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Class 19 Sections 10 1 - 10 2 — Transcript

by vic zaloom · 2,937 words · 544 segments · language en · Watch on YouTube

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0:02hello
0:03and uh welcome to uh today's class
0:07uh which will cover sections 10.1
0:10and 10.2 uh which deals with
0:13inflation um and
0:17i'll go through you know the usual
0:19routine
0:20first you should start on the start here
0:22page on blackboard and
0:24and check out the assignments and
0:27because they do change from time to time
0:30and you should read pages 302 to 312 in
0:34your text that sec
0:35that covers these two sections um
0:40you will be watching this instructor
0:43video
0:44these lecture notes are critical to your
0:48success in the course
0:49and if you really want to be
0:52highly successful you need to work as
0:54many problems as you possibly can
0:57so we're going to talk about inflation
0:59now
1:00and
1:04how it impacts um the cost
1:08and and the the revenues and things like
1:11that which we deal with
1:14one of the most common well inflation
1:16refers to just
1:17simply the increase in cost
1:20over time to purchase goods and services
1:24um as an example
1:28of a service um if you bought an airline
1:32ticket and there
1:33and uh um the uh
1:38then you know a year later you bought
1:41that same
1:43uh type of ticket you're going to fly on
1:45the same
1:46type of aircraft you're going to fly the
1:48same route
1:50and it cost more well that would be
1:53an example of inflation in the cost of
1:56that
1:57service air travel
2:01if prices go down which they are
2:04with respect to air travel because of
2:06the pandemic
2:08then um that would be called deflection
2:13and and we're experiencing that for
2:15example with gas at the pump it's
2:17it's actually less now than it was maybe
2:2010 12 years ago
2:21so that's an example of deflation we
2:24rarely get deflation and it usually
2:26means something bad
2:28in this case it needs a pandemic is
2:30causing a decrease in the
2:33amount of oil
2:36needed to make the gasoline
2:39but inflation refers to the increase in
2:42cost
2:44of goods and services and that is a very
2:47common thing
2:49much more common than deflation
2:52a common measure of inflation is called
2:55the consumer price
2:57index actually it's a measure of
2:58inflation or deflation
3:01and the consumer price index
3:04is a is a measurement kept by the the
3:07federal government the bureau of
3:09statistics uh economic statistics and
3:13they
3:14publish a new number every month and so
3:17there's a yearly inflation
3:19rate and a monthly inflation rate and
3:23the consumer price index basically
3:26consists of a number of
3:30commonly used goods and services
3:34as an example food energy transportation
3:38health care
3:39and housing are all part of the consumer
3:42price index
3:43and what they look at is what is a an
3:46american
3:47family usually buy and then has that
3:50gone
3:51up in the last month uh if we take a
3:53weighted average of those things
3:56and and so equation 10.1
3:59tells us that the the dollars in period
4:03t1
4:04equals the dollars in period t2 now this
4:07is where t2 is in the future from t1
4:11times 1 plus the inflation from
4:14t1 to t2 from time 1 to time 2.
