the future than a year from five years ago. To reflect this, we assign "weights" (usually 1, 2, 3, 4...) to the years, giving the highest weight to the most recent year.

Step 1: Multiply each year's profit by its weight to get the "Product". Step 2: Calculate the Weighted Average Profit. Weighted Average Profit = Total of Products / Total of Weights Step 3: Calculate Goodwill. Goodwill = Weighted Average Profit × Number of Years' Purchase

Worked Example: Profits for the last four years are: 2020: ₹40,000; 2021: ₹50,000; 2022: ₹60,000; 2023: ₹70,000. Calculate goodwill at 3 years' purchase of the weighted average profit, assigning weights 1, 2, 3, and 4 respectively.

• 2020: 40,000 × 1 = 40,000
• 2021: 50,000 × 2 = 1,00,000
• 2022: 60,000 × 3 = 1,80,000
• 2023: 70,000 × 4 = 2,80,000
• Total of Products = 40,000 + 1,00,000 + 1,80,000 + 2,80,000 = ₹6,00,000
• Total of Weights = 1 + 2 + 3 + 4 = 10
• Weighted Average Profit = 6,00,000 / 10 = ₹60,000
• Goodwill = 60,000 × 3 = ₹1,80,000

Method 2: The Super Profit Method

The Average Profit method is good, but it has a flaw. It assumes all profit is due to goodwill. But that's not true. Any business, even a brand new one with zero reputation, will earn a basic, normal return just by investing capital into the market.

Goodwill should only be based on the extra profit a firm makes above the industry average. This extra profit is called Super Profit.

To calculate Super Profit, we need two new concepts:

1. 1Capital Employed: The actual amount of money invested in the business. You can calculate this from the asset side (Total Assets excluding fictitious assets and non-trade investments minus Outside Liabilities) or the liability side (Partners' Capital + Reserves).
2. 2Normal Rate of Return (NRR): The standard percentage of profit that a normal, average business in the same industry earns on its capital. (This will always be given to you in the exam).

The Logic of Super Profit

If you invest ₹10,00,000 in a standard business, and the industry average return (NRR) is 10%, you expect to earn ₹1,00,000. That is your Normal Profit. If your specific firm actually earns ₹1,50,000, that extra ₹50,000 is your Super Profit. You only earned that extra 50k because of your firm's special reputation (Goodwill).

Worked Example: Super Profit Method

A partnership firm has a Capital Employed of ₹5,00,000. The Normal Rate of Return in this industry is 12%. The firm's actual average profit over the last few years is ₹85,000. Calculate goodwill at 2 years' purchase of super profit.

• Actual Average Profit: ₹85,000
• Normal Profit: ₹5,00,000 × (12 / 100) = ₹60,000
• Super Profit: ₹85,000 (Actual) - ₹60,000 (Normal) = ₹25,000
• Goodwill: ₹25,000 × 2 = ₹50,000

Method 3: The Capitalization Method

The Capitalization Method looks at goodwill from a completely different angle. Instead of asking "How much extra profit are we making?", it asks: "How much capital *should* we have needed to earn our current profit, compared to what we *actually* invested?"

Let's say your firm earns ₹1,00,000 a year, and the normal industry return is 10%. Normally, to earn ₹1,00,000 at 10%, a business would need to invest ₹10,00,000. But your firm is so efficient and well-loved that you only had to invest ₹6,00,000 to earn that same ₹1,00,000. You saved ₹4,00,000 in capital because your reputation did the heavy lifting. That ₹4,00,000 difference is your Goodwill.

Notice that in this method, we do not multiply by a "Number of Years' Purchase". The capitalization formula automatically calculates the total, permanent present value of the firm.

There are two ways to apply this method. Both will give you the exact same final answer.

3A. Capitalization of Average Profit

Step 1: Find the Capitalized Value of the Firm. This means finding out how much capital is normally required to earn the firm's actual average profit. Formula: `Capitalized Value = Actual Average Profit × (100 / Normal Rate of Return)`

Step 2: Find the Actual Capital Employed. (Total Assets - Outside Liabilities).

Step 3: Calculate Goodwill. Formula: `Goodwill = Capitalized Value of the Firm - Actual Capital Employed`

Worked Example: A firm earns an average profit of ₹72,000. The normal rate of return is 10%. The total assets of the firm are ₹9,00,000 and outside liabilities are ₹4,00,000. Calculate goodwill by capitalizing average profit.

• Capitalized Value of Firm: ₹72,000 × (100 / 10) = ₹7,20,000

(Meaning: A normal firm needs ₹7.2 Lakhs to earn ₹72k).

• Actual Capital Employed: ₹9,00,000 (Assets) - ₹4,00,000 (Liabilities) = ₹5,00,000

(Meaning: We only invested ₹5 Lakhs).

• Goodwill: ₹7,20,000 - ₹5,00,000 = ₹2,20,000

3B. Capitalization of Super Profit

Instead of capitalizing the total profit, we can just calculate the Super Profit and capitalize only that extra portion.

Step 1: Calculate Super Profit. (Just like we did in Method 2: Actual Profit - Normal Profit).

Step 2: Capitalize the Super Profit to find Goodwill. Formula: `Goodwill = Super Profit × (100 / Normal Rate of Return)`

Worked Example (Using the exact same data as above): Average profit = ₹72,000. NRR = 10%. Capital Employed = ₹5,00,000.

• Normal Profit: ₹5,00,000 × (10 / 100) = ₹50,000
• Super Profit: ₹72,000 (Actual) - ₹50,000 (Normal) = ₹22,000
• Goodwill: ₹22,000 × (100 / 10) = ₹2,20,000

As you can see, both Capitalization of Average Profit and Capitalization of Super Profit result in the exact same goodwill value (₹2,20,000). You can use whichever method you find easier unless the exam specifically requests one.

Quick Revision

Here is a rapid summary of the formulas to scan before your exam:

• Adjusting Profits: Always add back abnormal losses (fire, theft) and subtract abnormal gains (sale of assets) to find the true operating profit.
• Simple Average Method: Goodwill = Average Profit × No. of Years' Purchase.
• Weighted Average Method: Used when profits show a clear rising/falling trend. Goodwill = Weighted Average Profit × No. of Years' Purchase.
• Super Profit Method:
• Normal Profit = Capital Employed × (NRR / 100)
• Super Profit = Actual Average Profit - Normal Profit
• Goodwill = Super Profit × No. of Years' Purchase
• Capitalization of Average Profit: Goodwill = [Average Profit × (100 / NRR)] - Actual Capital Employed.
• Capitalization of Super Profit: Goodwill = Super Profit × (100 / NRR).
• Remember: The Capitalization methods do not use "Number of Years' Purchase".

Understanding these three methods ensures you can accurately value the invisible asset of reputation, setting the stage for a fair reconstitution of the partnership.