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cap budgeting question

(Guest)

in the following question, i would like to know how to calculate the equated annual cost of the machine if it is not replaced.i'm getting really confused and i would appreciate a simple to understand answer. anyone ?

A & Co. is contemplating whether to replace an existing machine or to spend money on overhauling it. A & Co. currently pays no taxes. The replacement machine costs Rs. 90,000 now and requires maintenance of Rs. 10,000 at the end of every year for eight years. At the end of eight years it would have a salvage value of Rs. 20,000 and would be sold. The existing machine requires increasing amounts of maintenance each year and its salvage value falls each year as follows:

Year	Maintenance (Rs.)	Salvage (Rs.)
Present	0	40,000
1	10,000	25,000
2	20,000	15,000
3	30,000	10,000
4	40,000	0

The opportunity cost of capital for A & Co. is 15%.

Required:

When should the company replace the machine?

(Notes: Present value of an annuity of Re. 1 per period for 8 years at interest rate of 15% : 4.4873; present value of Re. 1 to be received after 8 years at interest rate of 15% : 0.3269).

(10 marks)(May 2004)

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6 Replies

MOHIT MAHAJAN (LCS, ACA) (2050 Points)
Replied 13 October 2009

(i) calculate npv of new machine

-90,000-10,000*cdf for 1-8 yrs @ 15% + 20,000*df for 8th year @ 15%

divide the npv calculated above with 4.4873. You will get EAC of new machine

(ii) now calculate outflow/inflow if machine is not replaced. for example in 1st year

PV = -40000-10000*0.869+25000*0.869

Multiply the answer with 1.15 to get future value and compare it with EAC in first part. REPEAt SAME FOR SUBSEQUENT YEARS.

I am not too comfortable with concepts of capital budgeting. This is just an estimated ans. from me. Plz. analyze the correctness of answer yourself, specially of 2nd part.

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(Guest)

here is part of the solution. i don't understand it at all. also, even as per your solution, i don't think (correct me if i am wrong) we should discount 40000 at .869 since that value is at time 0. i think for every year starting with time period one , we should add up the maintenance and salvage value and dicount the total as per the relevant discount factor. then add up the same for all the years and divide by 4.4873 to get eac. i don't know, this is confusing and the solution goes above my head.

Equivalent Cost (EAC) of keeping the machine

Present value	I Year	II Year	III Year	IV Year
(p.v)	(Rs.)	(Rs.)	(Rs.)	(Rs.)
Value Present	40,000	25,000	15,000	10,000
Add p.v. of annual maintenance (Annual Maintenance/1.15)	8,696	17,391	26,087	34,783
Total	48,696	42,391	41,087	44,783
Less: p.v. of salvage value at the end of the year (p.v. /1.15)	21,739	13,043	8,696	Nil
	26,957	29,348	32,391	44,783
´	1.15	1.15	1.15	1.15
Equivalent Annual Cost (EAC)	31,000	33,750	37,250	51,500

Advice: The company should replace the old machine immediately because the Equivalent Annual Cost (EAC) of the new machine at Rs. 28,600 is lower than the cost of using the existing machine in first year, second year, third year and fourth year

aditya (student) (39 Points)
Replied 14 October 2009

Ankita

EAC/EAB as a concept is applied when the useful life of 2 options are not the same. Hence we arrive at the equated annual cost to make an informed judgement. That is the reason we divide the cost/benefit by the total discount factor for the period under consideration.

I dont agree with the answer provided as well. The concept is we compute total cost minus salvage value. The total cost component comprises of 2 components namely opportunity cost of not replacing in yr zero ( rs 40000) and maintenance cost. The salvage value and maintenance cost have to be brought to their present value terms. The opp cost will remain at 40000 for all yrs as pv for yr 0 is always 1.

I have arrived at the solution for option 2 alone as option 1 (replacing now) is pretty obvious. have a look at my solution and see if you are satisfied.... this is the best i could think for this solution. hope it helps

		Replace in year
		Yr 1	Yr 2	Yr 3	Yr 4
opp cost	Yr 0	40,000.00	40,000.00	40,000.00	40,000.00
Maintenance cost	Yr 1	8,695.65	8,695.65	8,695.65	8,695.65
	Yr 2		15,122.87	15,122.87	15,122.87
	Yr 3			19,725.49	19,725.49
	Yr 4				22,870.13
Total cost		48,695.65	63,818.53	83,544.01	106,414.14

less: PV of salvage		21,739.13	11,342.16	6,575.16	-
		26,956.52	52,476.37	76,968.85	106,414.14
Annuity factor		0.87	1.63	2.28	2.85
EAC		31,000.00	32,279.07	33,710.58	37,273.19

(Guest)

thanks for replying. but i don't understand, why would you take 40,000 every year? also why would you deduct salvage value?it's a cost, not a benefit right? this is what i think-

1. year 1- opp cost of 40000

2. year 2 - opp cost of 25000+ maintenance cost of 10000, the sum discounted back to present period.

3. repeat same procedure for the rest of the years.

4. add up step 1-3

5. divide by 4.4873

this will give eac. what do you say?

MOHIT MAHAJAN (LCS, ACA) (2050 Points)
Replied 14 October 2009

Ankita i have not discounted 40,000 with 0.869. Only maintenance cost and salvage value have been discounted.

- salvage value is our inflow, hence it is to be deducted from our costs. Hence maintenance cost and salvage value are not to be added. Try to understand it like this

If we keep machine throughout first year we will not get Rs. 40,000 hence it becomes opp. cost but if we sell it at the end of first year we will get 25,000. Hence for first year 25,000 shall become our inflow and it shall be deducted from (40,000+10,000).

Again if we dont sell machine at end of first year we will loose 25,000 & after running it throughout 2nd year if its sold we will get Rs. 15,000. Thus for 2nd year 25000 will become opp. cost lost and 15000 our inflow. Hence 15,000 deducted from (25000+20000). Similarly for third year 15000 will become our opp. cost and 10,000 our inflow.

you have suggested that opp. cost & maint. cost should be divided by 4.4873. But 4.4873 is annuity value for 8 years, whereas we have only 4 years for existing machine.

In your solution you have taken 10000 maint. cost for 2nd year but its for first year

Last thing - we have to make year by year analysis for replacing machine i.e. what will be the effect if machine is replaced at first year, then at second year and so on; hence we should not add maintenance cost for all 4 years collectively.

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(Guest)

ohhhhh ok. yes, you are right. thank you so much. appreciate the help.

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