The final course of the specialization expands the knowledge of a construction project manager to include an understanding of economics and the mathematics of money, an essential component of every construction project. Topics covered include the time value of money, the definition and calculation of the types of interest rates, and the importance of Cash Flow Diagrams.
Mathematics of Money - Project Evaluation
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来自 Columbia University 的课程
Construction Finance
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从本节课中
The Mathematics of Money
Professor Ibrahim Odeh discusses the Mathematics of Money beginning with a definition of the Time Value of Money. Calculating simple and compound interest rates are covered along with distinguishing between nominal and effective interest rates. Illustrated in this module is drawing a cash flow diagram.
与讲师见面
Ibrahim Odeh, Ph.D., MBAInstructor, Department of Civil Engineering and Engineering Mechanics, Columbia University
Director of Research and Founder, Global Leaders in Construction Management
Hello everyone.
We will be talking about today module about the mathematics of money, or
what we refer to from time to time,
as the time value of money, which is both are really just the same.
And we will be covering in our course the construction,
industry point of view, not any other industry from the mathematics of money,
because these are basics and the foundations that you can build
in any kind of investment or engineering field or discipline.
So basically construction firms acquire funds as any other individual as you or
as a family business or any kind of self contracted and so on.
And they acquire this money by borrowing it from banks or
and similar lending sources such as financial institutions.
The costs of money and the time during which that money
is tied up in any business decision processes,
are a crucial or it is crucial financial management factor.
So, these are some of
the questions we are going to help you address,
when it comes to the financial management for the time value of money.
So the number one here, the question is, is any individual project worthwhile?
I have a project and I want to understand if it is feasible to invest in and
move forward to put my money in it or
to borrow some money to invest in it or build it as a construction manager.
Another question, which refer to the second point here,
that we can address on this topic given a list of a feasible
project that you have in hand, and from these feasible projects,
you want to identify which one is the best project that I want
to move forward to invest my money in or to borrow money to execute that project.
So, from a single project to choose if it's worthwhile, to move forward or not.
Second, you have a list of projects and
you want to choose which one you want to select.
And last but not least, also, if we have a list of projects to invest in.
The same list, let's say.
And you want to prioritize the list, or you want to say like,
how does each project rank compared to the others from your list?
In this case, you can have more financial management decisions to tell
which project you want to move forward in it and which you don't want to or
you want to keep for later if you have the opportunity.
So what we are doing here is actually a project, evaluation
of our investments and the use of our money or someone else's money.
Some examples we can relate to our industry in specific are the following for
example If we say, let's say we want to purchase a truck,
a construction truck, with the discount right now.
Discount on the price of the truck, or the cost of the truck.
But we pay more interest rate on the truck.
This is one option.
Discount with more interest, or by the same truck with no discount.
So zero discount is going to be the same cost of the truck, but
you want to have more interest on it.
So less interest and discount, no discount more interest.
So, this kind of.
Example you might face.
One.
Another example would be the following: should my company
continue leasing the building or I can say,
I want to have the building for my use for a good number of years.
Maybe its worth to build a building or build a property
that I will host my head offices or my offices in it.
This is another example.
Last but not least, they say should my company rent or
purchase a certain piece of equipment to use in certain project or
cities of projects that coming.
Again, what we are doing here is actually
a project evaluation method of our investments or
anything else related to how to use our money or someone else's money.
From our course point of view, this course, we will focus,
as I mentioned earlier, on the construction industry.
So what kind of examples with now numbers we have in mind when it comes for
evaluation to advance more and
link it more to our industry is the following: let's say we have
a project that requires an investment of one thousand dollars today and
returns 1,100 dollars in one year from now.
Does it up, does it pay to make such investment or not.
Also [INAUDIBLE] I have a house project A and housing project B.
On both [INAUDIBLE] have a construction period
of around eight months For Housing Project B, the construction
period is let's say double the duration or the time to built it.
Let's say the cost per month might be the same
$12,000 per month for A and B.
The sale value for Project A is $160,000 and for B $300,000.
What's the total cost?
What's the profit for each one?
Which one we want to proceed?
So this kind of project evaluations.
Are the examples that we want to deal with for
the coming several modules a weeks in this course.
Moreover these are the type of examples we need to know
how to answer because the fundamentals mathematics of money.
In the coming modules will be able to help us address these questions,
as well as these project evaluation opportunities.
So let's get start.
Before I go into details, I want to re emphasize
again that when we use the term time value of money.
It is the same as the mathematics of money
which is a topic that will help us to do better in project evaluation.
So the main definition that I'd like to share with you,
about the time value of money and you will find in the literature there are tons
of definitions the definition that I found that is
much more relevant to our industry is the following: it is the payment of
interest over time for use of someone else's money.
So this is the basic definition.
The basic concept of this definition is that a dollar or any currency,
a dollar received tomorrow is not equivalent to a dollar received today.
The nominal quantity is the same.
$100 now is the same as $100 a year from now from a nominal quantity point of view,
but the dollar does not have the same usefulness or buying or purchasing power.
So that's something we need to put into consideration.
Because of this valuable [INAUDIBLE], we cannot estimate benefits or
costs simply by adding dollar amounts that are realized in different periods.
With that being said, let's then advance on our presentation to speak
about interests and interest rates, and what's the definition between both.
So by definition, the interest, the first one, not the interest.
Rate is the fee that a lender charges for the use of their money.
And it is directly proportionate to two things.
One, the amount borrowed.
Or loan.
For example the interest on $2000 is as twice
as high as the interest on $1000 when all factors are the same.
Second it's also proportionate to, directly proportionate,
to the time, the time that the money borrowed or loaned.
For example, interest is higher for a three year loan, than a one year loan.
Having the loan the same amount and all the factors the same.
On the other hand, the interest rate Is different than the interest.
The interest rate is the money that one dollar earns for
each unit of time that it is loaned.
And it is expressed in percentage.
[INAUDIBLE] To simplify it for you for not using just words and using numbers.
For example, if $20 earns, just write it quickly here.
If we have $20, and this $20
earns $2.4 over a year.
Then the interest rate will be the 2.4 over the $20,
which will be equal around .12 or
equal to the 12%.
In this case, the interest
would be the The 2.4 and
the interest rate would be the 12%.
The 2.4 over the principle,
which is the $20 that it will start investment with.
