# Ihab Saad – Construction Economics

The speakers discuss the value of money and the importance of considering the time value of equipment economics when buying equipment. They explain the impact of payments on the value of money and provide examples of how to convert a current value to a future value using a factor like F. They also discuss the use of a cash flow diagram and alternative options for replacing equipment, including the possibility of leasing a similar tractor for a fixed monthly rate. The present value is the one with the most favorable return, and the cost of ownership for the equipment is estimated using a cash flow diagram and alternative options for replacing equipment. The rate of return is an annual interest rate at which the sum of investment and expenditures equal the total income from the investment.
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Steve, Hello again. Today we're going to talk about the time value

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of money and equipment economics. So as we know,

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the value of money changes with time, so how does that affect our

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estimate on the equipment economics, whether it's going to

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be better to buy the equipment today, or buy it in a couple of

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years, or how we're going to pay for it. This is basically what

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we're going to be discussing in this lecture. So in the context of

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equipment management, a piece of equipment costs you \$50,000 to

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purchase. You could also lease it or rent it. Which option should

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you choose

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on one project, you need to excavate 10,000 cubic yards of

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earth. How much does it cost you?

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Equipment a costs you \$20,000 with a useful life of five years, while

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equipment B costs you \$30,000 with a useful life of seven years.

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Which one is a better value for your money? All of these are

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sample questions that any equipment manager or any project

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manager is going to be subject to, and we'll have to answer them

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based on an educated decision making process.

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So what's the real cost of money? Money is a valuable commodity that

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changes value with time. An increase would be evaluation, or a

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decrease would be devaluation, and it's a super resource, which means

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it's used to buy any other resources or to acquire all the

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other resources. Because if you remember our definition of a

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resource, it's something that you need for the project, you have the

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ability to manage it, and that you pay money to acquire it. If it

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does not meet all of these three conditions, it is not considered a

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resource. The issues of costing and financing, which are two

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different issues, can make or break a construction operation or

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even a construction organization. So most of the construction

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companies that fail or declare background bankruptcy, it's

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usually due to financing problems they have not been able to provide

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the required amount of money at the proper period or point in time

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to meet their obligations for the project. So money has a time value

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which increases with time. Since money increases as we move forward

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from the present to the future,

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it also decreases in value if you move backward from the future to

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the present.

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The other concept is the concept of interest, or usury. What's

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called interest is a fee assessed to use borrowed money. The

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percentage and amount of the fee will depend on the amount of money

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borrowed, the length of time it's borrowed, and the prevalent

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interest rate at the time of borrowing. So these are the three

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elements that control the amount of debt, percentage or debt

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interest. Interest rate is the percentage rate charged against

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the borrowed capital or principal. So we need to know how it is it,

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how is it calculated, and how is it going to affect our decision in

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buying or renting or leasing equipment.

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So what's the time value of money? We have to talk about something

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called the concept of equivalence. Payments that differ in magnitude

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but are made at different time periods may be equivalent to one

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another. In plain English, what does that mean any sum of money

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recorded as receipts or inflows received money, money that we get

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are called Cash in, and any sum of money recorded as disbursements or

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outflows, money that we pay out is called cash out. The difference

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between cash in and cash out at any point in time represents the

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cash flow at that point. So again, this is, as I said before, this is

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the major reason why most construction companies goes go

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bankrupt, because they did not cater for that difference between

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the cash out and the cash in. They might need certain sum of money at

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a certain point in time. Failing to provide that sum is going to

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result in bankruptcy.

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So an example on cash flow. For example,

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if you buy a car today for \$4,500

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you have an outflow cash out of 4500 which is represented by this

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negative 4500 and then at the end of year one, you you perform

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regular maintenance on that car to keep it in a good shape, good

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operating condition. So you spend, on average, \$350

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per year of ownership of that car. So the maintenance cost per year

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for year one was three, \$350

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for year two, the same thing. For year three, the same thing. And by

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the end of year four, you also pay that same amount to be able to

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sell the car. And then when you sell the car, you sell it for

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\$2,000 so as you can see here, all all of this, all the negatives are

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cash out, which are represented by negative sign. And then you get a

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positive inflow, or cash in of two.

