Ihab Saad – Calculating Equipment Cost
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The speaker discusses the importance of ownership costs and profitability in construction equipment, including depreciation, insurance, and licensing. They provide examples of factors affecting depreciation costs and operating costs, including depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method, depreciation method,
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Music. Hello again, and welcome to construction equipment. Today
we're going to talk about estimating equipment cost.
Definitely, as we have mentioned already in class, that cost is one
of the major functions that the project management manager is
responsible for. And today we're going to talk about estimating
equipment. Since this is a construction equipment class,
we're going to learn about what are the different components of
the equipment cost. And then we're going to talk in some more detail
about equipment depreciation, how it is part of the cost component,
and it has to come in our cost estimates as well.
So building and industrial construction depend more on labor
and material. So residential construction, for example, and to
certain extent, commercial construction, rely on labor and
material. So they are labor and material intense, intensive.
However, heavy construction, highway construction or heavy
civil projects, is very much equipment dependent, therefore the
equipment cost component is the most predominant one, much more so
than labor or even materials. So when you think about a pavement
project, for example, or heavy earthwork project, you're gonna
find that the cost of the equipment is the predominant cost,
because there's no cost of material. Pretty much the earth is
already there. So the cost of excavating, the cost of
transporting, the cost of compacting, etc, which is
predominantly the cost of the equipment with some parts of labor
component as well.
So construction equipment must earn sufficient revenue to cover
the contractor's investment cost, which is the ownership cost and
the operating cost.
Let's treat equipment like an asset. It is an asset. So the
contractor purchased it, purchase it, it to make profit out of it.
So we have to account for its costs. We have to account for any
expenditure that we make related to the equipment, and hopefully
we're gonna make a profit out of the utilization of that equipment
as well. So the contractors must be able to estimate the ownership
and operating costs, oh and oh for each piece of equipment that they
own. Equipment can be owned, it can be also rented or leased. The
contractor does not have to lock his or her money in a big asset
like equipment, they can rent it or they can lease it. However, the
rental cost and the lease cost, in some cases, might exceed the
ownership and operating cost. So there's an advantage of not
locking a large amount of capital in equipment, but at the same
time, you're going to pay a little bit more for that rental.
And costs are used to determine rates to charge projects for
equipment use, which is going to be charged as part of our bid and
decisions regarding disposal, purchase, rental or lease of
equipment, we need to know at certain points in time, is it
going to be better to purchase the equipment and depreciate it along
the project, or is it going to be more economical to rent the
equipment for short term? Or is it going to be more equipped more
economical to lease it for a medium term, not exactly the same
length as owning it and not as short as renting it.
So when we start talking about equipment, we have two major types
of equipment that's at least one of the classifications. One of
them is that it's production equipment which is producing units
that alone or in combination, lead to an end product that is
recognized as a unit for payment. So, for example, concrete mixers,
they produce concrete which can be a part of the bit items that is
concrete, asphalt, same thing and so on, so including pavers,
collars, loaders, rollers and trenches that excavate trenches
and so on. Because the unit, whether it's cubic yard or linear
foot or whatever, for the for the trench excavation, it's an end
product by itself, and it's produced by this piece of
equipment. So this is the first type, which is called production
equipment. The second type is called support equipment, and this
is equipment that's still needed for the project, yet it does not
produce end units that can be counted as bid items. So it's
required for operations related to the placement of construction,
such as movement of materials and personnel and activities that
influence the placing environment. These include hoists or cranes,
vibrators, scaffolds, transit mixers, etc. Scaffolds, for
example, are gonna need it for the project because that's where the
labor are gonna stand to place concrete or to place
masonry or whatever. But you cannot have a pay item in the bid
by itself, called scaffolds is going to be embedded and
calculated in the cost of the units where that scaffolding is
going to have an effect. So.
Now talking about equipment costs, it can be divided into four major
components, and these are going to be ownership, operation, including
maintenance and repair overheads, and finally, profit, because we
need to make profit out of that piece of equipment. So the
contractor's accounting system is the best source of information for
these figures, historical data is the best method of determining
cost. So we're going to look at historical data for similar
projects in the past. How much did we spend on these different parts
of that cost? And as you can see, the ownership cost is the
predominant part of that cost, because purchasing the equipment,
that huge asset, is a big bulk, and then the operational cost,
including running that piece of equipment, maintaining it,
repairing it from time to time, and then any overhead that's going
to be charged on that piece of equipment, including, for example,
the cost of storage. If that equipment is not being used, where
are we going to store it and keep it safe? And then finally, profit
we need to charge again. Since it's an asset that the contractor
locks his or her money to purchase that asset, they have to get a
return on that investment, which is going to be in the form of
profit that's going to be charged to the client or the owner.
The ownership and operation cost
for the equipment. Ownership costs are incurred, whether the
equipment is used or not. And think about it this way, if you
have a truck, and the truck is kept locked in a garage, for
example, you're not making use out of it. Well, you're not getting
any profit. First of all, the value of that car is going to
deteriorate with time. Although you have not used it, that's just
a fact of depreciation, so you are losing money by keeping it locked.
