Gravina Company is planning to spend $7,500 for a machine that it will depreciat

Question

Gravina Company is planning to spend $7,500 for a machine that it will depreciate on a straight-line basis over 10 years with no salvage value. The machine will generate additional cash revenues of $1,500 a year. Gravina will incur no additional costs except for depreciation. Its income tax rate is 30%. (For parts 3 and 4 of this question use Table 1 and/or Table 2.) Required:

1. What is the payback period of the proposed investment under the assumption that the cash inflows occur evenly throughout the year? (Round your answer to 2 decimal places.)

Payback period = ___________ years

2. What is the accounting (book) rate of return (ARR) based on the initial investment outlay? (Round your answer to 1 decimal place.)

Book rate of return = ? %

3. What is the maximum amount that Gravina Company should invest if it desires to earn an internal rate of return (IRR) of 14%? (Round your final answer to the nearest whole dollar amount.)

Maximum amount = ?

4. What is the minimum annual (pretax) cash revenue required for the project to earn a 14% internal rate of return? (Round your intermediate calculations and final answer to the nearest whole dollar amount.)

Explanation / Answer

Cost of new machine $7,500 Expected useful life 10 Additional cash revenues per year $1,500 Income tax rate 30.00% PV Annuity Factor, 14%, 10 years (from Appendix C, Table 2) 5.216 a) Cash revenues before tax $1,500 Less: Depreciation = $7500/10 $750 Operating Income before tax $750 Less: Tax 30% -$225 Operating income $525 Add: Depreciation $750 Annual after-tax net cash inflow $1,275 Payback period, in years = Initial investment/Annual after tax cash inflow Payback period, in years = $7500/$1275 5.88 Years b) Book rate of return Cash revenues before tax $1,500 Less: Depreciation = $7500/10 $750 Operating Income before tax $750 Less: Tax 30% -$225 Operating income $525 Book rate of return = Operating Income/Initial Investment Book rate of return = $525/$7500 7.00% c) Maximum investment, given desire to earn minimum IRR of 14% Maximum Amount= Annual after tax net cash inflow x PVOA( 14%,10) $6,651 d) Required net after-tax annual cash inflow ($7500 ÷ 5.216) $1,437.85 Tax savings on depreciation expense (($7500 ÷ 10 years) × 0.30) $225 Required net after-tax annual cash revenue (1437.85 - 225) $1,212.85 Pre-tax annual cash revenue needed to earn an IRR of 14% = ($1212.85 ÷ (1 0.30)) $1,733

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