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Gravina Company is planning to spend $8,000 for a machine that it will depreciate on a straight-line basis over 10 years with no salvage value
Gravina Company is planning to spend $8,000 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 $1,600 a year. Gravina will incur no additional costs except for depreciation. Its income tax rate is 35%. (For parts 3 and 4 of this question use Table 1 and 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.)
2. What is the accounting (book) rate of return (ARR) based on the initial investment outlay? (Round your answer to 1 decimal place.)
3. What is the maximum amount that Gravina Company should invest if it desires to earn an internal rate of return (IRR) of 15%? (Do not round intermediate calculations. Round your final answer to the nearest whole dollar amount.)
4. What is the minimum annual (pretax) cash revenue required for the project to earn a 15% internal rate of return? (Round your intermediate calculations and final answer to the nearest whole dollar amount.)
Expert Solution
Computation of Payback Period:
Annual depreciation = $8,000 / 10 = $800
Additional annual net income = (Additional cash revenue - depreciation) * (1-tax)
= ($1,600 - $800) * (1-0.35)
= $520
Additional annual cash inflows after tax = Additional income + Depreciation
= $520 + $800
= $1,320
Payback period = Initial investment / Annual cash inflows
= $8,000 / $1,320
= 6.06 years
Computation of Accounting Rate of Return:
Accounting rate of return = Average annual income / Initial investment
= $520 / $8,000
= 6.5%
Computation of Maximum amount that Graving should invest:
Desired rate of return = 15%
Maximum amount that Graving should invest = Present value of cash inflows discounted at 15%
= $1320 * Cumulative PV factor at 15% for 10 periods
= $1320 * 5.018769
= $6,624.78 or $6,625
Computation of Minimum annual cash revenue required:
Let minimum cash revenue required to earn 15% IRR = X
Now After tax cash flows = (X - $800) * (1-0.35) + $800
= X - 0.35X - $800 + $280 + $800
= $0.65X + $280
Now present value of cash inflows at 15% = $8,000
($0.65X + $280) * Cumulative PV factor at 15% for 10 periods = $8,000
($0.65X + $280) * 5.018769 = $8,000
3.2622X + $1,405.255 = $8,000
3.2622X = $8,000-$1,405.255
3.622X = $6,594.745
X = $2,021.56 or 2,022
Therefore, minimum annual cash revenue required = $2,022
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