The plant has accumulated savings of $60,000 to acquire a new machine for qualit
ID: 1102007 • Letter: T
Question
The plant has accumulated savings of $60,000 to acquire a new machine for quality assurance of its products. The new quality control machine cost $80,000. The extra $20,000 needed to acquire the new machine will be finance through a loan at 6% annual interest with the principal ($20,000) due at the end of the third year. The income tax rate is 0.35. The new equipment will save $35,000 each year and its economic life is 3 years. The salvage value is $30,000. Does the acquisition of this new machine satisfy the 6% minimum rate?
a) compute the after tax rate of return of this alternative using the present worth method. Solve this problem twice using the straight line and the MACRS depreaciation methods.
b)which depreciation method is more convenient?
*workout the problems step by steps
Explanation / Answer
Solution Cost of machine $80,000 Out of this $60,000 will be paid at the beginning and for the rest, a loan will be taken. Loan amount $20,000 Interest on loan 6% Interest amount $1,200 a. Straight line method of depreciation Cost of machine $80,000 salvage value $30,000 Life of the asset 3 years Amount of depreciation 16666.6667 Initial cash outlay $60,000 Yearly cash flows year 1 year 2 year 3 savings $35,000 $35,000 $35,000 Less: interest payment $1,200 $1,200 $1,200 Less: Depreciation 16666.6667 16666.6667 16666.6667 income before taxes $17,133 $17,133 $17,133 Less: taxes $5,996.67 $5,996.67 $5,996.67 Income after taxes $11,136.67 $11,136.67 $11,136.67 Add: depreciation 16666.6667 16666.6667 16666.6667 Cash flows $27,803.33 $27,803.33 $27,803.33 Less: principal payment of loan 20000 Add: salvage value 30000 Net cash flows $27,803.33 $27,803.33 $37,803.33 Calculating IRR Year Cash flows Present value factor at 20% Present value Present value factor at 25% Present value 0 ($60,000) 1 ($60,000) 1 ($60,000) 1 $27,803.33 0.83333333 $23,169 0.8 $22,243 2 $27,803.33 0.69444444 $19,308 0.64 $17,794 3 $37,803.33 0.5787037 $21,877 0.512 $19,355 $4,354 ($608) IRR = 20% + (4354/(4354+608))*5 IRR = 24.39% After tax rate of return is 24.39% MACRS method of depreciation Cost of machine $80,000 salvage value $30,000 Life of the asset 3 years Calculation of depreciation using MACRS Year Cost rate of depreciation amount of depreciation 1 $80,000 0.333 $26,640 2 $80,000 0.445 $35,600 3 $80,000 0.148 $11,840 4 $80,000 0.074 $5,920 $80,000 Book value after 3 years $5,920 Salvage value $30,000 Profit on sale of machine $24,080 Tax on profit $8,428.00 Net cash from sale of machine $21,572.00 Initial cash outlay $60,000 Yearly cash flows year 1 year 2 year 3 savings $35,000 $35,000 $35,000 Less: interest payment $1,200 $1,200 $1,200 Less: Depreciation $26,640 $35,600 $11,840 income before taxes $7,160 ($1,800) $21,960 Less: taxes $2,506.00 ($630.00) $7,686.00 Income after taxes $4,654.00 ($1,170.00) $14,274.00 Add: depreciation $26,640 $35,600 $11,840 Cash flows $31,294.00 $34,430.00 $26,114.00 Less: principal payment of loan $20,000 Add: net cash from sale of machine $21,572.00 Net cash flows $31,294.00 $34,430.00 $27,686.00 Calculating IRR Year Cash flows Present value factor at 25% Present value Present value factor at 30% Present value 0 ($60,000) 1 ($60,000) 1 ($60,000) 1 $31,294.00 0.8 $25,035 0.769231 $24,072 2 $34,430.00 0.64 $22,035 0.591716 $20,373 3 $27,686.00 0.512 $14,175 0.455166 $12,602 $1,246 ($2,953) IRR = 25% + (1246/(1246+2953))*5 IRR = 26.48% After tax rate of return is 26.48% b. Straight Line Method of depreciation is more convenient as the calculations are easy and there is usually no gain or loss on sale of the asset at the end of its economic life. Thus the additional calculations of tax on profit or loss is avoided.