4:18so um i'm sorry it's not times it's
4:23divided by
4:25there's a slash there okay divided by
4:281 plus the inflation now this does not
4:31say the inflation rate this is the
4:34entire amount of inflation from time 1
4:36to time
4:372. and we're taking the dollars in
4:40period 2
4:41and basically dividing by 1 plus the
4:44inflation rate between those periods
4:46gives us the the dollars
4:49at time 1. so we can use this equation
4:53for example we could multiply through
4:55this equation
4:56through the the the thing we're dividing
4:59by 1 plus the inflation
5:01if we multiply through the equation we
5:03can put the
5:05dollars at time 2 in terms of the
5:08dollars at time
5:09one um and um
5:12in this case we're kind of deflating the
5:14dollars at time
5:16two because we're dividing by this if we
5:19were to multiply through by one plus the
5:21inflation
5:22and and um get
5:25t2 in terms of t1 then we
5:28we would be inflating from t1 to t2
5:33um the term
5:37constant value dollars refers to
5:40um what the dollars are worth
5:44now what they could buy now um
5:47as opposed to what they what
5:50what it'll cost say in the future to do
5:54something like that so equation 10.2
5:57says constant value dollars
5:59equals future dollars divided by 1
6:02plus the inflation rate little f
6:05is the is a term that's analogous to the
6:09i that we've been using for interest
6:11rate
6:12it's analogous to that it's a rate and
6:15we
6:15we divide the future dollars by one plus
6:19uh the inflation rate to the
6:21nth power if there are n periods between
6:25the the the current time and the future
6:28time
6:30okay so this is just kind of another
6:33statement of this
6:35but it does it by period because f
6:38is a rate as opposed to a total amount
6:41of inflation
6:44if we solve equation 10
6:472 for future dollars we simply multiply
6:51through by 1 plus
6:52f to the n we get future dollars
6:55equals the constant value dollars times
6:581
6:58plus f to the nth power so in this
7:02case we're inflating the constant value
7:04dollars
7:05to get them out to the future this works
7:08just like
7:08f given p and p given f uh but
7:11now it's not the interest that's being
7:16that's causing the value to increase
7:18it's the inflation rate
7:20um so i have a lot of experience with
7:25this in
7:25in the aircraft industry and in the
7:29design of an airplane
7:31there may be a long period of time
7:33between
7:34the the time when you're designing the
7:37airplane and you're doing production
7:39cost estimates and when the actual
7:42airplane is going to be produced because
7:44with aircraft especially
7:48advanced aircraft if we want to call
7:50them that
7:52there's usually after the design phase
7:55there's you build a prototype you test
7:59the prototype
8:00build several of them actually so you
8:03build several airplanes you test the
8:05prototype
8:08with test pilots and they give you
8:11feedback
8:12you redesign and so on so there could be
8:15what i'm saying here is there could be
8:17as many as 10 or more years between the
8:19early designs
8:21and the final
8:24start of the production of the airplane
8:27as a
8:28as a unit so during that period of time
8:32inflation is occurring and very often
8:35then
8:36what you estimated the production cost
8:38would be has to be inflated
8:41then um up to get the true cost
8:45when the aircraft is actually going to
8:47go
8:48into production uh maybe 10 or 12 years
8:51later
8:52so this is what what we did we we
8:55basically used this
8:57uh this equation 10.3 to
9:00inflate what it would cost now to build
9:02that airplane which would be called
9:04constant value dollars
9:07times one plus the inflation rate
9:09actually we
9:11we didn't just use for example the
9:12consumer price index for the inflation
9:15rate
9:15we broke the airplane down into into
9:18major
9:18subsystems and and each of those had a
9:21different
9:22inflation rate and so we would apply
9:24that to the subsystems and then
9:26i add it all up but the bottom line is
9:28we were using this
9:30all the time because of the lar long
9:33time
9:33frame of our projects
9:36um so um
9:39[Music]
9:41i want to get into some some definitions
9:44so we call
9:45constant value dollars uninflated
9:48dollars
9:49if we want to inflate them one with the
9:52inflation rate
9:53f for n periods then that gives us
9:56future dollars and um if you recall
10:01the uh the
10:04rate i that we've been using throughout
10:07the semester we really didn't talk about
10:09inflation until this chapter
10:11actually we're not going to talk about
10:12it again after this chapter but
10:15um we used uh the real
10:18rate or the inflation-free interest rate
10:22i so that i that we've been using
10:26um theoretically is the inflation-free
10:30interest rate well there's another rate