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\$1,000 when you sell the car. So this is an example of cash flow.

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The question now is, are these \$350

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equivalent? Are they the same? Since you spend one

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in year one, one in year two, year three and year four, obviously

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it's not going to be the same, because \$350

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today is different from \$350 a year from now, from two years from

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now, and so on.

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So in order to graphically represent the cash flow, because

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once you are able to draw the problem, to draw the cash flow,

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that's basically half of the solution. If you understand

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properly how that cash flow is is disbursed, you can very easily

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solve the problem. The horizontal axis represents a timeline of the

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analysis, marked off in equal increments, whether they are

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months, years, weeks, whatever period equal period, receipts are

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represented by arrows directed upward. So the cash in is going to

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be moving upward. This burden disbursements, or cash out, or

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payments, are represented by arrows directed downward. That's

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the negative. The arrow length is drawn to a scale proportional to

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the magnitude of the cash flow. So it's relatively gone. These arrows

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are going to be relatively drawn to scale. Let's have a let's look

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at an example here. So here's the same example that we just

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discussed about the car that you purchased. You bought it for

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\$4,500 you paid \$4,500 so that's a cash out 4500

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by the end of year one, 350 end of year two, 350

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end of year three, 350 end of year four, 350, and then you sell the

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car for 2000 which means a cash in that's why it's pointing upward of

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\$2,000

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so once we do understand that, we can visualize graphically the cash

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flow of this property.

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So now we're going to start talking about the different

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payments and the impact of time on these payments. Single payments

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may occur either today or at some time in the future, like when you

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bought the car, you paid \$4,500

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that's a single payment, but it was made today, so it has a

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present value of \$4,500

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so P is used to indicate a sum bed or received today at the present,

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whereas the \$2,000 that you received four years from now,

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it's \$2,000 future, because you're going to receive it in the future.

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So it's going to be represented by F, which is used to indicate a

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future sum

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i is used to indicate the interest rate. So if you're going to borrow

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money and you're going to have to pay interest, what's the interest

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rate? The future value of the present sum invested at an

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interest rate I for a period of n years, is represented as the

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future value of the money that you're paying today is equivalent

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to p, which is the present value times one plus i to the power of

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n1,

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plus i to the power of n i here is going to be represented as a

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percentage. So 5% is going to be point o5,

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10% is going to be point one and so on. Therefore, if you got, if

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you're going to invest some money today, let's say \$1,000 today for

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five years at an interest rate of 10%

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we wish so at interest rate of 10% for five years, we want to know,

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what are these \$5,000

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What's this \$1,000 that I'm gonna pay today gonna be worth in five

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years? So F, that's the future value that we don't know about is

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equal to P, which is 1000 times one, plus I point one, the 10% to

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the power of n, which is five years. And that gives us the

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future value based on a known present value today and based on a

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known interest rate and known number of increments or number of

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years. The term one plus i to the power of n, is called Single

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payment compound amount factor, which is used to determine the

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future worth of a present sum of money. So to convert present to

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future, we use one plus i to the power of n.

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The present worth factor

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is actually the opposite of that. I have a future value. I know that

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I'm going to receive \$5,000 in five years. And I want to know

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what's their current value today? What's their present value today?

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So the reciprocal

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which is one over x, so it's one over one plus i to the power of n

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of the single payment compound amount factor is called the single

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payment present worth factor.

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100 it's used to determine the present worth of a future sum of

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money. So to convert present to future, I use one plus i to the

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power of n to convert from mutual to present. I divide by one plus i

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to the power of n.

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So let's look at an example. Here, a contractor plans to purchase a

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pickup truck in five years. He's going to purchase it in five

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years. So the purchase price we need to calculate is the one in

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five years, not today. So it's a future value. How much should he

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invest at a 6% interest rate today to have the \$30,000 needed to

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purchase the truck at the end of five years. Let's start thinking

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about it. Let's start drawing it. What are we looking for? Are we

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looking at for a present value, or are we looking for a future value?