So whether it's working or not, its value is going to decrease.
The operating costs, however, are incurred only when the equipment
is being used, because it's related to the equipment usage,
whether it's going to be fuel, grease, filters, maintenance, etc,
it's going to be related to the use and the amount of use of that
piece of equipment. So parts of ownership costs, we have
depreciation, interest that you have to pay for a loan, for
example, to purchase that piece of equipment, taxes, insurance,
again, whether you use it or not, storage and license fees. All of
these are part of the operating costs, regardless of whether the
equipment works or not. On the other hand, the operating costs
include maintenance and repair, which are, as I said, proportional
to the use of the equipment tires, including repair or replacement of
these tires, fuel that's going to use to be used to run that
equipment, service filters oils, grease, which are the things that
you need to keep replacing on a regular basis, downtime. We're
going to talk about that little bit later on. And finally, the
operator. Operator, if that equipment has an operator, a
driver, or someone who is going to run that piece of equipment,
that's going to be part of the operating cost, because their cost
is going to be only charged if the equipment is being used. That's
the major differentiation between ownership and operating
and as you can see here graphically, the ownership cost
goes down with time,
whereas the operating cost goes up with time, the older the piece of
equipment, the more operating cost is going to have. It's going to
require more maintenance, more repairs, etc. Whereas the
ownership cost is going to go down because of depreciation, the value
of that equipment is going to keep going down until it becomes, at
least on the books zero you might have the equipment still
functioning, still producing. And in this case, the ownership cost
is going to be pretty much nothing.
The ownership costs are best estimated by the time value of
money analysis method. We talked about the time value of money. In
the previous lecture, we learned about how to draw the cash flow
and the different types of the present value, the future value,
the annuities and so on. So this is one way of calculating the
ownership cost. The contractor will know the purchase price and
must estimate the ownership period for. How long are they planning to
own that piece of equipment, whether it's until it becomes
totally obsolete and its value becomes zero on the books, or are
they going to set it to use and get some residual or salvage value
from selling that piece of equipment? This information will
account for depreciation. We need to calculate this information to
be able to calculate the amount of depreciation that's going to be
charged on that piece of equipment every year.
The ownership cost is also called the fixed cost, because, again, it
does not depend on the utilization of the equipment how many hours or
how many days it is time dependent or time related because of the
effect of obsolescence or.
The effect of depreciation, as we have seen, it goes down over the
years. It's calculated by relating the estimated total service life
in hours to the total total cost of the equipment working during
these hours. If the equipment is idle for some of those hours, cost
is taken as part of the general overhead.
So if the equipment is in use hourly cost is charged to the
project, you're going to estimate how much it costs you per hour as
if you were renting it, not exactly at the same price of
rental. Because again, here we have another dilemma. What if a
contractor owns the equipment and charge the client for the price of
rental? Theoretically speaking, the contractor is going to make
more money because the price of rental is higher than cost of
ownership. But on the other hand, if that price is too high, the
total bid price for the contract is going to become too high, and
the contractor may be out of the competition. So these are the two
criteria that we have to balance at the same time, how much are we
going to charge the owner in a way that's going to enable us to
achieve maximum possible profit, and at the same time still be
competitive and be able to win the bid. So that ownership cost is
going to consist of the two main components, estimating the for
depreciation on the cost of using the equipment, and estimates for
of allowance for interest, insurance and taxes, which, again,
as we mentioned before, are part of the fixed or ownership cost.
This is by the definition of the IIT, the
industry Institute, construction industry Institute,
the ownership cost includes interest, taxes, insurance and
storage itis and license costs, and these are used to establish
the minimum attractive rate of return. Minimum attractive rate of
return, the interest is going to be charged for borrowed money or
the return expected from invested money, which is the cost of
opportunity, or the cost of the lost opportunity. If the money is
borrowed, you'd have to return it back with an increase that's
called interest. If the money is yours, you're going to assume as
if you have invested this money in another endeavor, and that money
is giving you a return on investment. That alternative
return on investment, you're going to charge it to the owner, because
you lost that other opportunity by locking your money for that
particular project. Taxes are going to be include the personal
property taxes for owning that asset, the insurance for general
liability insurance to cover damage or injury caused by the
equipment. And equipment insurance to cover physical damage to the
equipment, very similar to liability insurance, the full
coverage that you have on your car, if you want to have the peace
of mind of if anything happens to my car or my assets going to be
replaced, then you're going to have the full coverage if only you
want to protect against your own mistakes, against the others. So
if you hit someone, or if you hit another car that your insurance
company is going to pay for their payers, that's going to be the
just, just the general liability insurance storage is going to be
the cost of protecting the equipment when not in use on the
project. And that's a good practice, definitely. And finally,
the license costs, which are fees, pet for plates and other user
permits. Again, the The easiest example is your car. You have to
pay for the renewal of your license plates every year.
