3. A machine with a useful life of 3 years is purchased for $100,000. It is know

Question

3. A machine with a useful life of 3 years is purchased for $100,000. It is known that the market value of the machine decreases by 10% each year. The book value can be calculated by assuming straight-line depreciation over a 4-year depreciable life to a salvage value of S20,000. The machine generates a gross income of $50,000 annually. The operating and maintenance costs are $30,000 in year 1, increasing by $5,000 each year. Determine the after-tax marginal costs if the tax rate is 40% and i = 10%. If the minimum EUAC of a challenger is $56,000 when should the machine be replaced? (40 marks)

Explanation / Answer

Year P S A/P,10%,n EUAC=(P-S)*(A/P,10%,n))+S*.10 0 $                                      100,000.00 1 $                                      100,000.00 $                    90,000.00 1.1 ((100000-90000)*1.1)+90000*0.1 $ 20,000.00 2 $                                      100,000.00 $                    81,000.00 0.5762 ((100000-81000)*0.5762)+81000*0.1 $ 19,047.80 3 $                                      100,000.00 $                    72,900.00 0.4021 ((100000-72900)*0.4021)+72900*0.1 $ 18,186.91 4 $                                      100,000.00 $                    65,610.00 0.3155 (100000-$65610)*.3155+65610*.10 $ 17,411.05 Salvage Value Year 1= 100000-(100000*10%)=90000 Salvage Value Year 2= 90000-(90000*10%)=81000 Salvage Value Year 3= 81000-(81000*10%)=72900 Operating & Maintenance Cost=A+Gseries Year A/G,9%,n EUAC=(30000+5000*(A/g,10%,n) 0 1 $                                                       -   30000 $                                   30,000.00 2 $                                                0.476 (30000+5000*.476) $                                   32,380.00 3 $                                                0.937 (30000+5000*.937) $                                   34,685.00 4 0.1381 (30000+5000*.1381) $                                   30,690.50 Total EUAC Year Cap EUAC Operating & Maintenance EUAC Total EUAC $                                     -   $                                 1.00 $                                        20,000.00 $                    30,000.00 $                                   50,000.00 $                                 2.00 $                                        19,047.80 $                    32,380.00 $                                   51,427.80 $                                 3.00 $                                        18,186.91 $                    34,685.00 $                                   52,871.91 $                                 4.00 $                                        17,411.05 $                    30,690.50 $                                   48,101.55 Minimum EUAC=$48101.45 at economic life of 4 years In this case minimum EUAC of defender is $48101.55 ,which is less than the challenger minimum EUAC i.e $56000.Thus under repalcement repeatability assumptions,we will keep the defender at least 4 yars. P=Initial Amount S=Salvage Value

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