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Which one do we know? What are the knowns in this problem we have? N

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equals five. Which is the five years, we have i, which is equal

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to point, oh, six, the 6%

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and we have a future value, which is the value of that car

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in five years.

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That's \$30,000 so I want to know how much money does that

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contractor have to invest today to get to 330, \$1,000 in five years.

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So the purchase price in this problem is a known future value,

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f, 30,000 and the unknown is the present worth, which is p. In this

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case, P is equal to f over one plus i to the power of n.

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So 30,000 divided by one plus point oh six, which is 106 1.06

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to the power of five. That gives us that the contractor has to

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invest today \$22,417

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that's going to be equivalent to 30,005 years.

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Another example, a contractor bought a 15,000 pump, dollar pump

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with an expected service life of 10 years. So he bought it today

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for 15,000 that's a P its salvage value at the end of 10 years would

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be \$4,000 now at the end of 10 years, which means it's a future

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value. What is the total cost to the contractor for owning the pump

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if the annual interest rate is 8%

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again, here we have a present value. We have a future value. And

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we have n we have I. So we have all the ingredients we need to

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calculate the total cost at the end of

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these 10 years.

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So the purchase price is P, known the salvage value is a future

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value F. We can either calculate all of this cost of ownership

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today, or we can calculate it in 10 years. So we can calculate it

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in terms of p, or we can calculate it in terms of f. Doesn't matter,

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provided that we know what is the point of time, or point in time

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where we are making this calculation. So if we make this on

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the basis of p, is going to be the 15,000 which is the purchase price

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today, minus the future value that you're going to see 10 years from

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now, brought back to today's prices, which is a future value,

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brought back to a present value. So we divide by one plus i to the

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power of n. I is 8% n is 10. So we divide by 1.08 to the power of 10,

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which makes the \$4,000 in 10 years equivalent to 1800 52 today.

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Therefore, the total cost of ownership is going to be the

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15,000 minus 1852 which is 13,001 48 today, we could have solved the

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same problem in future to calculate what's the value at the

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end of the 10 years as well.

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Another example here, or another form of calculation is going to be

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based on a uniform series of payments. So if you're paying for

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something in installments, let's say you bought a car and you pay

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let's say \$500 every month for four years, the \$500 for the first

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month is different from the \$500 for the second month is different

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from the \$500 for the 48th month at the end of the four years. So

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it's sometimes necessary to determine the present worth P, or

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the future value, future worth F, of a uniform series of payments,

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these annuities or this regular amount that you're going to be

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paying every month or every year is called an annuity, uniform

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series of payments or receipts over a certain period of time. In

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other situations, it's necessary to determine the series of equal

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payments or receipts to equal a present value to.

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A future value f. So it's either we're going to convert the P or

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the F into annuities uniform series, or we're going to

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calculate, what are these uniform series of payments equivalent to,

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either today, at the present value or in the future at the future

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value?

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So this uniform series, compound amount factor is used to determine

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the future worth of a series of equal payments or receipts. It's

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represented as one plus i to the power of n minus one divided by I.

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That's the factor

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the uniform series, present worth factor is

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used to determine the present worth of a series of equal

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payments or receipts represented as one plus i to the power of n

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minus one divided by I times one plus i to the power of n. Let's

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look at an example which is going to make these things much easier

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to understand.

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So the uniform series sinking fund factor is used to determine a

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series of equal payments or receipts that's equivalent to a

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required future sum. So if I say, for example, at the end of four

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years, I should have had \$20,000

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how does that translate into annual payments

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and uniform series. Capital recovery factor is used to

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determine a series of equal payments or receipts that's

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equivalent to a present worth some if I pay 20,000 if I have to pay

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\$20,000 today, if the price of that car is \$20,000 a day, if I

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want to make that in four years on four installments, how is that?

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Are these in equal installments gonna amount to

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so let's look at the example here, which going to make things much

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clearer. A contractor is investing \$5,000 per year in saving

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certificates at an interest rate of 6%

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and plans to continue the investment program for six years

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in order to be able to pay the down payment for new equipment.

