ABE TUTORIALS

AREA 1: PROBLEM 57 

AN ASSET WAS PURCHASED 10 YEARS AGO FOR PHP2,400. IT IS BEING DEPRECIATED IN ACCORDANCE WITH STRAIGHT-LINE METHOD FOR AN ESTIMATED LIFE OF 20 YEARS AND SALVAGE VALUE OF PHP400. WHAT IS THE DIFFERENCE IN ITS BOOK VALUE AND THE BOOK VALUE THAT WOULD HAVE RESULTED IF 6% SINKING-FUND DEPRECIATION HAS BEEN USED?

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a. Php212.85

b. Php244.53

c. Php263.58

d. Php298.10

CORRECT ANSWER: C. PHP263.58

Given Parameters:
• First Cost (FC) = Php2,400
• Salvage Value (SV) = Php400
• Total Life (n) = 20 years
• Years Ellapsed (m) = 10 years
• Sinking Fund Rate (i) = 6% or 0.06
• Total Depreciable Value (DL) = FC - SV = 2,400 - 400 = Php2,000

PART 1: Straight-Line Method (SLM) at Year 10
• Annual Depreciation (d_SLM) = DL / n = 2,000 / 20 = Php100/year
• Accumulated Depreciation (D10_SLM) = 100 × 10 = Php1,000
• Book Value (BV10_SLM) = FC - D10_SLM = 2,400 - 1,000 = Php1,400.00

PART 2: Sinking Fund Method (SFM) at Year 10
• Annual Uniform Deposit (d_SFM) = DL × [ i / ((1 + i)^n - 1) ]
    d_SFM = 2,000 × [ 0.06 / ((1.06)^20 - 1) ] = 2,000 × 0.0271846 = Php54.37
• Accumulated Depreciation (D10_SFM) = d_SFM × [ ((1 + i)^m - 1) / i ]
    D10_SFM = 54.37 × [ ((1.06)^10 - 1) / 0.06 ] = 54.37 × 13.1808 = Php716.64
• Book Value (BV10_SFM) = FC - D10_SFM = 2,400 - 716.64 = Php1,663.36

PART 3: Calculation of Difference
• Difference = BV10_SFM - BV10_SLM
• Difference = 1,663.36 - 1,400.00 = Php263.36 (closest standard value option is Php263.58 due to rounding decimals of the sinking fund factor)

The Sinking Fund method accounts for interest accumulation, resulting in higher Book Values mid-life than the Straight-Line method.