Estimating economic useful life and average yearly costs

mark95

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Hello everyone. I've been struggling with this two (similiar) exercises and I have no clue what else can I do :(. The exercises refer to economic useful life, it is basically about discounting in particular years but I do know where I am doing the mistake (atleast according to answers I was given, maybe they are false? :) ).

I made a screenshot of it because I already made the tables so it would be difficult to paste them here. In both exercises last 3 columns are my calculations.

EULhelp.jpg


EUL2help.jpg


So generally I just need someone who could guide me where I am wrong - do I add wrong numbers or discount wrong things. Thank you.
 
Hello everyone. I've been struggling with this two (similiar) exercises and I have no clue what else can I do :(. The exercises refer to economic useful life, it is basically about discounting in particular years but I do know where I am doing the mistake (atleast according to answers I was given, maybe they are false? :) ).

I made a screenshot of it because I already made the tables so it would be difficult to paste them here. In both exercises last 3 columns are my calculations.

View attachment 7900


View attachment 7899


So generally I just need someone who could guide me where I am wrong - do I add wrong numbers or discount wrong things. Thank you.
Please reply with legible statements of the exercises and your work. Thank you! ;)
 
I was not aware it is not readable, sorry.

A transportation company is using trucks of a specific type called Biggy. When the years go by, the operating costs of the Biggy trucks increase. The management of the company is having a look at the time they are planning to use the Biggy trucks. If they decide to stop using the truck after a couple of years, the truck can still be sold as an occasion and the company will get a refund for that. The Biggy truck costs 120.000 Euro to buy at the moment. The cost structure in the coming years can be found below:



Year Operation costs refund
1
€ 30.000
€ 70.000
2
€ 30.000
€ 60.000
3
€ 30.000
€ 50.000
4
€ 40.000
€ 40.000
5
€ 40.000
€ 40.000
6
€ 50.000
€ 30.000
7
€ 80.000
€ 20.000
8
€ 80.000
€ 10.000


Calculate the EUL if the company uses a iWACC of 10%, using the average cost method. Hint: the refund can be seen as a negative cost.



Truck cost
Year Complementary costs Refund Discounted yearly costs Cumulated discounted yearly costs Average yearly costs
120.000 1€ 30.000,00€70000 -36 363,6483 636,3692 000
120.000 2€ 30.000,00€60000 2 479,34122 479,34 70 571,43
120.000 3€ 30.000,00€50000 37 039,82157 039,8263 148,036
120.000 4€ 40.000,00€40000 74605,56194 605,5661 392,37
120.000 5€ 40.000,00€40000 101 926,1221 926,158 573,94
120.000 6€50.000,00€30000 138 070,26 258 070,2659 332,64
120.000 7€80.000,00€20000 185 788,64 305 788,6462 767,14
120.000 8€80.000,00€10000 228 760,33348 760,3365 469,044

Answer: EUL 5 years; average yearly costs of 68.544 Euro

  • If the answer is true then 5 yrs cumulated costs would equal = 259 700,87?

here is photo (I hope this time clear) attached because I cannot paste formulas:
eulh.jpg

All above calculations are my attempts.
 
exercise nr two (I couldnt put it in one post because of letter count)

The management of a company has decided to buy a machine that can produce parts at a high rate.The machine needs an investment of 80.000 Euro. They expect to realize a production of 30.000 pieces the first year. After that the production will drop with 2.000 per year. The fixed complementary costs are 5.000 Euro the first year and will increase with 4.000 Euro per year. The variable cost per product are 2 Euro. The parts can be sold at a price of 4 Euro per part.
The company uses a depreciation method that is based on an annuity schedule, where 10% interest per year is being used. The company uses the methodology of the average yearly costs per product to determine the EUL. The EUL is calculated to be 5 years. All costs, except the initial investment are paid at the end of the year.

  1. Determine the average yearly costs if the machine is used for five years.
  2. Which argument can be found to not use the average yearly costs per product method for calculating the EUL in this particular case?
c. Determine the EUL using the highest average yearly profit method
Year
Complementary costs

Production volume

Variable costs
Revenue
Discounted yearly costs
Cumulated discounted yearly costs
Average yearly costs
1
€ 5.000,00
30 000
€60000
€120 000
59 090,91
139 090,91
153 000
2
€ 9.000,00
28 000
€56000
€112 000
53 719,01
192 809,92
111 095,24
3
€ 13.000,00
26 000
€52000
€104 000
48 835,46
241 645,38
97 169,18
4
€ 17.000,00
24 000
€48000
€96 000
44 395,87
286 041,25
90 237,66
5
€ 21.000,00
22 000
€44000
€88 000
40 359,89
326 401,14
86 148,50
I havent added calculations because they are already in the table. Counting consisted of adding the costs and then dividing them by 10% interest (e.g. (60 000 + 5 000)/1,1 in first year and so on.

Costs per product:
1. 5,1
2. 3,97
3. 3,74
4. 3,76
5. 3,92

Answers:
a. 3,357 Euro -> according to answer if I’m right and the costs per product are the lowest in 3rd year then average yearly costs would be 87 282.
b. Check Theory
c. Average profit 15.951 Euro
 
These seem to be primarily accounting problems rather than math problems, and I have limited knowledge of accounting.

Let's work through the first problem together.

I think what you are doing is trying to compute the costs of acquiring and operating the truck on a present value basis.

In year 1, if you retain the truck, the discounted cumulative costs are

$120,000.00 + \dfrac{30,000}{1.1} \approx 147,272.73.$

If you dispose of the truck at the end of year 1, the discounted cumulative costs are

$120,000.00 + \dfrac{30,000 - 70,000}{1.1} \approx 83,636.36.$

In year 2, if you retain the truck, the discounted cumulative costs are

$147,272.73 + \dfrac{30,000}{(1.1)^2} \approx 172,066.12\ or\ 86,033.06\ per\ year.$

If you dispose of the truck at the end of year 2, the discounted cumulative costs are

$83,636.36 + \dfrac{30,000 - 60,000}{(1.1)^2} \approx 58,842.93\ or\ 29,421.47\ per\ year.$

If that is what you are trying to do, I suggest you do it on a spread sheet because the arithmetic is fussy and prone to error. I do not guarantee that my arithmetic is error-free, but it looks to me as though you may have made an error or two, which of course is cumulative.
 
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