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What will be the value of the investment at the end of six

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years? What do we have here? We have the contractor paying 5000

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per year. So this is an annuity. This is a repetitive amount. It's

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not just the present value. Today is going to be today, a year from

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now, two years from now, etc. What we want to calculate is F, a

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future value at the end of six years. So what we have is n, is

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six, and we have i is also, in this case, six, which is a 6% so

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based on a which is the annuity 5000

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I, 6%

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n6, what we need to calculate is F, the future value at the end of

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these six years.

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Therefore, here's the equation. The annual investment is an annual

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uniform series, and the unknown is the future worth. Therefore, we

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will use the formula for uniform series, compound amount, factor f

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is equal to A, which is the 5000 times one plus i to the power of n

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minus one divided by i, which is 5000 times 1.06 to the power of

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six minus one divided by point oh six, and that gives f the this

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uniform series of \$5,000 over six years at the interest rate of 6%

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are going to be equivalent to \$34,875

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Another example, let's do the reverse. A contractor has

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purchased a new truck for \$125,000

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and plans to use it for six years. After six years of use, the

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expected salvage value will be \$30,000

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what is the annual cost, or any annual uniform series for the

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truck at an interest rate of 10% so here we're gonna use P, F and

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A,

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P is under 25,000 that's down a down arrow of under \$25,000

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which is cash out. N

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is six years.

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I The interest rate is 10% and then we have a future value, which

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is a salvage value at the end of these six years of \$30,000 so what

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are these equivalent to? In annual increments, equal annual

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increments.

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So in this problem, the purchase price or the present value is

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known as well as the salvage value or future value. The unknown is a

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series of equal annual payments. So we're going to convert the

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present value into annuities by using the equation, and we're

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going to convert the future value into annuities also by using the

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equation. But these are going to have two different signs, because.

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Us, this is negative and this is positive, or this is positive and

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this is negative because they point into do two different

00:20:07 --> 00:20:09

directions. So

00:20:10 --> 00:20:14

that amounted to 150,000 times point two, three, which is all of

00:20:14 --> 00:20:19

this stuff here, minus 30,000 times point divided by point o3,

00:20:19 --> 00:20:23

which point one three, which is this amount here, which makes the

00:20:23 --> 00:20:29

annual payment to account for all of this transaction of \$24,850

00:20:36 --> 00:20:41

okay, now we're gonna look at alternative analysis when two or

00:20:41 --> 00:20:45

more alternatives are capable of performing the same function, the

00:20:45 --> 00:20:49

economically superior alternative will be the one with the least

00:20:49 --> 00:20:55

present worth cost. So if I pay for this equipment

00:20:56 --> 00:21:02

in cash today, or if I pay for it in installments over five years or

00:21:02 --> 00:21:08

six years or whatever. Let me make the comparison at the same point.

00:21:08 --> 00:21:13

Either convert both of them into annuities or convert both of them

00:21:13 --> 00:21:16

to a present value. And that would be the better way so that I

00:21:16 --> 00:21:21

compare present to present today, the option that's going to be more

00:21:21 --> 00:21:25

financially appealing and feasible is going to be the one that has

00:21:25 --> 00:21:29

the lower present value. So the present worth comparison, however,

00:21:29 --> 00:21:33

should be used only for assets with the same lifespan. I cannot

00:21:33 --> 00:21:36

now compare two pieces of equipment, one that's going to

00:21:36 --> 00:21:39

serve me for five years and another is going to serve me for

00:21:39 --> 00:21:43

seven years or eight years. It has to have the same end number of

00:21:43 --> 00:21:49

years or lifespan. For assets with different lifespans, annual cost

00:21:49 --> 00:21:53

method of comparison should be used so it's going to be based on

00:21:53 --> 00:21:56

annuities. How much is it going to cost per year? The annual cost

00:21:56 --> 00:22:00

method assumes that the asset will be replaced by an identical

00:22:00 --> 00:22:04

replacement at the end of the useful life. And this is basically

00:22:04 --> 00:22:07

the concept, when we talked about the tax breaks and so on for the

00:22:07 --> 00:22:11

construction equipment and depreciation, this is basically

00:22:11 --> 00:22:16

the concept, why do we depreciate the equipment, basically to have

00:22:16 --> 00:22:19

some savings that enable us, at the end of the service life of the

00:22:19 --> 00:22:20

equipment, to replace it.

