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.
Changing and Comparing Compounding Periods
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來自 Columbia University 的課程
Construction Finance
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從本節課中
Real Estate Finance for Development Projects
Professor Anthony Webster introduces real estate finance providing an overview of the real estate project lifecycle, a discussion on zoning code parameters, and examples of estimating the sales price of a property.
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Ibrahim Odeh, Ph.D., MBAInstructor, Department of Civil Engineering and Engineering Mechanics, Columbia University
Director of Research and Founder, Global Leaders in Construction Management
All right, one last thing we've got to look over before we can jump back into
doing financial plans for development projects from a developer's perspective.
That's to review a little bit what you've learned with Professor Korda on
compounding periods, and to expand on that a little bit, okay?
So far, everything that we have done in this module and
in the previous module is to use annual compounding.
So, our percent interest per year, and T was always a real number.
It didn't have to be an integer, but we always measure time in years.
Now we need to be, and in the real world we need to be much more flexible.
We need to consider quarterly, monthly, daily compounding,
any of biweekly compounding, semiannual compounding.
The great news as you learned from Professor Odette is
that everything we have done regarding time value and
everything you did with Professor Odette can be generalized to longer or
shorter compounding periods by simply changing time units.
You'll see what I mean by that,
so we want to make this change consistently and
that means r and T, okay?
So, for example, if we have quarterly compounding periods,
we're going to say r% interest, compounded quarterly.
That means r% is paid every quarter, and
we're also going to say if we're in a quarterly compounding world,
T = 0 will still mean now as usual, but
T = 1 will mean one compounding period from now.
Something like one quarter from now, okay?
If we're in a quarterly compound world.
So, let's do an example, let's consider a three quarter mortgage.
Okay, so it's going to be a really short payback mortgage that happens
in three quarters.
Out there in the big bad world, BigShark Lenders offers Mr.
Small-Net-Worth this mortgage loan, okay?
They'll loan him $30,000 to help him buy a $50,000 shack today.
So that means Mr.
Small-Net-Worth is going to have to, of course, pay 20,000 of his own money.
He would be what we will call the equity or
the property manager in this property even though it says on property.
And here's the deal Mr. Small-Net-Worth would have to agree to pay BigShark back.
He's going to get this 30,000.
He has to pay back in Three equal quarterly payments
with 10% interest compounded quarterly.
How much?
We want to know for Mr. Small-Net-Worth, how much is each payment.
So let's go ahead and check this out.
What's the situation here?
We have this $30,000, he's going to get
10% compounded quarterly.
So this PV total is going to equal 30 Okay,
that's going to be equal to his Payment 1 discounted by one quarter
and this is two quarters here and this is three Q is here.
So, the first payment going to Payment 1 discounted back and
1 time period with r measured in.
Where we compounding.
Okay, same thing for the second payment and
its going to be discounted back by what two quarters now.
So that's why we have two in the exponent and we got to remember we have
quarterly compounding in our similarly for payment three.
So we want to know that we said by definition.
All these payments are equal.
Okay.
So we can simplify a little bit.
We can pull payment out.
Okay.
And this is still equal to 30K.
All right.
So I've just done a little bit of algebra.
On this line to simplify.
And now I've done some more algebra
down here to isolate that uniform payment he's going to have to make.
And if you do the algebra on that,
you find he has to pay Pay $12,060 per quarter.
All we had to do to do this, exactly the same as everything we've done annually,
except we've consistently changed all our units to quarters.
So r is interest per quarter compounded quarterly and
T is Measured in quarters and that's it.
It's really that simple.
All right, so in general, you're going to find in the real big,
bad world of finance Generally, real estate financing particular,
projects will be done in monthly time periods, quarterly time periods,
semi annual time periods, sometimes bi-annual periods, and
to understand one project compared to another.
We wanted to put everything in annual compounding periods.
It just makes it easier for us to understand and
it's necessary to compare different projects.
So the way we do that is with what's called the equivalent annual
interest rate.
What is the equivalent annual interest rate?
Define to me The amount of interest generated in a year
by a pile of money, irrespective of compounding period, okay?
So here's how it goes.
The EAIR, that's the amount of interest Generated in a year, okay?
Is going to be 1 + r,
where this is going to be monthly,
Quarterly or etc, okay?
So that's called our native r.
r, (1 + r), native r.
Monthly compounding, quarterly compounding, semiannual compounding,
raised to the number of compounding periods per year minus 1.
Why do we do this, again?
We use EAIR to make these apples-to-apples comparisons of
interest rate projects with different compounding periods.
Okay, so let's see, let's go on a little farther, and
see how Know exactly this works.
Let's do two examples.
First one is let's say what's the equivalent annual interest rate of
Bigshark's offer to Mr. Small Net Worth that three quarter mortgage?
Remember was 10% compounded quarterly.
So if we're thinking about it as most people do in annual Terms,
let's see what the equivalent annual interest rate is.
So all we do is apply the formula.
Okay.
So we have for Mr.
Small-Net-Worth the offer on the table is 10% compound ad quarterly.
Okay.
And plugging in the formula four compounding periods four quarters per
year so, we have (1+ 01.1) raised to the 4- 1 = a whopping 46%.
Actually, this in the United States is considered usurious.
And is an illegally high rate, okay?
So by comparison, a more normal and
legal, in the United States, lender might have offered Mr.
Small Or something like this, 10% compounded annually.
What's the equivalent annual interest rate of that?
Well, it's of course (1 + 0.1) raised to the 1.
One yearly compounding period in the year.
This one equals 10%, okay?
So this is a good way to understand what
interest rates are in a time frame that we're all used to.
And it's very good and very necessary to compare projects Under some
circumstances,here is another example where we see how its necessary to compare
projects,so lets say you considering to lend some money in money market and
you have two banks,Bank 1 says will give you 5% compounded annually,Bank
2 says will give you 0.375% per compounded
monthly,which one is better,all we have to convert everything.
To annual too, so we can do apples to apples.
So for Bank 1, the equivalent annual interest rate,
it's already in annual compounding terms, that's 5%.
For Bank 2, we just apply the formula, 1 + r raised to the number of compounding
periods per year, 12 in the case of monthly compounding,- 1 = 4.6%.
So Bank 1 is clearly offering a better deal, but
we have no way of knowing that until we put everything in annual terms.
