Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,300,000; the new one will cost, $1,560,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $300,000 after five years.

The old computer is being depreciated at a rate of $260,000 per year. It will be completely written off in three years. If we don't replace it now, we will have to replace it in two years. We can sell it now for $420,000; in two years, it will probably be worth $120,000. The new machine will save us $290,000 per year in operating costs. The tax rate is 38 percent, and the discount rate is 12 percent.

1. Suppose we recognize that if we don't replace the computer now, we will be replacing it in two years. Should we replace now or should we wait? Hint: What we effectively have here is a decision either to “invest” in the old computer (by not selling it) or to invest in the new one. Notice that the two investments have unequal lives.
2. Suppose we consider only whether we should replace the old computer now without worrying about what's going to happen in two years. What are the relevant cash flows? Should we replace it or not? Hint: Consider the net change in the firm's after tax cash flows if we do the replacement.

Answer 1

SOLUTION:-

Equivalent Annual Cost (EAC) method is used to determine the best option under mutually exclusive condition for available alternatives of different lives. In order to compute EAC the present value of cost of alternatives shall be divided by the annuity factor.

An old computer is to be replaced with new computer. The old one costs $1,300,000 and new one will cost $1,560,000. The new computer is depreciated straight-line to zero over five years. The new computer will be $300,000 after five years, the new machine saves $290,000 per year of operating cost. The tax rate is 38% and discount rate is 12%

Compute the EAC of new Machine as follows: First step: Compute the annual depreciation of new machine. Depreciation - Cost of the machine Life of machine $1,560,000 = $312,000 Thus, the annual depreciation of new machine is $312,000.

Second step: Calculate the Operating Cash Flow (OCF) from year-1 through year-5 as follows: OCF = Operating cost savings x (1 – tax rate) +( Depreciation x tax rate) =[$290,000×(1-38%)]+($312,000x38%) = $179,800+$118,560 = $298,360 Thus, the OCF of new machine is $298,360.

Third step: Compute the after-tax salvage value of the machine at the end of the 5th year as follows: After-tax salvage value=Salvage valuex (1-tax rate) = $300,000×(1-38%) = $186,000 Thus, the after-tax salvage value of new machine is $186,000.

Fourth step: Compute the NPV (Net Present Value of new machine as follows: NPV = CF + CF CF__ CF, CF CF; 1+ (1+r)? (1+r) 1+r) (1+r) S298,360 $298,360 $298,360 $298,360 (1+0.12) (1+0.12) (1+0.12) (1+0.12) =-S1,560,000+ (S298,360+$186,000) (1+0.12) --$1,560,000+ $266,392.857143+$237,850.765306 +$212,366.754738+ $189,613.173873+$274,838.871836 = $378,937.58 Thus, the NPV of new machine is $378,937.58

Now, compute the EAC of the new machine as follows: NPV EAC = Annuity factor NPV 1-(1+Interest rate) Years Interest rate -$378,937.58 1-(1+0.12) 0.12 -$378,937.58 1.123 0.12 _-$378,937.58 3.6047762 = -$105,120.97 Thus, the EAC of the new machine is -$105,120.97 .

-curre Compute the EAC of Old Machine in the following steps: First step: Compute the current opportunity cost to retain the machine. Opportunity cost Current market price+ Annual depreciation it market price remaining lives tax rate =$420,000+((($260,000x3) - $420,000)x38%) = $420,000 +($360,000x38%) = $556,800 Thus, the opportunity cost cost of retaining) of old machine is $556,800.

Second step: Compute the after-tax salvage value in two years. After-tax salvage value -salvage value + depreciation -salvage value) tax rate) =$120,000+(($260,000 - $120,000)x38%) = $120,000+($140,000 x 38%) =$173,200

Thus, the after-tax salvage value of old machine is $173,200.

For old machine the annual operating cash flow will be the depreciation tax shield only Third step: Operating cash flows as follows: OCF-depreciation tax rate -$260,000x38% -$98,800 Thus, the OCF of old machine is $98,800.

Fourth step: Compute the NPV of Old Machine. OCF, OCF, +after-tax salvage value NPV = Opportunity cost +- (1+rate) (1+rate) $98,800 $98,800+$173,200 (1+12%) (1+12) = -$556,800+ $88,214.285714+$216,836.734694 =-$251,748.98

Now, compute the EAC of the old machine as follows: EAC = Strate) Years NPV Annuity factor NPV 1-(1+Interest rate) Interest rate -S251,748.98 1-(1+0.12) 0.12 -$251,748.98 1.12 -S251,748.98 1.690051 --$148,959.398 Thus, the EAC of the old machine is -S148,959.398 It is evident from the above computation that the EAC of new machine is the least. In other words, replacing of old machine today has least EAC. Hence, the old machine should be replaced today.

In order to determine whether or not replace the old computer now, without worrying about what's going to happen in 2 years compute the NPV (Net Present Value) of the differentials. The relevant cash flows are the initial cash expenditure of the new machine, the opportunity cost of old machine, operating cash flows, and after-tax salvage value. Compute the NPV of differentials using "NPV function of spreadsheet. Enter values and formulas in the spreadsheet as shown in the image below. с years А в Input data 2 Discount rate 0.12 3 Life of new machine 5 4 Life of old machine 3 Initial cost of new 5 machine 1560000 Opportunity cost of 6 old machine 556800 7 OCF of new 298360 8 OCF old machine 98800 After-tax salvage 9 value of new 186000 After-tax salvage 10 value of old 173200 12 Calculations: 13 Year 140 15 1 16 2 17 3 18 4 New Machine Old Machine Difference =B5 =-B6 =B14-C14 =B7 =B8 =B15-C15 =B15 =C15+B10 =B16-C16 =B16 =B17-C17 =B17 =B18-C18 -B18-B9 =B19-C19 19 5 Net Present Value >> =NPVB2 D15-D19)+D14

Obtained results are provided below: А Input data 2 Discount rate 12% 3 Life of new machine 5 years 4 Life of old machine 3 years Initial cost of new 5 machine $1,560,000 Opportunity cost of 6 old machine $556,800 7 OCF of new machine $298,360 8 OCF old machine $98,800 After-tax salvage 9 value of new machine $186.000 After-tax salvage 10 value of old machine $173,200 12 Calculations: Year 0 New Machine Old Machine -$1,560,000 -$556,800 $298,360 $98,800 $298,360 $272,000 $298,360 $298,360 $484,360 Difference -$1,003,200 $199,560 $26,360 $298,360 $298,360 $484,360 Net Present Value >> -$127.188.60 Thus, the NPV of replacing the old machine today is -S127,188.60 If the future events are not a concern in replacing the old machine in two years, then the machine should be replaced today.