Book value by SOYD and sinking fund

Assumption: the machine was bought for P = Rs 50,000 and will have S = Rs 10,000 after 3 years, so its life is N = 3 years. "Now" is the end of year 2 (two years after purchase).

(i) Sum-of-the-years'-digits (SOYD)

Sum of digits = N(N + 1)/2 = 3(4)/2 = 6; P − S = 40,000.

D₁ = 40,000 × 3/6 = 20,000
D₂ = 40,000 × 2/6 = 13,333
Book value after 2 years = 50,000 − 20,000 − 13,333 = Rs 16,667

(ii) Sinking-fund method (i = 10%)

Yearly deposit = (P − S)(A/F,10%,3) = 40,000(0.30211) = Rs 12,085. Depreciation in year k = deposit × (F/P,10%,k − 1).

D₁ = 12,085
D₂ = 12,085(1.10) = 13,293
Book value after 2 years = 50,000 − 12,085 − 13,293 = Rs 24,622

Answer: Book value now = Rs 16,667 by SOYD and Rs 24,622 by the sinking-fund method.