A company has invested $60,000 in machinery with a 5-year useful life. The machinery will have no salvage value, as the cost to remove it will equal its scrap value. The annual benefits from the machinery are $15,000. The firm has a tax rate of 45% and will use the sum-of-years.. digits depreciation, compute the after-tax rate of return. The company uses a MARR of 7%.

19.7%

Explanation:

initial cost $60,000

depreciation expense:

5 + 4 + 3 + 2 + 1 = 15

Year 1: 5/15 = 33%  = $19,800

Year 2: 4/15 = 27%  = $16,200

Year 3: 3/15 = 20%  = $12,000

Year 4: 2/15 = 13%  = $7,800

Year 5: 1/15 = 7% = $4,200

yearly benefits:

Year 1 = ($15,000 - $19,800) x 45% tax credit = $2,160 deferred tax benefit

Year 2 = ($15,000 - $16,200) x 45% tax credit = $540 deferred tax benefit

Year 3 = $15,000 - $12,000 = $3,000 ⇒ $1,350 in taxes are offset by the previous deferred tax benefits x 45% tax  = $2,160 - $1,350 = $810 remaining tax benefits

Year 4 = $15,000 - $7,800 = $7,200 - $3,240 in taxes + $810 in deferred tax benefits = $4,770

Year 5 = ($15,000 - $4,200) x (1 - 45%) = $5,940

this investment yields 3 positive benefits during years 3-5, if we discount them to find the present value = $3,000/1.07 + $4,770/1.07² + $5,940/1.07³ = $2,803.74 + $4,166.30 + $4,848.81 = $11,818.85

after-tax rate of return = $11,818.85 / $60,000 = 19.7%

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