- 2072 Asoj · 1+2+3+2 marks
Depreciation and book value by four methods
Short answer
SL: $1,000/yr, BV $6,000 to $2,000. DB (22.16%): $1,551, $1,208, $940, $732, $569, BV ends $2,000. SOYD: $1,667, $1,333, $1,000, $667, $333. Sinking fund (10%): $819, $901, $991, $1,090, $1,199. All end with BV $2,000.
Considering the following information, compute the annual depreciation and book value of each year by (i) SL method (ii) DB method (iii) SOYD method and (iv) Sinking fund method.
| Cost basis | Salvage Value | Useful Life | MARR |
|---|---|---|---|
| $ 7,000 | $ 2,000 | 5 years | 10% |
Data: cost basis P = $7,000; salvage S = $2,000; N = 5; depreciable amount P − S = $5,000; MARR (sinking-fund rate) = 10%.
(i) Straight line
D = (7,000 − 2,000)/5 = $1,000 per year. BV_k = 7,000 − 1,000k.
(ii) Declining balance
The rate that brings the book value to S is R = 1 − (S/P)^(1/N) = 1 − (2,000/7,000)^(1/5) = 1 − 0.7784 = 22.16%. D_k = R × BV_(k−1). Year 1: 0.2216 × 7,000 = 1,551; BV₁ = 5,449.
(iii) Sum of years' digits
Sum = 5(6)/2 = 15. D_k = 5,000 × (6 − k)/15: 1,667; 1,333; 1,000; 667; 333.
(iv) Sinking fund (10%)
Deposit = 5,000(A/F,10%,5) = 5,000(0.16380) = 819. D_k = 819(1.10)^(k−1).
Summary (depreciation D and end-of-year book value BV, in $)
| Year | SL D | SL BV | DB D | DB BV | SOYD D | SOYD BV | SF D | SF BV |
|---|---|---|---|---|---|---|---|---|
| 1 | 1,000 | 6,000 | 1,551 | 5,449 | 1,667 | 5,333 | 819 | 6,181 |
| 2 | 1,000 | 5,000 | 1,208 | 4,241 | 1,333 | 4,000 | 901 | 5,280 |
| 3 | 1,000 | 4,000 | 940 | 3,301 | 1,000 | 3,000 | 991 | 4,289 |
| 4 | 1,000 | 3,000 | 732 | 2,569 | 667 | 2,333 | 1,090 | 3,199 |
| 5 | 1,000 | 2,000 | 569 | 2,000 | 333 | 2,000 | 1,199 | 2,000 |
All four methods end with BV = $2,000 at year 5. DB and SOYD are accelerated (large early charges); the sinking-fund method gives small early and large late charges.
✓ Answer checked by Claude Opus 5.5 (high effort)
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