Ilana Industries Inc. needs a new lathe. It can buy a new high-speed lathe for $1.5 million. The lathe will cost $40,000 per year to run, but it will save the firm $136,000 in labor costs and will be useful for 10 years.

Suppose that for tax purposes, the lathe is entitled to 100% bonus depreciation. At the end of the 10 years, the lathe can be sold for $540,000. The discount rate is 6%, and the corporate tax rate is 21%.

What is the NPV of buying the new lathe?

(A negative amount should be indicated by a minus sign. Enter your answer in dollars, not in millions. Do not round intermediate calculations. Round your answer to 2 decimal places.)

NPV = _______

To calculate the NPV of buying the new lathe, we need to discount the cash flows associated with the lathe over its useful life to their present value.

The cash flows can be summarized as follows:

Initial cost: -$1,500,000

Annual savings in labor costs: $136,000

Annual operating cost: -$40,000

Sale proceeds at the end of 10 years: $540,000

Considering the 100% bonus depreciation, we can assume the entire cost of the lathe is deductible in the first year. This means that for tax purposes, the net cash flow in the first year will be the sum of the annual savings in labor costs and the salvage value:

Net cash flow in Year 1 = Annual savings in labor costs + Salvage value = $136,000 + $540,000

To calculate the NPV, we discount each cash flow to its present value and sum them up. Using a discount rate of 6% and the corporate tax rate of 21%, we can calculate the NPV as follows:

NPV = Net cash flow in Year 1 / (1 + Discount rate)^1 + (Annual savings in labor costs - Annual operating cost) / (1 + Discount rate)^1 + ... + Salvage value / (1 + Discount rate)^10 - Initial cost

Substituting the values into the equation:

NPV = ($136,000 + $540,000) / (1 + 0.06)^1 + ($136,000 - $40,000) / (1 + 0.06)^2 + ... + $540,000 / (1 + 0.06)^10 - $1,500,000

Simplifying the equation and calculating the NPV:

NPV = $676,000 / 1.06 + $96,000 / 1.06^2 + ... + $540,000 / 1.06^10 - $1,500,000

To evaluate the expression, we need to calculate the present value of each cash flow and then subtract the initial cost of $1,500,000. Let's calculate the NPV:

NPV = $676,000 / 1.06 + $96,000 / 1.06^2 + ... + $540,000 / 1.06^10 - $1,500,000

NPV = $636,792.45 + $84,484.42 + ... + $296,518.35 - $1,500,000

Evaluating the expression by summing up the present values of each cash flow and subtracting the initial cost:

NPV = $636,792.45 + $84,484.42 + ... + $296,518.35 - $1,500,000

Evaluating the expression by summing up the individual cash flows:

NPV = $636,792.45 + $84,484.42 + $74,917.94 + $66,927.53 + $59,453.11 + $52,440.63 + $45,849.80 + $39,643.53 + $33,788.82 + $28,255.13 + $23,014.21 - $1,500,000

Summing up the cash flows:

NPV = $1,087,571.45 - $1,500,000

NPV = -$412,428.55

A negative value indicates a loss.

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