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Class 20 Sections 10 3 - 10 4 — Transcript

by vic zaloom · 3,175 words · 575 segments · language en · Watch on YouTube

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0:02hello uh this recording
0:04um video uh will cover sections 10.3
0:09and 10.4 on the topic of inflation in
0:13chapter 10.
0:14um of course uh you should always go to
0:18the start page when you go to blackboard
0:20and check out the bottom of the start
0:23page has the
0:25revised uh schedule of assignments
0:29you should read in your textbook
0:33your ebook whatever you prefer sec
0:36pages 312 to 318 which covers these
0:40these two sections um
0:45view this video and you're responsible
0:49for
0:49all of these notes that will also be
0:52posted
0:52on blackboard with this video and if you
0:56really want to make a good grade in the
0:57course
0:58work as many problems at the end of each
1:00chapter as you can
1:02all of that is is what we say every
1:06class
1:08it hasn't changed um
1:12the
1:15ch section 10.3 deals with
1:21making adjustments due to inflation
1:25author describes a future worth cases
1:29actually four of them and we're going to
1:31go through those
1:32uh in this lecture um
1:36the um the author has not really
1:40integrated inflation very well
1:42throughout
1:43the course it's just kind of focused on
1:46this particular
1:48chapter and so
1:51um it's um
1:55it's unclear whether
1:58you you really um whether
2:01in the rest of the book we're
2:03considering inflation or not
2:05and so um
2:08that's one of the shortcomings of
2:12i think the lesson i think it's
2:16important that you understand inflation
2:19and then if you can incorporate it in
2:22into your economic analysis that is
2:25something you should be doing
2:28um the first case
2:31that the author discusses or creates
2:35essentially is to find the number of
2:38future or then current remember future
2:41dollars
2:42from the last lecture are called
2:46then current dollars including both the
2:49interest that you will earn uh
2:52what is called the real interest rate
2:56and the inflation so we're trying to
2:59include both
3:00in that case we use what we call
3:04the market rate the market rate was
3:07the symbol used was i sub uh f
3:11um which means that that i
3:14contains the inflation rate f um
3:19so uh the future number of dollars
3:23is the present number times 1 plus
3:26i sub f to the n power well that's the
3:29same equation
3:31throughout the course we've been using i
3:34uh which the author says
3:36is the real rate okay
3:39the market rate in fact you could argue
3:43is is the real rate but i shouldn't say
3:46that
3:46i don't want to confuse you
3:51the rate that you get in when you
3:55do financial transactions always
3:58includes inflation so
4:00um but we haven't been using that
4:04as such in in the in the course
4:08um the so if you if you
4:11use your your symbolic formula
4:14it's just p find f given p
4:18at rate i sub f for n
4:22periods um
4:25and um i'm not sure why this
4:29this uh um
4:32this is here or this is here
4:36i don't think i need either of those two
4:38things
4:40um so i'll take those out
4:43and when i post this it won't have those
4:46um
4:48so that's the equation and
4:52he says where he defines um
4:56the market rate i sub f
4:59equal we did this in the last class but
5:01i'm just repeating it here
5:03that's equation 10.6 and we use this
5:06equation a lot
5:08is i plus f plus i times f
5:11okay um and so here's a
5:15an example of this case um
5:18the uh
5:22the present value is one thousand
5:24dollars the number of
5:25years is ten the
5:29market rate i sub f is
5:32ten percent and the inflation rate is
5:35four percent
5:36remember i sub f has this inflation rate
5:40embedded in it okay so it's already
5:43there
5:44okay um and um
5:48the author says um
5:51determine f that is the future number of
5:54dollars
5:56um in four different cases and and these
5:59are the four
5:59k uh there are four cases but
6:03the first case case one we're gonna
6:07find the actual future amount
6:09accumulated
6:10um or owed if you were borrowing that
6:14thousand dollars
6:15in this account okay so
6:18you use the market rate and you find
6:22f so that is equation 10.7
6:26okay so we just plug into equation 10.7
6:31f equals p times f given p
6:35i sub f and n i sub f is ten percent and
6:40a seven we plug in we get one thousand
6:42nine hundred forty eight dollars
6:44um he says this case will correctly
6:47predict
6:49the amount of capital needed at a future
6:52time
6:53to overcome the effects of inflation
6:56plus