10:33that we call the adjusted rate
10:36inflation adjusted rate which is i
10:40sub f so the i sub f
10:44includes inflation and this
10:48is also called the market rate that's
10:51the most common term
10:52to use this affliction adjusted rate
10:55market rate
10:56is i sub f okay
11:00and that rate includes
11:03both the increase in price due to
11:06inflation
11:07plus the increase due to
11:10time and the interest rate i so um
11:14we'll we'll talk about that relationship
11:18here and some other equations but
11:20um the next chapter
11:24the author actually defines the market
11:27rate
11:28i sub f equals to
11:31i that's the real rate
11:34real interest rate plus f the inflation
11:38rate
11:38plus the product of those two i times f
11:42so equation 10.4
11:45in section 10.2
11:48which tells us how to adjust our
11:51calculations
11:52to account for inflation if we have some
11:55future dollars then
11:58we need to divide that by one plus
12:01f to the nth power that
12:05takes out the inflation so then i'll
12:08have constant value
12:10dollars here and then i divide that by 1
12:12plus
12:13i to the n which takes out the time
12:16value of money and so
12:19if we multiply these two quantities
12:22together
12:23we get this should be a
12:27capital f here
12:32we get f times 1
12:36plus i plus f plus i f all i've done is
12:39multiply
12:40to the nth power and um
12:43so that is equation 10.4
12:47and then um uh so
12:50by dividing by 1 plus f to the n
12:54that adjusts for inflation then you're
12:56dividing by 1 plus i to the n
12:59and that adjusts for the real interest
13:01rate and
13:02um we call the quantity
13:05that is i plus f plus i f we call that
13:08the market rate
13:09and um if we take 1 plus
13:12i sub r i sub r i'm sorry
13:16i sub f recall is the inflation rate i'm
13:20sorry the market rate
13:21uh and that's equal to one plus i
13:25times one plus f which is one plus
13:28i plus f plus i f and if we subtract one
13:31from both sides
13:33we get equation six that is the market
13:36rate
13:36i sub f equals the interest rate the
13:40real rate
13:42plus the inflation rate plus the product
13:45of the interest rate
13:46and the inflation rate and then if we
13:49substitute
13:50equation 6 into equation 4 here you can
13:54see that what we're going to get there
13:56we get that p is equal to capital f
13:59times 1 plus
14:00i sub r to the n i'm sorry divided by 1
14:04plus
14:04i to the i sub f to the
14:08n which is the same thing as
14:11f p given f i sub f
14:15and n okay so that's equation
14:18five uh we kind of went backwards there
14:21but
14:21but i needed this equation to plug into
14:24this
14:25to get me to this um
14:28and then there's a an example of if the
14:32real interest rate i is six percent
14:35and the inflation rate f is four percent
14:39then the market or inflation adjusted
14:42rate i sub f is six percent
14:47plus four percent plus the product which
14:49would give me
14:50you know this is going to be 0.0024
14:53which would give me 10.24 percent
14:57so we're going to do an example of
15:00looking at what would happen to
15:03a lottery winner who has three
15:07options on collecting your money that
15:10would be nice to be a lottery winner i
15:12suppose
15:13um although i don't think many of them
15:15have been
15:16more happy after they get it anyway
15:20um here's the situation
15:23um the the
15:26the lottery the lottery winner can take
15:29their winnings in one of three ways and
15:33he says f is equal to the inflation
15:35rates four percent
15:36and the interest rate is six percent so
15:38that's a uh that will give us
15:40a a market rate which is the product of
15:44these
15:44two plus each one uh is going to be
15:4810.24 percent so
15:50you can either take these are your
15:52options three options
15:54uh the red option is to take a hundred
15:57thousand right now
15:58the blue option number two is to take
16:01eight payments of fifteen thousand
16:03that's
16:04uh each uh starting one year from now
16:07well that's
16:08just an a series right uh of fifteen
16:11thousand dollars for
16:12eight years and then there's a third
16:14option this is the green
16:16option which is forty five thousand now
16:19forty five thousand
16:20after four years and another forty five
16:23thousand
16:23after eight years so let's look at what
16:27is the present value of each of those
16:30using the market rate which is ten point
16:32two four percent
16:34which we we found that on the previous
16:36page
16:38well the present value of this one is
16:41just a hundred thousand dollars
16:42of course we're gonna forget about
16:44income taxes for now
16:46um the present value of plan two which
16:49is an a
16:50series of fifteen thousand is fifteen
16:52thousand p
16:53given a um the market rate
