Trying to find the NPV for this problem. I have had no luck getting the correct

ID: 2609910 • Letter: T

Question

Trying to find the NPV for this problem. I have had no luck getting the correct answer.

One year ago, your company purchased a machine used in manufacturing for $115,000. You have learned that a new machine is available that offers many advantages; you can purchase it for $170,000 today. It will be depreciated on a straight-line basis over ten years, after which it has no salvage value. You expect that the new machine will contribute EBITDA (earnings before interest, taxes, depreciation, and amortization) of $35,000 per year for the next ten years. The current machine is expected to produce EBITDA of $21,000 per year. The current machine is being depreciated on a straight-line basis over a useful life of 11 years, after which it will have no salvage value, so depreciation expense for the current machine is $10,455 per year. All other expenses of the two machines are identical. The market value today of the current machine is $50,000. Your company's tax rate is 42%, and the opportunity cost of capital for this type of equipment is 11 %. Is it profitable to replace the year-old machine? The NPV of the replacement is(Round to the nearest dollar)

Explanation / Answer

Answer:

Replacing the machine increases EBITDA by 35,000$21,000=$14,000.

Depreciation expenses rise by $17,000$10,455=$6,545.

Therefore, the free Cash flow(´C´) will increase by

=$14,000×(10.42)+0.42×$6,545

=$10,868.90 in years 1 through 10.

In year 0, the initial cost of the machine is $170,000. Because the currentmachinehasabookvalueof$115,000$10,455 (one year of deprecia²on)=$104,545, selling it for $50,000 generates a capital loss of

= $50,000$104,545

=$54,545.

This loss produces tax savings of 0.42×$54,545=$22,909,

so that the after-tax proceeds from the sales including this tax savings is $72,909.

Thus, the cash flow in year 0 from replacement is

=$170,000+$72,909

=$97,091

Now we will find NPV as under

Year

Cash
flow

PV factor
at 11%

Prasent
value

1 to 10

10,868.90

5.8892

64009.126

Less:

Initial Investment

-97,091

NPV

-33,082

SO NOV = (33082) negative

So it is not profitable to replace the machine