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Homework answers / question archive / 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

Finance

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.)

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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