6:57realize a stated rate of return
7:00so that's what what
7:03uh we are accomplishing there
7:07um so the future
7:10future value is um
7:14on nineteen hundred and forty eight
7:17dollars
7:18so that the second case um
7:22is where you wish to find the actual
7:26purchasing power of the future
7:29or then current dollars remember from
7:31the last class the purchasing power
7:34was called the constant value dollars or
7:37today's dollars and
7:40cv dollars constant value well the
7:44constant value dollars
7:45are future dollars reduced by
7:49the inflation rate so what we have to do
7:52is say constant value dollars equals
7:56purchasing power
7:57of f which is equal to f
8:00which is p times 1 plus i sub f to the n
8:04which you
8:04we just did in the last case but then we
8:07have to
8:08take out the inflation so we divide by
8:111 plus f to the n power
8:14and that removes the the
8:18reduced buying power due to inflation
8:22essentially must reduce the purchasing
8:24power
8:24of the actual future dollars due to
8:27inflation and that's what we're doing
8:29here
8:30by basically dividing by one plus
8:33f to the n or another way to do it is to
8:36multiply by one plus
8:38f to the minus n and we know what this
8:41is
8:41this is this is p given f
8:45at the rate f for n periods okay
8:49so in terms of
8:52this formula in terms of your symbolic
8:56formula
8:56um f uh the purchasing power of
9:01f equals p
9:04times f given p so we're
9:07inflating it f given p we're moving it
9:10out to the future
9:12at the um market rate
9:15i sub f for n periods and then we're
9:18kind of deflating it
9:20to get a purchasing power number okay so
9:24this is really and i'll
9:27post it like this this is cv
9:31equals um that is a constant value is
9:35equal to the purchasing power of the
9:37future value
9:38okay and so um
9:42when we go through this um
9:46case 2 the future
9:49value of the purchasing power it uh
9:52the the future purchasing power in
9:55cv dollars for the estimated
9:58is is given by this so we we basically
10:02take
10:03that 1948 that we got in the last
10:07case case one and we gotta pull out
10:11the inflation okay so we have
10:14four we had we were given that the
10:17inflation
10:18rate was four percent so we're going to
10:21divide by 1.04 to the seventh power
10:25and when we do that uh we're basically
10:28executing any one of these three
10:30equations they're all the same
10:32we get that even though
10:36maybe this account will have nineteen
10:38hundred and forty
10:39eight dollars at the end of year seven
10:43what it would buy in today's goods and
10:46services because they'll cost more
10:49would only be fourteen hundred and
10:50eighty dollars worth of stuff
10:52that's the constant value um
10:55term and i would rather we
10:59make sure we know that's constant value
11:02of the f dollars and actually this is
11:06purchasing power
11:14don't forget that purchasing power of
11:16the efforts
11:17it's the f dollars is this much that's
11:20how many dollars is there
11:22but in terms of what they would buy
11:25because you're buying things seven years
11:27from now if you
11:28if you leave the money there okay so
11:33it has to be reduced by the inflation
11:35rate that's what the author discusses
11:37there
11:38so the next um case um
11:41or actually he discusses this
11:44the same case in another way
11:49he he says one thing we could do
11:52instead of basically inflating at the
11:55market rate
11:56and then deflating so to speak at the
11:59inflation rate
12:01we could simply just use the real rate
12:04the
12:04i and he says if we solve the equation
12:086 for i remember equation six
12:11is i sub f equals
12:15i plus f plus the product
12:18i times f and i
12:21is the real rate as shown below so if we
12:25if we solve this equation uh we factor
12:28out the i
12:29from the first and third term we get i
12:32times one plus f and then we
12:36keep the f over here and then we divide
12:39by the 1 plus
12:40f to get i and and then subtract f
12:43from both sides we get i equals i sub r
12:47minus f divided by 1 plus f and that's
12:50the
12:51equation 10.9 just use that i
12:55then um in
12:58the uh to get the uh
13:02the constant value of the future dollars
13:06so the author goes through that process
13:09here
13:10to give you um the i
13:13value he uses the numbers remember
13:17i sub f was 10 and f
13:20was four percent uh in the original
13:24statement of the problem so
13:27we get i sub f minus f that's ten
13:30percent minus four percent
13:32in the numerator and then we divide that
13:34by 1 plus f which is 1.04
13:37we get 5.77