16:56for eight periods that's seventy nine
16:58thousand
16:59um three hundred and twenty nine dollars
17:02and the third option forty five thousand
17:05now forty five thousand four years and
17:07forty five thousand in eight years
17:09if you plug in and um the forty five
17:12thousand now is worth forty five
17:14thousand that's why there's a one here
17:16and then the forty five thousand four
17:18years from now you have to multiply it
17:20on p
17:21given f ten point two four percent for
17:23four years
17:24and then the eight years will be
17:26multiplied by p
17:27given f ten point two four percent for
17:30eight years
17:31if you do that multiplication you get
17:33ninety six thousand
17:34and ninety nine dollars so the best
17:37option is to take your hundred thousand
17:39dollars now
17:41of course that is before income taxes so
17:46the outcome after income taxes might be
17:48a little bit different
17:49and we'll learn a little bit about
17:52income taxes in chapter 13
17:54but for now i want to just
17:58look at a couple of problems just to
18:00solidify this theory
18:03the first problem example problem that
18:05i'm going to
18:06talk about here is
18:09in an inflationary period the dollar
18:11based currency
18:13what is the difference between inflated
18:16dollars
18:16and then current dollars okay there is
18:20on inflated dollars and then
18:23current dollars remember there is no
18:26difference
18:27inflated dollars are then current
18:30dollars
18:30they're also called future dollars i i
18:33forgot to mention that in a lecture
18:35that they are called then current
18:37dollars
18:38okay so there's no difference and and
18:41then i go on to say in industry we refer
18:44to
18:44inflated dollars as future dollars uh
18:48or future dollars as during current
18:50dollars
18:51um part b
18:54what is the difference between then
18:56current dollars
18:58future dollars and constant value
19:00dollars well remember that was one of
19:02our equations
19:03to convert from future dollars to
19:06constant value dollars
19:07and vice versa that those were equations
19:11two
19:11and three in in chapter ten
19:15so the difference between then current
19:17future dollars
19:19and constant value dollars is that then
19:22current dollars include inflation and
19:25constant value dollars do not
19:28this is expressed by equations 10.2
19:32and 10.3 constant value dollars equals
19:36future dollars divided by
19:38one plus the inflation rate to the nth
19:40power
19:41dividing by one plus the inflation rate
19:43to the nth power removes inflation
19:47okay future dollars eq constant value
19:49dollars times
19:50times 1 plus the inflation rate to the
19:53nth power
19:54multiplying by 1 plus the inflation rate
19:57to the n power
19:58adds inflation so that's how we do it
20:01notice that this
20:02is exactly the same as interest rates
20:05and future worth and present worth
20:07uh only when when we were doing that we
20:10used
20:11the rate i the interest rate now we're
20:14using the rate
20:16f the inflation rate
20:20okay this will be the last part of
20:22today's uh
20:23lesson um this is example
20:27two um according to the data of the
20:31national association of colleges
20:33colleges and employers engineering
20:37graduates
20:38average starting salary of 61
20:42872 dollars were among the highest of
20:45all majors
20:46of the class of 2011.
20:51what will be the average starting salary
20:53amount
20:54uh in 2019 if salaries increase at the
20:59rate of 2
21:00per year so let's look at that part
21:03using uh equation 10.3
21:07uh and f equals two percent we get
21:10f the future value
21:13uh in 2019 equals p
21:16well which is really constant value
21:18dollars 20
21:2011 times one plus the uh
21:23inflation rate to the nth power and of
21:25course that inflation rate is two
21:27percent so
21:28f 2019 is equal to
21:3161 872 that's essentially constant value
21:37dollars or present dollars
21:391.02 to the eighth power gives us 72
21:45493. um
21:49part b what if uh
21:52the inflation rate of
21:55of uh is twice the inflation what if the
21:59the rate of increase of salaries
22:02is twice the inflation rate of three and
22:05a half percent so
22:06two times three and a half percent at
22:08seven percent so it's
22:09asking you what will the future
22:13average starting salary be if
22:17they went up by seven percent per year
22:20so the future value in 2019
22:23is the constant value p in 2011 times
22:27one plus
22:28f to the eighth power again but now
22:31the f is seven percent so when we
22:34multiply
22:35um sixty one thousand eight hundred and
22:38seventy two one
22:39times 1.07 to the 8th power we get
22:43106 308.
22:46so that concludes today's lesson
22:49on sections 10.1 and 10.2
22:52thank you

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