00:22:24 --> 00:22:27

So the first step to compare alternatives is to construct the

00:22:27 --> 00:22:31

cash flow diagram for each a common basis for comparison is

00:22:31 --> 00:22:34

selected, whether it's going to be present value, future value or

00:22:34 --> 00:22:39

annuity, and an equivalent sum of uniform annual series is

00:22:39 --> 00:22:43

determined for each. Then the alternatives are compared to

00:22:43 --> 00:22:45

select the one that is most favorable.

00:22:47 --> 00:22:51

The contractors usually use the minimum attractive rate of return

00:22:51 --> 00:22:56

to perform cash flow analysis, which means, if I had invested

00:22:56 --> 00:23:01

this money in another enterprise, it would have given me a return on

00:23:01 --> 00:23:06

investment. What would be the minimum acceptable return on

00:23:06 --> 00:23:12

investment, or interest rate that I would accept to use that money

00:23:12 --> 00:23:16

for this to buy this equipment. So for example, if I invested this

00:23:16 --> 00:23:20

money in the stock market, it would have given me a 6%

00:23:22 --> 00:23:23

return on investment,

00:23:24 --> 00:23:28

I should not buy equipment that's going to give me a return on

00:23:28 --> 00:23:32

investment of only 5% it's going to be more profitable to invest in

00:23:32 --> 00:23:35

the stock market, but if buying that equipment is going to get me

00:23:35 --> 00:23:39

a return on investment of 7% now it's more profitable than

00:23:39 --> 00:23:43

investing in the stock market, and that can make me make my decision

00:23:44 --> 00:23:47

is used as the effective interest rate in cash flow analysis.

00:23:48 --> 00:23:53

So again, examples make things much easier to understand. A

00:23:53 --> 00:23:56

contractor is considering the purchase of a used tractor

00:23:56 --> 00:23:57

\$480,000

00:23:58 --> 00:24:02

that could be used for 10 years n is 10 years, and then sold for an

00:24:02 --> 00:24:06

estimated salvage value of \$10,000 so f is 10,000

00:24:07 --> 00:24:11

annual maintenance and repair costs are estimated at 15,000 per

00:24:11 --> 00:24:13

year. So this is an annuity, a

00:24:14 --> 00:24:18

and an alternative. So this is the first part to be considered. The

00:24:18 --> 00:24:23

alternative is the contractor could lease a similar tractor for

00:24:23 --> 00:24:27

\$4,000 a month. With the lease, he doesn't have to pay a high

00:24:27 --> 00:24:30

purchase price at the beginning. He's not going to have a salvage

00:24:30 --> 00:24:36

value at the end. And we know that the annuity that's going to be pet

00:24:36 --> 00:24:40

per month is fixed. Annual operating cost is the same for

00:24:40 --> 00:24:45

both alternatives, fuels, filters, lubricants, etc, is going to be

00:24:45 --> 00:24:48

the same. So we're going to disregard it in both cases, the

00:24:48 --> 00:24:53

minimum attractive rate of return is 12% which option should the

00:24:53 --> 00:24:58

contractor select? So what we have to do here is to draw two

00:24:58 --> 00:24:59

different cash flows and come.

00:25:00 --> 00:25:05

Pair these two and then calculate the present worth or the annuity

00:25:05 --> 00:25:09

or the future value for both of them, and look at which one is

00:25:09 --> 00:25:10

going to be more appealing.

00:25:11 --> 00:25:13

So for the first option,

00:25:16 --> 00:25:16

we're going to pay \$180,000

00:25:18 --> 00:25:19

at the beginning.