And for each piece of equipment, the equipment manufacturer is
going to include a some pages in their users manual that show you
how much to charge for how many hours that equipment is going to
be used. So if it's going to be used, for example, 6000 hours a
year, then this is what you're going to charge if it's going to
be 5000 4000 3000 2000 and so on. So it tells you guide for
estimating hourly cost of interest, insurance and taxes
based on the number of hours that equipment is going to be used per
year. That comes for a caterpillar contractor. It comes with within
the manual of that country, of that piece of equipment, of that
tractor.
Now let's look at an example. Here. A contractor has purchased a
tractor for $155,000
they are not coming cheap, with an expected useful life of 12,000
hours,
12,000 operating hours, not calendar hours, and estimates. The
contractor estimates that its annual usage will be about 2000
hours per year. So from that, we can expect that we're gonna own it
for or a service life of six years. That's 12,000 divided by
2000
the salvage value at the end of the tractors useful life, which is
six years, is estimated to be about 12% of the purchase price,
12% of this 155,000
the contractor estimates his ownership cost factors to be the
interest is going to be 9% everything is related to the.
The purchase price, 9% the tax is 2% the insurance, 2% storage, 1%
license, none.
What would be the estimated annual ownership cost if it's operated
under average conditions?
So again, we need to calculate the total ownership cost and then
divided by the number of service lives, service life years to get
that operating cost per year, ownership cost per year. So the
expected useful life, 12,000 hours period of ownership, 12,000
divided by 2000 that six years minimum attractive rate of return,
which is basically the sum of these numbers, nine plus two plus
two plus one, that's equal to 14%
the sandwich value. Imagine that's going to be 12% of the purchase
price, which is 155,000
so you're going to be able to sell that piece of equipment at the end
of the six years for $18,600
so the present worth
of that salvage value today, this is going to be in six years. What
is the worth of these $18,000.06
100 today? The present worth of the sandwich value is 8,481.6
subtract the present worth
of the salvage value from the purchase price. So this is
basically the cost of using that piece of equipment today convert
to an annual series. You remember when we did that in the previous
class by you using an annuity based on the present value. So
it's going to be equal to $37,655.23
therefore the cost per hour is going to be that 37,655
divided by 2000 hours per year, which comes up to 18 $83 per hour.
So for each hour this piece of equipment is going to be working,
is going to cost you 1883 you have now to charge the owner a little
bit over and above that, to include for your own profit,
the operating cost. So far, we have talked about the ownership
cost. Now let's talk about the operating cost. The operating cost
is also called the variable costs, and it's a function of a number of
operating hours, quantity proportional. It's not exactly
time related, because, again, if the equipment is kept locked or
unused, there is no operating cost. There is ownership cost, on
the other hand, so it's quantity proportional, includes fuel,
lubricants and other consumables, filters, tires, etc, maintenance,
overhauls and repair and operators wage including fringes. Again,
remember here when we talk about, for example, a
crane operator getting $50 an hour. The $50 an hour are not
exactly the cost of that grain operator, because you're going to
charge more for that. There's going to be insurance, workers
comp, taxes, Social Security, etc, so, and the other benefits. So
basically, it might be something like maybe $80 an hour. So that's
the exact that's the actual cost of that labor.
The best source of data for estimating operating costs is from
historical records, again, looking at our track record how much it
costs in the past. The next best source is to use cost factors
provided by equipment manufacturers for the specific
equipment. As we have seen in that book on Caterpillar Tractor.
They're gonna give you some indices on how much to calculate
for that cost. That's if you do not have any historical
information. So the operating costs can are generally
influenced, or greatly influenced by the age of the equipment. Of
course, the older, the more it's gonna cost you, because it's gonna
require more repair, more replacement of consumables. It's
state of repair and maintenance. If you keep it in good condition,
it's going to cost you less. If you abuse it, it's going to cost
you more. And it's operating conditions. Again, if it's working
in a very harsh environment, that's going to need more upkeep
cost. If it's working in normal conditions, then again, that cost
is going to be reduced.
Maintenance and repair costs are roughly estimated by using a
percentage of the annual straight line depreciation amount.
There's going to be a table that provides factors to be used to
estimate hourly maintenance and repair costs, again, depending on
the type of equipment, since the factors are based on 10,000 hours
of operating hours. They must be adjusted so the hourly repair cost
is going to be the equipment repair factor from the table,
times the useful life in hours times.
Times the hourly depreciation rate divided by 10,000 hours or divided
by 10,000 Let's see an example of that. So here is the table, for
example. It shows equipment repair factors based on a 10,000 hour
useful life. If the number of useful hours is going to be more
than that, the equation has to be adjusted so it gives you here
based on the different types of equipment. If it's a bottom dump
without the tires, under favorable conditions, then the repair is
going to be 30% under average condition is going to be 35%
unfavorable condition is going to be more 45%
for general contracting, a crawler tractor is going to cost that
much. For quarrying, which is more abusive, is going to cost that
much. Haulers, loaders, scrapers. So for different types of
equipment, it can give you percentages on the equipment,
repair factors,
the tire costs. Tires are treated as a separate operating cost, as
they have a different useful life than the equipment. The equipment
might be working for seven years, 10 years, 10,000 hours, 20,000
hours, but definitely, the tires are not going to serve for that
whole period. They have to be replaced regularly. Track
replacement for track mounted equipment is included in the
maintenance and repair cost.
