Question

One year​ ago, your company purchased a machine used in manufacturing for $ 100 comma 000. You have learned that a new machine is available that offers many advantages and that you can purchase it for $ 150 comma 000 today. The CCA rate applicable to both machines is 20 %​; neither machine will have any​ long-term salvage value. You expect that the new machine will produce earnings before​ interest, taxes,​ depreciation, and amortization​ (EBITDA) of $ 50 comma 000 per year for the next 10 years. The current machine is expected to produce EBITDA of $ 25 comma 000 per year. All other expenses of the two machines are identical. The market value today of the current machine is $ 50 comma 000. Your​ company's tax rate is 35 %​, and the opportunity cost of capital for this type of equipment is 11 %. Should your company replace its​ year-old machine?

a) the NPV of replacement is $_________?

Answer 1

NPV of replacement = Present value of Cash inflows on replacement - Present Value of Cash outflows on replacement

NPV = $ 116311.7 - $ 89500

= $ 26811.7

Now, the company should replace the old machine as the NPV on replacement is positive. This means that the replacement shall lead to increased revenue for the company.

Working Notes

1. Calculation of Present value of cash outflows

Cash outflow on purchase of new machine = $ 150000

Less - Sale value of old machine = ($ 50000)

Less - Tax saving on loss of sale = ($ 10500)

Total cash outflow = $ 89500

Present value of cash outflow = Cash outflow * Present value factor (11%, year 0)

= $ 89500 * 1

= $ 89500

Calculation of Market value of old machine

Purchse price of the machine = $ 100000

Tax rate = 35%

CCA rate = 20%

one year Depreciation = $ 100000* 20/100 = $ 20000

Book value of old machine = $ 100000- $20000 = $ 80000

Market value is the realisable value , if the old machine is sold today.

So, sale value = $ 50000

Loss on sale is incurred as the sale price is less than the book value

Loss on sale = Sale price - Book value

= $ 50000 - $ 80000

= ($ 30000)

Tax( @ 35%) saving on loss of sale = $30000 * 35/100 = $ 10500

2. Calculation of Present value of cash inflow-

Given -

Time period = 10 years

Discount rate = 11%

Tax rate = 35%

CCA rate = 20%

Annual EBIDTA of new machine = $ 50000

Annual EBIDTA of old machine = $ 25000

Annual Depreciation of old Machine = $ 100000 * 20% = $20000

Annual Depreciation of new Machine = $ 150000 * 20% = $30000

Now,

Incremental EBIDTA on replacement = $ 50000- $25000 = $ 25000

Less - Increase in Depreciation = $ 30000- $ 20000 = ($ 10000)

Profit before tax = $ 25000- $ 10000 = $ 15000

Less tax @ 35% i.e. $ 15000* 35/100 = ($ 5250)

Profit after tax = $ 15000- $ 5250 = $ 9750

Add Depreciation = $ 10000

Cash inflows = $ 9750+ $ 10000 = $ 19750

Present value of Cash inflow = Cash inflow * Present value annuity factor ( 11%, 10Years)

= $ 19750 * 5.8892

= $ 116311.7