A machine, costing $32,000 to buy and $2,700 per year to operate. will save mainly labor...

A machine, costing $32,000 to buy and $2,700 per year to operate. will save mainly labor expenses in packing over seven years. The anticipated salvage value of the machine at the end of seven years is $4,500.

(a) if a 12% return on investment (rate of return) is desired, what is the minimum required annual savings in labor from this machine?

(b) The service life us just five years, instead of seven years, what is the minimum required annual savings in labor for the firm to realize a 12% return on investment?

Solutions

Expert Solution

a. Annual Savings is a point at which NPV is zero

NPV = 0

Present Value of cash inflows + Present value of salvage value - Present Value of Cash outflow = 0

X * PVAF ( 12%, 7) + 4500 * PVF(12%,7) - 32000 - 2700 * PVAF(12%,7) = 0

X * PVAF ( 12%, 7) + 4500 * 0.4523 - 32000 - 12322.14 = 0

X * PVAF ( 12%, 7) = $42286.57

X = $42286.57 / 4.5638

Annual Savings = $9265.74

b. Annual Savings is a point at which NPV is zero

NPV = 0

Present Value of cash inflows + Present value of salvage value - Present Value of Cash outflow = 0

X * PVAF ( 12%, 5) + 4500 * PVF(12%,5) - 32000 - 2700 * PVAF (12%,5) = 0

X * PVAF ( 12%, 5) + 4500 * 0.5674 - 32000 - 2700 * 3.6048 = 0

X * PVAF ( 12%, 5) = $39179.47

X = $39179.47 / 3.6048

Annual Savings = $10868.77

c. Annual Savings is a point at which NPV is zero

NPV = 0

Present Value of cash inflows + Present value of salvage value - Present Value of Cash outflow = 0

X * PVAF ( 12%, 7) + 4500 * PVF(12%,7) - 32000 - 2970 * PVAF(12%,7) = 0

X * PVAF ( 12%, 7) + 4500 * 0.4523 - 32000 - 13554.36 = 0

X * PVAF ( 12%, 7) = $43518.79

X = $43518.79 / 4.5638

Annual Savings = $9535.74

ekkarill92 answered 1 year ago

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