Tires are subtracted from the purchase price when determining
ownership cost. So when you have and we're going to see an example
of that, a separate cash flow analysis is performed for the
tires, when are you going to buy them for? How much? When there are
they going to be replaced and so on. And we're going to use a table
to estimate the tire life. With the table
data and tire cost, develop a cash flow analysis to know, again,
whether you're making profit on that piece of equipment or not.
Tire maintenance and repair is going to be 15% of the hourly
straight line depreciation for the tires.
So let's look at the table here again. It shows for different
types of equipment, under different operating conditions,
what would be the service life of the tires. So for haulers, for
example, under average conditions, the tires are going to serve for
3200 hours, whereas under unfavorable conditions, you lose
1000 hours, that's quite a lot.
Fuel consumption. The rate of fuel consumption for equipment varies
with the rated horsepower. The higher horsepower, the more fuel
thirsty is gone. Thirsty is going to be and the duty cycle of the
engine, the percentage of the time the engine is operating at maximum
output, which varies with each piece of equipment and the
operating conditions. Again, if you're working in harsh
conditions, for example, you're going to have more fuel
consumption, whereas if you're working in more favorable
conditions, it's going to be less fuel consumption. Think about it
again. To simplify things, think about it as your own car.
The hourly fuel cost is going to be the fly with horse, horsepower,
time, fuel factor, time, the fuel cost, and for the fuel factor, we
again, each piece of equipment is going to have its own tables that
can be used for that. So again, here for different types of
equipment, and we have two columns, one for average
conditions and one for unfavorable conditions. And then we have the
two different types of of fuel, gasoline and diesel. By the way,
these numbers are relatively old. They come from an old manual, and
these have to be updated to reflect the increase in fuel
prices. Of course, these prices are not valid right now, because,
as we have seen just in the past couple of weeks or so, the gas
prices have gone up. So it fluctuates from month to month,
from year to year and so on. But in general, the trend is going up.
Servicing costs again, to keep the equipment in a good condition, you
have to maintain it. You have to spend some money to keep it in
good condition. Filter oil and grease costs are estimated as a
percentage of the hourly fuel cost. It Again, depends on the
number of hours of operation of the equipment. So again, here we
have a table that shows for different operating conditions,
what would be the Equipment service factor as a percentage of
the hourly fuel cost. The
in
downtime, we have already mentioned in class something about
that piece of equipment working 50 minutes an hour or 45 minutes an
hour or 55 minutes an hour or 30 minutes an hour. This is called
downtime. Downtime is.
Considered by using an operating factor when determining
productivity rates. This operating factor, also known as efficiency
factor, is a percentage equal to the amount actual number of
minutes per hour the equipment is working and not idling. So the
productive number of minutes per hour sometimes you need a few
minutes to adjust the equipment, to orientate it, or to for the to
start it up, to warm it up, or to cool it down, and things like
that. This is not productive time, but it counts as part of the total
duration the equipment is working. So it reduces the productivity of
that equipment. We would say in this case that if the equipment
works or produces 45 minutes of one hour. That's 45 over 60. So
the efficiency of that piece of equipment, or the operating
factor, is 75%
there's no equipment that works at 100% efficiency. So the skill here
is to maximize that efficiency. We know we're not going to be able to
reach 100% but at the same time, we don't want it to be 30% or 20%
that would be a lot of loss.
And finally, the labor cost for the operator must be estimated
using local wage rates and fringe percentages. And again, the human
resources department in your company is going to know about
that, and they're going to be responsible for giving you the
numbers for the labor cost, the hourly wage rate, plus the cost of
fringe benefits, including vacation, retirement insurance,
whether it's health insurance and so on, workers comp, any other
fringe benefits will have to be added to the labor cost. I
dollars.
Now let's look at an example. Contractor has purchased a wheeled
loader. Wheel Loader means we're going to have tires $414,000
and plans to use it about 2000 hours per year.
The contractor anticipates disposing of the loader after
using it for six years. So the estimated total number of hours is
12,000 hours, and realizing a salvage value of $35,000.06
years from now,
tires, tires for the loader cost 4000 for a set of four, quite
expensive, and the brake horsepower rating of the loaders.
Diesel engine is 105 horsepower. The operator will earn $35 an
hour, including fringe benefits and diesel fuel costs 1.2 dollars
per gallon. As you can see, these are old prices. Right now, it's
close to $4 a gallon
at the minimum, attractive rate of return of 12%
what are the contractors, hourly ownership and operating costs for
the loader? So let's break down this information into smaller
pieces and take it step by step to calculate what we need to know.
First of all, as we have mentioned, we're going to subtract
the cost of the tires from the purchase price of the equipment.
So we have total purchase price 114,000
the cost of the tires, 4000 therefore the cost of the
equipment, we're gonna consider it as 110,000
so the purchase price less tires, 114,000 minus 4000 that's 110,000
the ownership cost is going to be the annual ownership cost plus
labor cost plus operating cost plus repair cost. And what we have
here at the bottom is a cash flow for that equipment. So we have a
purchase price minus the tires at the beginning, and then six years
later we have a salvage value. And in between, we're going to assume
we have annual cost, which is going to be like an annuity.
