Question

One year ago, your company purchased a machine used in manufacturing for $90,000. You have learned that a new machine is available that offers many advantages and that you can purchase it for $170,000 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 $40,000 per year for the next 10 years. The current machine is expected to produce EBITDA of $20,000 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%. Should your company replace its year-old machine? What is the NPV of replacement? The NPV of replacement is $ . (Round to the nearest dollar.) Should your company replace its year-old machine? O A. No, because there is a loss from replacing the machine. OB. Yes, because there is a profit from replacing the machine. OC. No, because the only time a machine should be replaced is when it stops working completely. OD. Yes, because a new machine will always be an improvement for the company.

Answer 1

The NPV calculations are as shown below:

$ $ New machine cost Old machine cost Tax rate (T) Depriciation rate of old machine Depriciation rate of new machine Cost of capital (R) Remaining book value of old machine (=cost * (1-20%) 1,70,000.00 90,000.00 42% 20% 20% 11% 72,000.00 $ year: 0 2 3 4 5 8 9 10 row 1 New machine cost -170000 2 After tax current salvage value (market price) of old machine (=5000 *(1-42%)) 29000 3 Net cost of new machine -141000 20000 11600 20000 11600 20000 11600 20000 11600 20000 11600 20000 11600 6 Annual incremental EBITDA (new-old) After tax incremental EBITDA Old machine depriciation (=20%* cost) New machine depriciation (=20%* cost) Additional depreciation (New-Old) Tax savings on additional depriciation (Addnl deprn * 42%) 20000 11600 18000 34000 20000 11600 18000 34000 16000 20000 11600 18000 34000 16000 20000 11600 18000 34000 16000 34000 34000 16000 10 6720 6720 6 720 6720 14280 11 Total incremental Cash flows (row 3+6+10) -141000 18320 18320 18320 18320 25880 11600 11600 11600 11600 11600 Prsent value of cash flows (=CF / (1+R) year) -141000 16504.5 14868.92 13395.43 12067.95 15358.52 6201.834 5587.238 5033.547 4534.727 4085.34 NPV of replacement (= sum of PV of cash flows) -43,361.99

So, NPV= -43,361.99

Coming to the options given in the choices, c & d are incorrect as those generalized statements cannot be passed for every case as old machines can cause loss of efficiency resulting in net loss as compared to replacement similarly new machines can cost too much compared to the likely advantage the provide. So we always need to analyze based on NPV etc. objective measures.

So here option A is correct as negative NPV implies a loss from replacing the machine.

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