Profit-Sharing & Sacrificing Ratios on Partner Admission

Why Do We Need New Ratios?

When a new partner is admitted, they acquire a share in the firm's future profits. This share is given up, or "sacrificed," by the existing partners. This change necessitates the calculation of two important ratios:

1. New Profit Sharing Ratio (NPSR): The ratio in which all partners (including the new one) will share future profits and losses.
2. Sacrificing Ratio (SR): The ratio in which the old partners have agreed to sacrifice their share of profits in favour of the new partner. This ratio is particularly important for adjusting goodwill, as we will see in a future lesson.

The fundamental formula to keep in mind is:
$\text{Sacrificing Share}=\text{Old Share}-\text{New Share}$

Let's explore the different scenarios you will encounter when calculating these ratios.

Calculating the New Profit Sharing and Sacrificing Ratios

The method for calculating the NPSR and SR depends entirely on the information provided in the partnership agreement or the problem. We will cover the most common cases.

For a comprehensive overview with solved examples for each case, the following video will be our primary guide. We will break it down section by section.

Now, let's dive into the practical calculations.

Case 1: New Partner's Share is Given, but Sacrifice is Not Mentioned

This is the most common and basic scenario. You are told the new partner's share, but the problem is silent about how the old partners contribute to this share.

The Logic:
In this case, we assume the old partners continue to share the remaining profit in their old profit-sharing ratio. Consequently, they also sacrifice their share in their old ratio.

The Steps:

1. Assume the total share of the firm is 1.
2. Calculate the remaining share: Remaining Share = 1 - New Partner's Share.
3. Calculate the new share for each old partner: Old Partner's New Share = Remaining Share × Old Partner's Old Share.
4. The new partner's share is already known. Ensure all shares have a common denominator to express the NPSR.
5. Calculate the sacrificing ratio using the formula: Sacrificing Share = Old Share - New Share.

Let's watch this in action.

Key Takeaway: When the problem only gives the new partner's share, the old partners' sacrificing ratio is the same as their old profit-sharing ratio.

Case 2: New Partner Acquires Share in a Specific Manner from Old Partners

This scenario is more direct. The problem explicitly states how the new partner gets their share from the old partners. The keywords here are "acquires from," "takes from," or if the sacrifice is given "equally" or in a specific ratio.

The Logic:
The sacrificing share of each old partner is directly given or easily calculated. The new share is found by simply subtracting the sacrificed share from the old share.

The Steps:

1. Identify the share sacrificed by each old partner from the problem statement.
2. Calculate the new share for each old partner: New Share = Old Share - Sacrificed Share.
3. The other old partners who are not sacrificing retain their original share.
4. The new partner's share is the sum of the shares sacrificed by the old partners.
5. The sacrificing ratio is simply the ratio of the shares sacrificed.

The video covers three variations of this scenario.

Case 3: Old Partners Surrender a Fraction 'OF' Their Share

Pay close attention to the wording here. "A surrenders 1/4 of his share" is different from "A surrenders 1/4 share from his share." The word "of" implies multiplication.

The Logic:
First, you must calculate the actual fraction being sacrificed by multiplying the surrender fraction with the old partner's share. Then, you subtract this amount to find the new share.

The Steps:

1. Calculate the share sacrificed by each old partner: Share Sacrificed = Old Partner's Share × Fraction Surrendered.
2. The ratio of these calculated sacrificed shares is the Sacrificing Ratio.
3. Calculate the new share for each old partner: New Share = Old Share - Share Sacrificed.
4. Calculate the new partner's share by summing the shares sacrificed by the old partners.

Let's see how this is handled.

To reinforce this specific calculation, here is a clear visual summary.

Case 4: Both Old and New Ratios are Given

This is the most straightforward scenario for calculating the sacrificing ratio.

The Logic & Steps:
Simply apply the formula directly for each old partner:
$\text{Sacrificing Share}=\text{Old Profit Share}-\text{New Profit Share}$
A positive result means a sacrifice, while a negative result would mean a gain.

Watch the final segment of the video for a quick example.

Conclusion

Excellent work! You have now covered the essential calculations required to readjust profit-sharing ratios upon the admission of a new partner. This is a foundational skill for this chapter.

Key Takeaways:

• New Profit Sharing Ratio (NPSR) is for sharing future profits among all partners.
• Sacrificing Ratio (SR) is the proportion in which old partners give up their profit share. It is calculated as Old Ratio - New Ratio.
• Case 1 (Implicit Sacrifice): If only the new partner's share is given, the SR is the same as the old partners' old ratio.
• Case 2 (Explicit Sacrifice "from"): If the sacrifice is specified (e.g., "from A," "equally"), the SR is given. Calculate NPSR by subtraction: New Share = Old Share - Sacrificed Share.
• Case 3 (Explicit Sacrifice "of"): If a partner surrenders a fraction 'of' their share, first multiply to find the amount sacrificed, then subtract to find the new share.

Preview of the Next Lesson:

Now that you can calculate the sacrificing ratio, you are ready to use it. In the next lesson, we will address the learning outcome: Account for goodwill on admission using the premium method (cash) and adjustment through capital accounts (non-cash). You will see how the sacrificing ratio is used to credit the old partners for the goodwill brought in by the new partner.