I would like you to to try to work on that problem at home and show
me your answer and be glad to discuss it in class. Or we can
discuss it one on one, just follow the instructions and follow the
tables that we have used. It's a very straightforward problem.
Now we're going to move to overheads, which are added to the
direct operating cost. These include allowances for general
overhead expenses
and project overhead expenses, general overhead expenses, like,
for example, you have a headquarters and you are renting a
building, and you have telephone costs, stationary heat, trend cost
of either equipment,
etc. All of these are general overheads or administrative
overheads. And at the same time, you also have indirect cost on the
project itself, including the salary and the cost of the
superintendent, the project manager, a secretary outside, a
security guard, maybe a temporary fence around the site, maybe a
temporary access road. All of these are considered as overheads
because they are not part of the permanent construction.
It. And you cannot pinpoint
any particular cost item for the cost of the project manager. For
example, the salary of the project manager. The project manager is
not gonna lay bricks or pour concrete or erect steel and so on.
He's going to be supervising the whole operation. Therefore, the
salary of the project manager has to be absorbed by all of these
different pay items in the bid.
Finally, profit. And that would vary from one company to another
and to vary from one market to another based on the current
market conditions and based on the competition. So it's a percentage
of the markup which is added to provide for an income or profit
element, because, again, you have money locked in that piece of
equipment, you need to have a return on that investment in the
form of that profit.
That ends our first part of the lecture talking about the
different costs components of ownership, operation, overheads
and profit, and now we're going to focus on equipment depreciation.
How does that affect the cost of the equipment? And how are we
going to calculate the depreciation? What are the
different methods for the calculation of depreciation? So
first of all, what is depreciation? It is the decrease
in equipment book value due to its usage or due to time.
So if you have purchased a piece of equipment today, brand new, it
costs you $200,000
you have used it for a year,
then it has lost part of its value because of the consumption of that
equipment, the wear and tear.
On the other hand, if you kept this piece of equipment brand new,
locked in a storage area
and try to sell it, one year later, the price is going to drop
down again. Why? Because of relative obsolescence, there's got
to be a new model with new features and so on. Same thing
again, as your car. Think about your car as a piece of equipment.
Most of the cars, unless it's an is considered as an antique car or
something like that. Don't watch these shows on on TV, but regular
cars, the one that you and I drive,
if you use it, you're going to lose money. If you don't use it
and keep it garaged, you're still going to lose money. So you lose
either way,
it's an expense that can be deducted from revenues, resulting
in lower taxes. Now this is the positive aspect of depreciation.
Since the value of your asset has decreased, you have to pay less
taxes on that asset.
The resulting tax savings can be used to replace the equipment. So
instead of saying, Okay, I have a tax break because of the age of
that piece of equipment, so I'm gonna use these savings to go on a
trip, for example. No, that's not the purpose of the tax break. The
purpose of the tax break is enabling you, enabling you to save
some more money so that when this piece of equipment becomes totally
obsolete, you would be able to replace it with these savings.
That's the major purpose of these tax breaks due to depreciation,
as we mentioned, it's caused by wear and tear, deterioration,
obsolescence or reduced need, and the depreciation determines the
decline in market value during time period. So if I want to know,
for example, at the end of the third year, what is that piece of
equipment worth, how much has it depreciated, I should be able to
determine that determines the depreciation amount to use in
replacement decision analysis. So knowing how much by how much has
the equipment depreciated, and what's the book value?
When am I going to be able to save enough money to replace that piece
of equipment? That's going to come from these calculations. It's also
used to evaluate the tax liability, how much taxes do you
have to pay? And realistically reflects the asset and the
liability of a company. This is something related to accounting
and bookkeeping. When maintaining the assets and liability columns,
depreciation is going to come into play there.
There are four different methods to calculate depreciation. Which
one are you going to follow? Either one is fine. Any of these
four methods is fine. Each one has its pros and cons. We're going to
learn about that in a minute. So there we have something called a
straight line depreciation method, which is the most straightforward,
the easiest one to calculate some of the years. Method, declining
balance method, and finally, production method. Production
method depends on the equipment is going to depreciate depending on
how much use you actual usage? Have we used it for? So for
example, you'd say, all right, in the first year I drove my car
30,000 miles, but in the second year I drove it only 5000 miles.
Should the depreciation be the same? No, in this case, according
to the production method, it's going to depreciate more during.
The first year because you drove it more and less during the second
year because you drove it less. So let's look at each one of these
four different methods and see what it entails. How to make the
calculations and make some comparison between them.
The straight line depreciation method depreciates the equipment
value equally in each of the years the equipment is owned. So
regardless of how much you have used it, as long as you have owned
it for a year, there's a fixed amount of depreciation for that
year. It doesn't vary between the first year and the last year of
the life of that equipment. It's exactly the same amount.
