VIPSolutionsgive answer in 2 step with explanation at the end of each step and final answer at the end:2. Assume a similar asst was bought or 15,000 tht has a 3-year depreciable lf. Fil in the empty boxes in ie yr S00 be ie FL tein bok ls nd dy ET [Fine [Boot va [a op rT I I EN NE I ER + MACKS meta [Fie Jove [op 7] rT I A I EY A I TY A A
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give answer in 2 step with explanation at the end of each step and final answer at the end:
2. Assume a similar asst was bought or 15,000 tht has a 3-year depreciable lf. Fil in the empty boxes in
ie yr S00 be ie FL
tein bok ls nd dy
ET
[Fine [Boot va [a
op
rT
I I EN
NE I ER
+ MACKS meta
[Fie Jove
[op 7]
rT
I A I
EY A I
TY A A
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Asked by: Rahul
Created at: 2025-12-11 07:55:39
Asked by: Rahul
Created at: 2025-12-11 07:55:39
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Let's solve the problem step by step for both methods:
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# **Step 1: Double-Declining Balance (DDB) Method**
### **Formula**
- Depreciation rate = 2 × (1 / Useful life)
- Book value at start of year × Depreciation rate = Depreciation for the year
#### **Given:**
- Cost = \$15,000
- Useful life = 3 years
- Depreciation rate = 2 × (1/3) = **66.67%**
### **Table Calculation**
| Time | Book Value | d_t (Depreciation) |
|------|------------|--------------------|
| | 15,000 | - |
| 1 | 15,000 | 15,000 × .6667 = **10,000** |
| 2 | 5,000 | 5,000 × .6667 = **3,333** |
| 3 | 1,667 | (1,667)* |
- After 2 years: Book value = 15,000 - 10,000 - 3,333 = **1,667**
- In the last year, depreciate the remaining amount to reach zero: 1,667
### **Filled Table**
| Time | Book Value | d_t (Depreciation) |
|------|------------|--------------------|
| | 15,000 | - |
| 1 | 5,000 | 10,000 |
| 2 | 1,667 | 3,333 |
| 3 | | 1,667 |
**Explanation:**
At each step, multiply the book value at the start of the year by 66.67% to get the depreciation. In the last year, depreciate whatever is left.
---
# **Step 2: MACRS Method (3-Year Property Class)**
The typical MACRS percentages for 3-year property are:
- Year 1: 33.33%
- Year 2: 44.45%
- Year 3: 14.81%
- Year 4: 7.41%
#### **Given:**
- Cost = \$15,000
### **Table Calculation**
| Time | Book Value | d_t (Depreciation) |
|------|------------|--------------------|
| | 15,000 | - |
| 1 | 10,000 | 15,000 × .3333 = **5,000** |
| 2 | 3,333 | 15,000 × .4445 = **6,668** |
| 3 | 1,111 | 15,000 × .1481 = **2,222** |
| 4 | | 15,000 × .0741 = **1,111** |
### **Filled Table**
| Time | Book Value | d_t (Depreciation) |
|------|------------|--------------------|
| | 15,000 | - |
| 1 | 10,000 | 5,000 |
| 2 | 3,333 | 6,668 |
| 3 | 1,111 | 2,222 |
| 4 | | 1,111 |
**Explanation:**
Each year's depreciation is found by multiplying the original cost by the MACRS percentage for that year. Subtract depreciation cumulatively from the original cost for the book value.
---
## **Final Answer (Summary Tables):**
### **Double-Declining Balance (DDB)**
| Time | Book Value | d_t (Depreciation) |
|------|------------|--------------------|
| | 15,000 | - |
| 1 | 5,000 | 10,000 |
| 2 | 1,667 | 3,333 |
| 3 | | 1,667 |
### **MACRS**
| Time | Book Value | d_t (Depreciation) |
|------|------------|--------------------|
| | 15,000 | - |
| 1 | 10,000 | 5,000 |
| 2 | 3,333 | 6,668 |
| 3 | 1,111 | 2,222 |
| 4 | | 1,111 |
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