Depreciation & Sinking Funds: Methods, Calculations & Business Uses

What is Depreciation?

Depreciation is the gradual loss in value of a fixed asset (like machinery, vehicles, or buildings) over time due to wear and tear, obsolescence, or usage. Businesses must account for this loss to show accurate financial statements.

Why is Depreciation Important?

• Matches expenses with revenue: If an asset helps generate income, its cost should be spread over its useful life.
• Tax benefits: Depreciation reduces taxable income.
• Accurate financial reporting: Shows the true value of assets on the balance sheet.

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Observation: Straight-line depreciation is constant, while reducing balance decreases each year.

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Methods of Depreciation

There are four main methods taught in NEB syllabus:

1. Straight-Line Method (SLM)

Definition: Depreciation is spread equally over the asset’s useful life. Formula: $$\text{Annual Depreciation}=\frac{\text{Cost of Asset}-\text{Scrap Value}}{\text{Useful Life (in years)}}$$ Example: A car costs Rs. 500,000, has a scrap value of Rs. 50,000, and a useful life of 5 years. $$\text{Annual Depreciation}=\frac{500,000-50,000}{5}=\text{Rs. 90,000 per year}$$ Depreciation Schedule:

When to Use? ✅ Simple to calculate. ✅ Good for assets that lose value evenly (e.g., buildings, furniture). ❌ Does not account for faster wear in early years.

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2. Reducing Balance Method (RBM)

Definition: Depreciation is a fixed percentage of the book value at the start of each year. Formula: $$\text{Annual Depreciation}=\text{Book Value at Start of Year}\times \text{Depreciation Rate}$$ Example: Same car (Rs. 500,000, scrap Rs. 50,000, 20% depreciation rate).

When to Use? ✅ Better for assets that lose value faster early on (e.g., computers, vehicles). ✅ Higher depreciation in early years (tax benefits). ❌ Book value never reaches zero (scrap value is ignored in calculations).

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3. Sum-of-Years’ Digits (SYD) Method

Definition: Depreciation is higher in early years and decreases over time, based on a weighted fraction. Formula: $$\text{Annual Depreciation}=\left(\frac{\text{Remaining Life}}{\text{Sum of Years’ Digits}}\right)\times (\text{Cost}-\text{Scrap Value})$$ Step 1: Calculate Sum of Years' Digits (SYD). For 5 years: $5+4+3+2+1=15$. Step 2: Apply the formula for each year. Example: Same car (Rs. 500,000, scrap Rs. 50,000).

When to Use? ✅ More realistic than SLM for assets that wear out faster early. ✅ Higher depreciation in early years (good for tax planning). ❌ More complex calculations.

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4. Machine Hour Method (Not in NEB Syllabus but Useful for Understanding)

Definition: Depreciation is based on actual usage (e.g., machine hours worked). Formula: $$\text{Depreciation per Hour}=\frac{\text{Cost}-\text{Scrap Value}}{\text{Total Estimated Hours}}$$ Example: A machine costs Rs. 200,000, scrap value Rs. 20,000, and is expected to run 10,000 hours. If it runs 2,000 hours in Year 1: $$\text{Depreciation}=\frac{200,000-20,000}{10,000}\times 2,000=\text{Rs. 36,000}$$

When to Use? ✅ Best for assets used unevenly (e.g., factory machinery). ❌ Requires tracking usage data.

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What is a Sinking Fund?

A sinking fund is a separate fund created to replace or repair an asset at the end of its useful life. It is calculated using compound interest principles.

Why Use a Sinking Fund?

• Ensures money is available when needed.
• Avoids last-minute financial stress.
• Helps in planning for replacements.