So n, r is the annual depreciation rate. We're going to learn about
that in a minute. N is the number of years the equipment is owned,
so r is the reverse of N. It's one over n. If you're going to piece
that own that piece of equipment for six years, then r is equal to
one over six. If you're going to own it for 10 years, R is going to
be one over 10. If you're going to own it only for two years, then 1r
is going equal to one over 2d.
Is the annual depreciation amount in dollar amount. P is the
purchase price, and F is a salvage value at the end of n years.
Again, if you're going to own this equipment for six years and then
sell it, then you're going to get some money at the end of six
years. That's the salvage value, which is f. Therefore the
depreciation, the annual depreciation amount, the actual
amount you have to deduct for depreciation, is equal to r times
p minus F, r times p minus F,
the book value, equipment value at the end of each year after the
annual depreciation has been subtracted. So at the end of the
first year, what's my equipment worth at the end of the second
year, which would be BV two, the book value at the end of year two,
BV four, at the end of year four, etc. So BVM is equal to BVM minus
one the previous year minus dM, the book value at year M, let's
say at year five is equal to the book value at year four minus the
amount of depreciation for year
five, which, in case of straight line, is going to be the same, DM,
d1, is equal to d2, is equal to D, M, it's exactly the same. So book
value m is the book value in year M, dv, m minus one is the book
value at the year m minus one, and DM is the annual depreciation
amount, again, in straight line method, that amount is the same
regardless of the year.
And this is the graphical representation of the straight
line method. As you can see, it's a straight line.
We start with the purchase price,
and we end with the salvage value,
and we depreciate the price of the equipment over the years. In this
case, for example, the service life of that equipment is five
years. We depreciate it over the years, and that amount would be
the annual depreciation amount. So it's $3,000 per year, as you can
see from the graph.
Again, an example is going to make things very clear,
a contractor purchase a greater for $250,000
so P is 250,000
and plans to use it for six years. N is six years. The estimated
salvage value is 60,000 F is 60,000
using the straight line method of depreciation accounting, what is
the annual depreciation amount of and the book value of the
equipment at the end of the third year? So m is equal to three.
Let's look at the application of the equations R, the annual
depreciation rate. These are the equations here, D, annual
depreciation amount, which is r times p minus F, the book value at
year M is BVM minus one minus dM. So book value at the end of year
one book value at the year zero, which is the purchase price minus
depreciation at year one book value at the end of year two is
the book value of year at the end of year one minus depreciation.
Book value at year three, book value at year two minus
depreciation. Let's look at the numbers.
We said that the service life is going to be six years. Therefore R
is the verse of n, reverse of n1, over n. So it's point 167,
the annual depreciation amount is R. D equals r times p minus f,
which is point 167, that factor times the purchase price, 250,000
minus 60,000 the salvage value, which is 190,000
and that gives us 31,006
166.6
$7 per year, the value of that equipment is going to go down by
that fixed amount every year, the book value, BVM, BVM minus one
minus dM. So at the end of year one, the book value at the
purchase price 250,000 minus the depreciation for year 130 1000 so
the book value at the end of year one 218 333,
at year two, we're gonna start with the book value of the
previous year. 218 333, minus 31 666,
which gives us 186.666
at the end of year three, which is what we're looking for. We're
going to start with 186
minus 31 666,
which gives us $155,000
value of that equipment at the end the book value of the equipment at
the end of year. Three, very straightforward, very easy.
So here's a table that shows the value of that equipment, the book
value at the end of each year up till the time you sell it at the
end, at the salvage value, which is the 60,000
and as you can see, depreciation amount does not vary with the
years. It's the same every year. That's a straight line method,
a second method, which is called the sum of the years method.
In this case, we do not have a fixed amount for the depreciation.
It varies from one year to another. The annual depreciation
rate differs for each year. In this case, the annual depreciation
rate is equal to n minus m plus one divided by sum of the years.
What does that mean? N is the number of years the equipment is
owned the service life of that equipment. In the previous
example, it was 6m.
Is the specific years in which depreciation is being determined.
So in the previous example, we wanted to know what's the book
value at the end of the third year. In this case, M would be
equal to three.
Soy, which is the sum of the years, is the sum of the years
that equals n plus n minus one plus n minus two, and so on, which
is sort of the factorial of n divided by two. So the sum of the
years is equal to n times n plus one over two.
Remember this equation
and the annual depreciation amount very similar to the previous
example, straight line, DM equals RM times p minus f, so the sum of
the years is already incorporated in the RM, and therefore DM
becomes same equation as with a straight line. The annual
depreciation amount is the annual depreciation rate times purchase
price minus salvage value,
looking at the same example with exactly the same numbers,
250,006
years, average value, 60,000 now we're going to use the sum of the
years method and see what's the value of that equipment at the end
of the third year. Let's go back a couple of slides here. At the end
of the third year, according to straight line,
the value was $155,000
remember that, and the depreciation amount per year was
31,666.67
now let's see, according to the sum of the years, how are these
numbers gonna differ?
Notice here that at the very beginning, the depreciation amount
is really high, and then it starts going down and down and down.