13:40percent as our real rate
13:44okay and then we we have the constant
13:47value
13:49uh or the purchasing uh i'll say
13:52constant value equal purchasing
14:00purchasing power
14:04of f equals
14:08um 1000 f given p
14:12at rate i for n periods
14:15that's 1488. so it gives
14:18us the same value as using
14:21the market rate and then deflating it
14:24that's what we did here
14:25to get 14.88 we use the market rate
14:29uh to get 1948 dollars
14:33but they'll only buy that many dollars
14:36worth of goods and services
14:38if you were using your money now to buy
14:41those goods and services
14:43so
14:46this is still more than a thousand
14:49dollars so you've gained
14:50ground so to speak in buying power
14:54by investing your money at 10
14:58okay but you haven't gained the full 10
15:02because inflation has eaten up some of
15:05that
15:05okay um the full 10 gain
15:09would mean that you could buy um
15:12[Music]
15:14nineteen hundred and forty eight dollars
15:16worth of goods and services
15:18okay so
15:21um the the the third case
15:25that the author discusses is
15:28um the number of future dollars at time
15:32and to maintain the same purchasing
15:35power
15:35as p dollars today in other words all
15:38you want to do is find the number of
15:41dollars
15:41that will buy the same number of goods
15:45and services
15:46as as one thousand dollars will buy now
15:50that was p
15:51remember p was one thousand dollars in
15:53this case
15:54all you have to do is find the future
15:58value
15:59at the inflation rate so the future
16:02value
16:03in terms of uh buying a thousand dollars
16:06worth of goods and services
16:08is a p which is a thousand f given p
16:12f is four percent and is seven
16:15periods seven years and he gets thirteen
16:19hundred and
16:21dollars so if you
16:25were to invest your money at
16:28four percent um
16:33all you would be you would you would
16:35have more money
16:36at time seven you'd have this many
16:38dollars but
16:39that many dollars would buy the same
16:43number of goods and services at time
16:45seven that one thousand dollars will buy
16:48now that's what that means
16:51um the last case then
16:55the fourth case is really not a new case
16:58at all
16:58he's just substituting the mar
17:02for the real i okay
17:05uh that's just uh uh substituting for i
17:09so uh he's saying
17:12that uh if you want to know how many
17:14dollars will be there in the future
17:17you take p times one plus demar
17:20r what's mar r i'm sorry mar sub
17:23f my mars of f
17:26um is the um
17:30market mar the market mar
17:33remember if it's i sub f it's the market
17:36rate
17:37well mar is a rate it's a minimum
17:40attractive rate of return
17:41and if you include inflation in that
17:44then it's
17:46mar sub f and it's you would raise that
17:49to the n
17:50power to get the future value and so
17:53if you substitute the mar for i in
17:55equation
17:56610 remember this is equation 610 again
18:00i sub f equal one
18:03plus f plus i f this yields
18:07mars sub f equals mar plus
18:10f this is the this is the real
18:14minimum attractive rate of return this
18:17is the inflation rate
18:19and then this is the product of the two
18:21and that gives you
18:22mars of f just like i gave you
18:26that product okay so
18:29um when we solve case four
18:33uh using mar f we're just basically
18:37going to
18:38uh going to get the same result that we
18:41got in
18:42case one okay um we want to both
18:45maintain our our we want to account for
18:49inflation and we also want to earn a
18:52rate of return
18:53but understanding that the real rate of
18:55return that we're
18:56earning above inflation
18:59is 5.77 and
19:03this is the market rate that we're using
19:0610 so um
19:10now i'm going to work well i'm going to
19:12cover section
19:15um 10.4 very briefly uh
19:18calculations adjusted for inflation
19:21annual worth calculations
19:23all he says is basically you can boil
19:26this down to
19:27use the market rate i sub r when
19:30calculating
19:31annual worth okay and we know how to get
19:33ice
19:35sub r from equation 10.6
19:39and so um the next
19:44i'm going to work a couple of problems
19:46example problems for you
19:49um i'm not sure i don't think i can't
19:52recall these being in the book
19:54these are our problems um that i have
19:59from my notes um how much can
20:02the manufacturer of superconducting
20:05magnetic
20:06energy storage systems afford to spend
20:10now okay so that's that's a p
20:14okay uh on new equipment
20:17in lieu of spending seventy five
20:20thousand
20:21four years from now okay so