Formula for Sinking Fund Installment

$$\text{Annual Installment}=\frac{\text{Amount Needed at End}}{{\left(1+\frac{r}{100}\right)}^n-1}\times \left(1+\frac{r}{100}\right)$$ Where:

• $r$ = interest rate per period
• $n$ = number of periods

Example: A company wants to replace a machine worth Rs. 500,000 in 5 years. If it earns 10% interest, what should be the annual sinking fund installment? $$\text{Installment}=\frac{500,000}{{\left(1+0.10\right)}^5-1}\times 1.10$$ $$=\frac{500,000}{1.61051-1}\times 1.10$$ $$=\frac{500,000}{0.61051}\times 1.10\approx \text{Rs. 90,400 per year}$$ Sinking Fund Table:

Note: The slight difference from Rs. 500,000 is due to rounding.

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Depreciation vs. Sinking Fund

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Solved NEB-Style Problems

Problem 1: Straight-Line Depreciation

A machine costs Rs. 80,000 and has a scrap value of Rs. 10,000 after 5 years. Calculate annual depreciation. Solution: $$\text{Annual Depreciation}=\frac{80,000-10,000}{5}=\frac{70,000}{5}=\text{Rs. 14,000}$$

Problem 2: Reducing Balance Depreciation

A vehicle costs Rs. 300,000 with a 15% depreciation rate. Calculate book value after 3 years. Solution:

Answer: Rs. 184,237.50

Problem 3: Sum-of-Years’ Digits

A printer costs Rs. 60,000 with a scrap value of Rs. 10,000 and a life of 4 years. Calculate depreciation for Year 2. Solution:

1. SYD = 4 + 3 + 2 + 1 = 10
2. Depreciable Amount = 60,000 - 10,000 = Rs. 50,000
3. Year 2 Fraction = 3/10
4. Depreciation = (3/10) × 50,000 = Rs. 15,000

Problem 4: Sinking Fund

A company wants Rs. 200,000 in 4 years with a 12% interest rate. What is the annual sinking fund installment? Solution: $$\text{Installment}=\frac{200,000}{{\left(1+0.12\right)}^4-1}\times 1.12$$ $$=\frac{200,000}{1.57352-1}\times 1.12$$ $$=\frac{200,000}{0.57352}\times 1.12\approx \text{Rs. 39,300}$$

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Exam Tips for NEB Business Mathematics

1. Understand the Difference:

   • Depreciation is a book entry (no cash flow).
   • Sinking fund involves actual savings.

2. Memorize Formulas:

   • Straight-Line: $\frac{\text{Cost}-\text{Scrap}}{\text{Life}}$
   • Reducing Balance: $\text{Book Value}\times \text{Rate}$
   • SYD: $\frac{\text{Remaining Life}}{\text{SYD}}\times (\text{Cost}-\text{Scrap})$
   • Sinking Fund: $\frac{\text{Amount Needed}}{{\left(1+r\right)}^n-1}\times (1+r)$

3. Practice Tables:

   • NEB often asks for full depreciation schedules (like the ones above).

4. Watch Units:

   • Ensure years, rates, and amounts are consistent (e.g., annual vs. monthly).

5. Real-World Application:

   • Relate to business scenarios (e.g., "A factory buys a machine...").

6. Common Mistakes to Avoid:

   • Forgetting scrap value in SLM and SYD.
   • Misapplying compound interest in sinking funds.
   • Incorrect SYD calculation (e.g., using wrong digits).

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NEB Board-Style Questions (Practice)

1. Short Answer:

   • Define depreciation. Why is it important for businesses?

2. Calculation:

   • A computer costs Rs. 40,000 with a scrap value of Rs. 5,000 and a life of 4 years. Calculate: a) Annual depreciation under SLM. b) Book value after 2 years under RBM (25% rate).

3. Conceptual:

   • Explain the difference between depreciation and a sinking fund with an example.

4. Long Answer:

   • A company buys machinery for Rs. 250,000 with a scrap value of Rs. 50,000 and a life of 5 years. a) Calculate depreciation for each year using SYD. b) If the company wants to replace it in 5 years with a 10% interest rate, what should be the annual sinking fund installment?

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Good luck with your NEB exams! 🚀 Remember: Practice at least 10 problems from past NEB papers to master this unit.