So the sum of the years again, n equals six, so soy equals six
times six plus one, seven divided by two, so six times seven over
two that's 21
now Rm is equal to n minus m plus one divided by Soi, n 6m
at the end of third year, three plus one divided by
Soi, which is 21 so six minus three plus one divided by 21
that's the rate that we're looking for for the third year,
which is point 1905,
the depreciation amount is that factor point 1905,
which is going to vary again from one year to another, times
purchase price minus salvage value. So point 1905, times
250,000 minus 60,000 and that gives 36,000 $190.48
compare that again with the number that we got from here. 31 660,
6.67
you.
Find that the sum of years gives a higher
depreciation rate at still at year three, year four is going to be
less.
And the book value here is equal to $114,285.70
in the previous example, I believe it was 115 Oh, it was 155
so again, the book value is much less in this case,
which means you're going to pay less taxes, so you have a higher
depreciation rate, and that's going to enable you to have lower
taxes to pay for the equipment. That's one of the benefits of
using the sum of the year's method.
The third method is called declining balance. Declining
Balance also assumes that you're going to have a higher
depreciation at the beginning, lower depreciation at the end.
Looking at the same example that we've been giving your car,
if you purchase a used car, the difference between a 2007 and a
2008 model is not going to be that much. Of course, the 2008 is going
to be more expensive, but the differential is going to be small.
Compared to a 2011 from a 2012
as they always say, you lose about
maybe 10% of the value of your car in the first 15 minutes.
If you drive it out of the lot of the car dealership for five miles,
you lose about 110 of the value of that car because it's already a
used car. So the depreciation at the very beginning is very high,
and then it keeps on going down as the equipment becomes older.
When applied to equipment purchased secondhand, if you buy a
used equipment, it assumes that the initial value is 150%
of the straight line rate.
And for new equipment, the rate is calculated by dividing 200%
by the number of service life years. So that's why it's called,
sometimes double declining balance, that you assume that the
value of the equipment is 200% of its own, of its value if it's
calculated at the straight line method. We're going to see a
numerical example on that as well,
just graphically looking at a declining balance, or double
declining balance and straight line. If you can see here, the
amount of depreciation for the straight line is fixed. The height
of each step is exactly the same for the service life of the
equipment, whereas in case of declining double declining
balance, huge depreciation the first year little bit less the
second year less the third year by the fourth year is much less than
the straight line.
So again, that enables you to deduct a lot of the value of the
equipment at its early service life.
Now, for the calculations of the declining balance, the annual
depreciation rate is applied each year to the remaining book value.
The annual depreciation rate is x over n.
In the previous examples, we had one over n. Now here we have x
over n. That's the major difference, that x is it can range
anywhere between 1.25 to two. We mentioned that for new equipment,
it's going to be two. For used equipment, it's going to be in a
good condition, it's going to be 1.5 in a not so good condition, it
might be as low as 1.2 5n.
Is the number of years the equipment is going to be owned,
and the actual annual depreciation amount is going to be the book
value
at that year minus one times r.
So again, same example, just to have a comparison,
250,006
years, 60,000 and we need to know
at the end of the third year. Now assuming that, when the contractor
purchased that piece of equipment, was it new, or was it used? Let's
see. It says assume x is 1.5 which means it was used, because if that
equipment was purchased new, then x would be equal to two. So based
on this information, let's see how we're going to calculate the
depreciation rate.
R equals 1.5 over 6x over n, which is equal to point two five. So the
depreciation rate is point two five, and that's fixed. However,
the depreciation amount is going to vary again, if you look at it
this way, at the very first year, very high depreciation rate, which
is based on this equation,
the book value at here.
By m minus one divided by times r.
So in this case, it was the 250,000
which is the book value at year m minus one year zero
times R, which is point two five, which means 250,000
divided by four gave us the depreciation amount 62,500,
subtracting that amount from the from the book value at Year Zero,
which was the 250,000
gives us a book value at year one of 187,500
we're going to use that book value at year one to calculate
depreciation at year two, the value at year two to calculate
depreciation at year three, and so on. And look at this. We started
with a depreciation, rate of depreciation amount of $62,500
by the end of year one. And look at this at the end of year six,
it's $56
negligible. So we have already consumed all of the that piece of
equipment.
Okay,
so again, here, here's an example between buying a piece of
equipment using it for five years. If it's purchased new, then 200%
is going to be divided by five years, giving 40% every year. If
it's purchase used, we're going to use 150%
so 150% divided by five years, gives 30% every year, and based on
the value of equipment, we're going to calculate the
depreciation for each year. And as you can see, it's dropping down
very quickly.
The last method, which is the production or use method, it's
very simple. It's not a function of age of the asset for a specific
year, the depreciation depends on the amount of asset usage in that
year. So if we're gonna you purchase that piece of equipment
for 250,000
sell it in six years for 60,000 and we know we're gonna use it for
a total of, let's say, 100,000 hours, or 10,000 hours, whatever
number of hours we're going to have, a proportion of that for
each year. If I use it for 2000 hours per year, the cost per hour
is that much. So the depreciation for that year is that much. If I
use it more in the second year or less in the second year, the
depreciation can go up or down. In all the other examples, we found
that the depreciation either was straight line equal, or it started
going down as in the sum of years, or in the declining balance here,
however we have the exception, it can go up, because if you use it
more, the depreciation amount can go up.