00:25:20 --> 00:25:24

We're gonna receive \$10,000 at the end salvage value, and then in the

00:25:24 --> 00:25:29

interim, for 10 years, we're gonna be paying \$15,000 per year in

00:25:30 --> 00:25:35

maintenance or whatever. Since the monthly rental rate is known,

00:25:35 --> 00:25:35

\$4,000

00:25:36 --> 00:25:40

we will compare the alternative on an annual cost basis. So the

00:25:40 --> 00:25:44

annual cost for the rental alternative. Now remember that

00:25:44 --> 00:25:47

this is monthly, and the other one here, this is annual, so we have

00:25:47 --> 00:25:48

to bring it to the same

00:25:49 --> 00:25:53

increment. So we're going to assume, for simplicity, that

00:25:53 --> 00:25:59

\$4,000 times 12, which is going to be the 40,040 \$8,000 this is what

00:25:59 --> 00:26:03

you have to pay as an annuity to be compared to this 15 and the

00:26:03 --> 00:26:07

eight, 180 and the 10. So for the purchase alternative, the cash

00:26:07 --> 00:26:09

flow will look like that, 180,015

00:26:10 --> 00:26:14

1515, until the 10th year, and then you receive 10,000 back.

00:26:16 --> 00:26:20

So for the purchase option, the annual costs can be determined

00:26:20 --> 00:26:22

using the formula, we have an interest rate

00:26:24 --> 00:26:28

of 12% for 10 years. So

00:26:30 --> 00:26:35

the purchase price, which is a P times the formula to convert it to

00:26:35 --> 00:26:39

a plus the A's the 15,000

00:26:40 --> 00:26:45

per year, minus the 10,000 which is the future value, converting it

00:26:45 --> 00:26:49

into annuities, which is going to amount to \$46,290

00:26:52 --> 00:26:57

per year. So this is cost of ownership. Okay, we have just

00:26:57 --> 00:27:01

mentioned that the cost of lease or rental is going to be \$48,000

00:27:02 --> 00:27:07

per year. So we are comparing 48,000 for the lease option to 46

00:27:08 --> 00:27:12

290 for the ownership option. Obviously this is less expensive,

00:27:13 --> 00:27:16

therefore owning the equipment is going to be more economical than

00:27:16 --> 00:27:18

renting it or leasing it.

00:27:21 --> 00:27:24

Now this is a summary of all the equations that we've discussed.

00:27:25 --> 00:27:28

The single payment compound, the single payment present worth etc.

00:27:28 --> 00:27:31

So to convert from P to f,

00:27:32 --> 00:27:34

this is the form that we use.

00:27:35 --> 00:27:40

So f is equal to P times one point plus i to the power of n. To do

00:27:40 --> 00:27:44

the opposite, to convert an F to A p. So what we know is F and we

00:27:44 --> 00:27:52

want to get p. So p is equal to f times one plus r1, divided by one

00:27:52 --> 00:27:56

plus i to the power of n to convert F to A. This is the

00:27:56 --> 00:28:02

equation to convert P to a, to convert A to F and to convert a to

00:28:02 --> 00:28:06

p. Now I'm not going to ask you to memorize all of these equations,

00:28:06 --> 00:28:11

so on the test, I'm going to allow you to have a simple note card

00:28:11 --> 00:28:15

with these equations so that you don't have to memorize them.

00:28:19 --> 00:28:23

Contractors often want to estimate the prospective rate of return of

00:28:23 --> 00:28:27

an investment, or compare anticipated rate of return for

00:28:27 --> 00:28:31

several alternative investments, just as we did, is it better to

00:28:31 --> 00:28:34

buy the equipment? Is it better to lease the equipment? Is it better

00:28:34 --> 00:28:38

to invest in this project or another project, or just the stock

00:28:38 --> 00:28:42

market? So we're going to look at different rates of return. The

00:28:42 --> 00:28:46

rate of return is an annual interest rate at which the sum of

00:28:46 --> 00:28:49

investment and expenditure equal the total income from the

00:28:49 --> 00:28:54

investment. It involves setting receivables equal to expenditures

00:28:54 --> 00:28:56

and solving for the interest rate. In

00:28:57 --> 00:29:00

many cases, the interest rate can be obtained from a trial and error

00:29:00 --> 00:29:04

method of solution. So two or more interest rates are assumed,

00:29:05 --> 00:29:10

equivalent present worth or annual costs are calculated, and the rate

00:29:10 --> 00:29:13

of return is found by interpolation. Let's look at an

00:29:13 --> 00:29:16

example, which, again, is going to make things much easier.