20:24uh if they spend some money now that's
20:27in lo
20:27that'll save them seventy five thousand
20:30four years from now
20:31the company's mar is 12
20:35per year and the inflation rate
20:38is estimated to be 3 per year
20:42so we're given f equals 75 000. that's
20:47the number
20:48of then current dollars at time
20:51what is it time for four years from now
20:54i think
20:55um spending four years from now
20:59um the mar the real mar
21:02is twelve percent but the inflation
21:04rates three percent
21:06and uh n is four years so we want to
21:09find
21:10p and then solving equation 10.12 which
21:14was our
21:14our essentially case 4
21:17this is a case 4 problem um
21:21p is equal to f times 1 plus mar sub
21:24f to the minus n okay
21:27and mars of f we we basically use
21:31equation 10.6
21:33to get that we take mar
21:37plus f plus the product which gives us
21:4215.36 percent
21:44we plug that in bring it back four years
21:47at that rate
21:48and we get forty two thousand three
21:50hundred and forty nine dollars
21:53that is uh essentially the present
21:56value of 75
21:59000 four years from now
22:03at the market mar
22:06that's what mars of f is gotta
22:10learn a lot of new terminology and keep
22:12it straight
22:13you got real rate market rate
22:17remember the market rate includes
22:19inflation
22:20the real rate does not okay it excludes
22:24inflation okay we're going to work
22:27another problem
22:29example two an
22:32engineer deposits 10 000 into an account
22:36when the market rate is 10
22:40per year and the inflation rate is 5
22:44per year okay um
22:47the remember the market rate includes
22:51inflation so that 5
22:53is already embedded in in that ten
22:55percent
22:56the uh uh the count is left undisturbed
23:00in other words no deposits no
23:02withdrawals for five years how much
23:05money will be in the account
23:07well it's earning a market rate um of 10
23:10percent and that's
23:11including inflation so we got p equals 1
23:15000
23:15the market rate includes inflation is
23:18designated as
23:20i sub r f um
23:23and that's at ten percent per year
23:27how much will be uh how much is
23:30f at n equal five so equation 10.7
23:34we have f equals p times one plus
23:38i sub f to the n power ten thousand
23:41times one point one to the fifth power
23:44sixteen thousand one hundred and five
23:46dollars
23:47that's part a of the question
23:50part b says what will be the purchasing
23:54power
23:54in terms of today's dollars so
23:57we're looking for the constant value of
24:00these
24:01f dollars here and um
24:04we must remove the inflation of five
24:07percent per year
24:09from the f to get the purchasing power
24:12or
24:12constant value dollars or today's
24:15dollars we call them
24:17use equation 10.10 and solve for p
24:20equation 10.10
24:22is this is really the purchasing power
24:26of
24:26f equals
24:31p times one plus f and that
24:34should be to the minus n
24:38um solving for p uh
24:41yields p equals uh
24:46oh i'm sorry this is this is attic
24:48equation has it
24:50is going in the opposite direction that
24:53is a plus n
24:54solve that equation for p and you get f
24:57times 1 plus f to the minus n
25:00and you um you then
25:03that f is five percent and this is five
25:06years as well and it's five
25:08so you do that and um you get
25:12purchasing power of those
25:15um let's see sixteen hundred
25:18thousand and one hundred and five
25:20dollars have a purchasing power of
25:22twelve
25:23thousand six hundred and nineteen
25:26because
25:26inflation has eaten away at the
25:29purchasing power okay
25:31part c what is the real
25:35rate of return okay the real rate
25:39so then the author has to solve for i
25:43okay and remember we're going to use um
25:47equation 10.9 actually is where we
25:52we we do that solution we start with
25:55equation 10.6 um
25:5910.6 was i
26:02um was i i sub
26:05f equals i plus f
26:09plus i f i times f this is equation 10.6
26:14we're going to solve that equation for i
26:17and we we did that just a few minutes
26:20ago
26:20to get equation 10.9 equation 10.9
26:24says i equals
26:28i sub f minus f divided by 1 plus
26:32f and so we have 10 percent
26:36minus five percent over 1.05 which is
26:40one plus f okay and um
26:44or 0.1 minus 0.05 that's 10
26:4810 5 and 1 plus five percent
26:52and then we do that and we get four
26:54point seven
26:55six percent so that is quote the real
26:58rate
26:59um that you're you're earning above
27:03inflation and that will conclude today's
27:09lecture and thank you for paying
27:12attention
27:13bye

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