So here is an example
at the end of Year Zero, we did not use it. That was the book
value.
And this is the salvage value. So the consumption is going to be
100,000
we used. We produced 2800 cubic yards. So 2800
times 10, which is the cost per hour, gave us 28,000 so the
equipment value dropped by 28,000 the following year we only used
1600 cubic yards, so which means a certain number of hours, therefore
the consumption was 16,000 less than the previous year, and then
the third year, we used it more. So the consumption went up, the
depreciation went up as well, and so on. It can go up or down
depending on the amount of usage, and that's why it's called the
usage.
There's another concept that's called amortization of the
equipment. Amortizing the equipment comes from more M, O, R
T, which means that that's a Latin word. So the practice we're going
to assume that we're going to consume totally that piece of
equipment with zero salvage value on this particular project. So we
bought the equipment new by the end of the project, that equipment
is going to be worthless, therefore we're going to charge
all of its cost to the client as part of our bid price. So the
practice of charging the owner an amount to be used to purchase
replacement equipment is referred to as amortizing the equipment. We
are killing that equipment gradually, amortization leads to
larger revenue, resulting in taxes on the amount charged to the owner
to amortize the equipment. So that's sort of an opposite of
depreciation.
It's again, we're going to assume that the total value of the
equipment is going.
To be used over that particular project, so we're going to charge
the whole value of the equipment to that particular project, which
is going to result in more receivables from the owner higher
price, which means we're going to have to pay more taxes.
Now renting versus purchasing, there are some advantages to
renting and there are advantages to purchasing. Purchasing
definitely will give you a lower price per unit for the production
that you achieve. However, what are the benefits of renting that?
Advantages of renting equipment include, first of all, no large
inventory of specialized equipment with infrequent use, so we're not
gonna buy every piece of equipment that we need. There are some
pieces of equipment that we're gonna use probably once every
other project, once every other year. There's no meaning in
keeping that equipment on our books and locking the money in the
value the asset of that equipment. So it would be better to rent it
whenever we need it,
continuous access to new and efficient equipment. Again, you're
going to rent the state of the art. If there are any new
developments in the equipment market, they're going to be
reflected in the newer models. Whereas your older, older model,
if you do not upgrade it or update it, which is going to cost you
money, is not going to be the state of the art.
No need for warehouse and storage facilities. You're going to bring
it only when you need to use it and return it whenever you don't.
So you don't have to keep it stored, saving on insurance
premiums because you do not own that piece of equipment. Therefore
you don't have to pay the insurance for owning it. And
reduced need for maintenance and easier accounting. Easier
accounting, because very clearly, the cost of equipment, in this
case, is going to be the rental price that you pay. We're not
going to worry about Depreciation or Amortization or anything like
that. It's just the rental price that you pay and no maintenance
fee. However, no maintenance fee on the other hand, because again,
you're gonna rent it in a good condition, you're going to return
it in a good condition. The renting agency is going to service
that equipment. Is going to maintain it so that next time you
rent it again, it's still in a good condition. Going back to the
same example, think about going on a long trip, and you don't want to
overuse your car, or you're not sure whether your car is in good
condition or not. Is it going to break down or not? So in this
case, you may decide, okay, I'm gonna rent I'm gonna rent a car.
It's gonna be more expensive to rent the car. You know, the your
car doesn't cost you $50 a day or $100 a day, right? So, but on the
other hand, you're getting the peace of mind that if anything
goes wrong, I'm just gonna return that car and I'm gonna get a new
one, and this car is going to be the latest model, is going to be
well maintained. I don't have to pay any insurance, I don't have to
pay any taxes. It's just a rental price that I'm going to be paying.
And finally, here is an example on the ownership cost. It shows the
different elements that we have talked about so far, and it shows
sort of a breakdown of the example that we have discussed at the
beginning of this lecture. I hope that in this lecture, you've
learned about what are the elements of equipment cost,
including ownership, operation, overheads
and profit
and utilization, including
taxes, including permits, etc. And then we learned about how the
breakdown of each one of these, how to calculate each one of
these. We also learned about the different methods for depreciating
the equipment. We talked about four different methods. We looked
at the comparison of the four. It's all on accounting principles,
by the way, and the IRS accepts any of these different methods for
accounting. All of them are accepted, whether it's going to be
straight line or some of the years, or is going to be the
double declining balance or the utilization and use method. And
then we talked about amortizing the equipment. What do we mean by
amortization? And then finally, if we are able to calculate the cost
of ownership of the equipment at every year, or based on the number
of hours or number of units of utilization, we can easily compare
that to the cost of rental, and we can make the decision whether it's
going to be more economical to rent the equipment, or is it going
to be more feasible to own that equipment and account for all of
these differences. I hope you learned about all of these things,
and I'd be glad to answer any questions when we meet in class.
Have a great day bye.