00:29:17 --> 00:29:19

So a contractor plans to invest \$300,000

00:29:20 --> 00:29:24

in used construction equipment, the estimated annual maintenance

00:29:25 --> 00:29:30

and repair cost. Now the first one is a present value. Here we have

00:29:30 --> 00:29:33

annual maintenance and repair cost annuity, \$60,000

00:29:34 --> 00:29:39

expected annual income, also an annuity. 115,000

00:29:40 --> 00:29:44

the expected profitable service life of the equipment is eight

00:29:44 --> 00:29:48

years. So n is eight years. What is the prospective rate of return

00:29:48 --> 00:29:52

on these investment? What is i? So what we're looking for here in

00:29:52 --> 00:29:54

this equation is I,

00:29:57 --> 00:29:59

let's draw the cash flow again. So.

00:30:00 --> 00:30:03

We have a present value that we're gonna spend of 300,000

00:30:05 --> 00:30:09

and then we're gonna spend each year \$60,000 in operating cost in

00:30:09 --> 00:30:12

return. We're gonna have a return on investment of \$115,000

00:30:14 --> 00:30:18

every year in return. So the problem can be solved based on the

00:30:18 --> 00:30:21

present worth P, or the annual cost a.

00:30:23 --> 00:30:26

The annual cost formula can be abbreviated as now based on the

00:30:26 --> 00:30:31

table that we have looked at A and P and I and N. So to get the A

00:30:32 --> 00:30:33

based on the p1,

00:30:35 --> 00:30:37

00:30:38 --> 00:30:40

is equal to P,

00:30:41 --> 00:30:43

is equal to another A, which is

00:30:45 --> 00:30:50

the 60,000 in the other other direction, plus converting the P

00:30:50 --> 00:30:52

into annuities.

00:30:53 --> 00:30:58

So basically we're gonna put this on the other side. So here we have

00:30:59 --> 00:30:59

55,000

00:31:01 --> 00:31:02

is equal to 300,000

00:31:04 --> 00:31:09

and then the equation of converting a p into an A, the only

00:31:09 --> 00:31:10

unknown is the i,

00:31:12 --> 00:31:17

which is going to give us point 183, solution of this equation is

00:31:17 --> 00:31:18

going to give us point 183,

00:31:19 --> 00:31:24

through trial and error and using interest tables, we can start with

00:31:24 --> 00:31:26

9% which gives point what a 181

00:31:27 --> 00:31:32

trying 10% gives point 197, these tables, by the way, you can find

00:31:32 --> 00:31:33

them in any

00:31:34 --> 00:31:41

economics book, or you can find them Online, even so, the 9% gives

00:31:41 --> 00:31:45

point 181, the 10% gives point 197, what we're looking for is

00:31:45 --> 00:31:46

1.183

00:31:47 --> 00:31:51

which is closer to the 9% so by interpolation, we're going to find

00:31:51 --> 00:31:54

that the rate of return is 9.3%

00:31:55 --> 00:31:57

which is somewhere between the nine and

00:31:59 --> 00:32:05

10. That's basically our lecture on construction economics. We

00:32:05 --> 00:32:09

learned in this lecture about how to convert a present value into a

00:32:09 --> 00:32:12

future value, how to convert the future into present, how to

00:32:12 --> 00:32:16

convert either a present or a future into annuities, and how to

00:32:16 --> 00:32:20

have combinations, if the problem includes present value annuities

00:32:20 --> 00:32:23

and future value at the same time, how to bring it into single terms,

00:32:23 --> 00:32:28

whether it's converting everything to future or present or annuities

00:32:28 --> 00:32:33

and then calculating for the rate of return. I'll see you next time

00:32:33 --> 00:32:34

in another lecture you.

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