Question

Dickens, Inc. purchases and puts into service equipment costing $750,000. The equipment has a six-year useful life and no salvage value. Dickens faces a tax rate on pretax income of 30%. a. Calculate the present value of the tax benefit of using double-declining balance rather than straight-line depreciation over the life of the equipment. Use a discount rate of 10%. b. Calculate the present value of the tax benefit of using double-declining balance rather than straight-line depreciation over the life of the equipment if the salvage value is $60,000. Again, use a discount rate of 10%.

Answer 1

Cost of Equipment Life of Asset $ 7,50,000.00 6 years Solution a. Salvage Value Depreciation as per SLM (SLM-Straight Line method) Cost of Asset - Salvage Value Life of asset = $750000 - 0/6 = $ 1,25,000.00 every year = $125000 x 30% = $ 37,500.00 each year Tax Shield @ 30% Depreciation as per Double decline Method Depreciation rate = 1/useful life x 100 = 1/6 x100 = 16.67% Double-Decline formula 2 x Cost of Asset x Depreciation rate = 2 x $750000 x 16.67% = 250000 Table showing Depreciation as Per DDM @ 16.67x 2 = 33.34% Year Opening Depreciation Tax Sheild @ Value (A) Closing Value 30% (A x 30%) 1 $ 7,50,000.00 $2,50,000.00 $5,00,000.00 $ 75,000.00 2 $ 5,00,000.00 $1,66,666.67 $3,33,333.33 $ 50,000.00 3 $3,33,333.33 $1,11,111.11 $2,22,222.22 $ 33,333.33 4 $2,22,222.22 $ 74,074.07 $1,48,148.15 $ 22,222.22 5 $ 1,48,148.15 $ 49,382.72 $ 98,765.43 $ 14,814.81 6 $ 98,765.43 $ 32,921.81 $ 65,843.62 $ 9,876.54

Statement showing Comaprison of Tax sheild on SLM and DDM PV (Dep - Year Dep (SLM) Dep (DDM) PV @ 10% PV (Dep-SLM) DDM) $ 37,500.00 $ 75,000.00 0.909 $ 34,090.91 $ 68,181.82 $ 37,500.00 $ 50,000.00 0.826 $ 30,991.74 $ 41,322.31 $ 37,500.00 $ 33,333.33 0.751 $ 28,174.31 $ 25,043.83 $ 37,500.00 $ 22,222.22 0.683 $ 25,613.00 $ 15,178.08 $ 37,500.00 $ 14,814.81 0.621 $ 23,284.55 $ 9,198.83 $ 37,500.00 $ 9,876.54 0.564 $ 21,167.77 $ 5,575.05 TOTAL $1,63,322.28 $1,64,499.92 PV of Tax shield using Double Decline Method $1,64,499.92 PV of Tax shield using Straight Line Method $1,63,322.28 Excess of DDM over SLM $ 1,177.65

Solution b. Salvage Value Depreciation as per SLM (SLM-Straight Line method) $ 60,000.00 Cost of Asset - Salvage Value Life of asset = $750000 - 0/6 = $1,15,000.00 every year = $115000 x 30% = $ 34,500.00 each year Tax Shield @ 30% Statement showing Comaprison of Tax sheild on SLM and DDM PV (Dep - Year Dep (SEM) Dep (DDM) PV @ 10% PV (Dep-SLM) DDM) $ 34,500.00 $ 75,000.00 0.909 $ 31,363.64 $ 68,181.82 $ 34,500.00 $ 50,000.00 0.826 $ 28,512.40 $ 41,322.31 $ 34,500.00 $ 33,333.33 0.751 $ 25,920.36 $ 25,043.83 $ 34,500.00 $ 22,222.22 0.683 $ 23,563.96 $ 15,178.08 $ 34,500.00 $ 14,814.81 0.621 $ 21,421.79 $ 9,198.83 $ 34,500.00 $ 9,876.54 0.564 $ 19,474.35 $ 5,575.05 TOTAL $1,50,256.49 $1,64,499.92 PV of Tax shield using Double Decline Method $1,64,499.92 PV of Tax shield using Straight Line Method $1,50,256.49 Excess of DDM over SLM $ 14,243.43

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