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

We will use the equivalent cost method. This method is used to determine the best option under mutually exclusive condition for available alternatives having different lives.

EAC = NPV/Annuity factor

EAC computation of new machine Depreciation = Cost of machine - life of machine = $1,560,000 · 5 Dept = $312,000 we wide now calculate Operating Cash flow CO (F) from yeart to 5: OCF = operating cost savings x ( 1 -tax%) + C def" x tax?) . s [290,000 x( 1 - 387.)] + [ 312,000 x 387 3 TO CF = $298,360] Next we find the after tax salvage value at the end of the 5th year! After-tax salvage value = salvage value = 300,000x (1-38%) $186,000 X (Itax 7)

Now, we will calculate the apy- Nov=CF + CFi ar + (F2 cito)? + CF3. Citri (298,360 +298,360 -1, 560, 000 + (1+0.12) C1+0.12,2 298,360 +298, 360 (140-123 . (1+0-12)4 T L (298,360 + 1860,000) (1 +0.125 = -1,560,000+ 266,392.85714 + 237,850.765306 + 212, 366.754738 + 189,613.173973 + 274,838.871836 NPV = -$378,937.581 LAC - NPV Annuity factor - NPU 1 - (1 + intrate years int rate

5 - 378,937.58 [ 1-(10.12)*5 0.12 = - 378,937.58 3.6047.762 EAC new machine = - 3105,120.97 EAC computation of old machine opportunity cost = current market price + I Annual deprx - current , market X - remaining life price! tax% = 420,000 + [(1260,000 Ⓡ3) -420,000) 1 x 38%] loc = $556,800! After tax salvage value = salvage value t [ (defr - Salvage value) xtax?) = 120,000+ [(260,000-120, 000)x387) = $173,200

0 (F=deprxtax%. 260,000 x 387. TOCF = $18,800 NPV = Opportunity cost + OCF1 Citrate) + OCEz + after-tax salvage - Citrate) 2 -556,800't 98,800 t (1+0.12) :98,800 + 173,200 1 (t.122 INPV = -$251,748.98 EAC = = NPV Annuity factor NPV 1 Clt int-rate) years int rate - 251,748.98 r1- (1 +0.12) 0.12

EA Cold me Cold machine = - $148, 959.398 EAC (nem a EAC machine) cold machine) old machine should be replaced today.

Now, to determine whether or not to replace the old computer now without worrying about what is going to happen in the next 2 years we will compute the NPV of the differentials.

Discount rate	12%
	New Machine	Old Machine
Life	5	3
OCF	$           2,98,360	$         98,800
After-tax salvage	$           1,86,000	$     1,73,200
Initial Cost of New machine	$         15,60,000
Opportunity cost of old machine	$           5,56,800
Value
Year	New Machine	Old Machine	Difference
0	$       -15,60,000	$    -5,56,800	$ -10,03,200
1	$           2,98,360	$         98,800	$     1,99,560
2	$           2,98,360	$     2,72,000	$         26,360
3	$           2,98,360		$     2,98,360
4	$           2,98,360		$     2,98,360
5	$           4,84,360		$     4,84,360
NPV	$    -1,27,188.60
The machine should Be replaced today

Formulae used:

. Discount rate 0.12 New Machine Old Machine Life OCF After-tax salvage 298360 186000 98800 173200 Initial Cost of New machine 1560000 Opportunity cost of old machine 556800 Value Year New Machine --C8 =C5 =C14 =C15 =C16 =C17+C6 Old Machine --C9 =D5 =D14+D6 Difference =C13-D13 =C14-D14 =C15-D15 =C16-D16 =C17-D17 =C18-D18 5 NPV =NPV(C2, E14:E18)+E13