hello hello this is module six not a module about time value of money so let's again review this material or learn it boat or we learn it is so is good so here the learning objective is tree we're going to look at cash flow that our value level cash flow annuities and perpetuities we are going to look how loan are calculated loan payment and then how we can find the interest rate and then we are going to look at how long our ties and talk about the nominal rate the periodic rate effective read APR services the learning objective for this module so three section value level cash flows that include annuities and perpetuities and then we are going to look at comparing rates and then pure discount loan and amortized loan as to third section so the first section value level cash flow and with decent perpetuity so here's the definition an annuity is a finite series of equal payment so you have equal payment and those payments are occurring at regular interval every year so if the first payment is at the end of the period then this is an ordinary annuity if the payment is at the beginning of the period well then this is an unweeded you so does choose the terminology and review if needed the timeline we give you last time or look at this one so that's an ordinary annuity payment at the end and that's an annuity due payment and the beginning okay so when we have a series of payment with a specific numbers of payment we have an annuity if we had an infinite numbers of payment like for instance if this is infinity then that will be a perpetuity so when the number of payment is infinite we have a perpetuity otherwise we have an annuity plus the difference now when we have a perpetuity to calculate the present value you will just take the payment see the cash flow and divide by the rate so C is the cash flow and you're going to divide by R that's it now you text presenter formula that you could use to calculate the present value or the future value of an annuity we are not going to use those formula because we will work with the calculator but in case you're interested they're presented here nice price calculators are concerned again in the practice section for the previous module and for this module there is four or five videos that review how to setup and use your calculator so please review those videos and then remember if you have an ordinary annuity you can set your calculator to the end mode and if you have an annuity due you can set your calculator to the beginning mode so let's illustrate so I'm reading after carefully going over your budget you have determined you can afford to pay six hundred and thirty-two dollars per month toward a new sport card and you call up your bank and you find out that the rates the going rate is 1% per month for 48 months so step one let's be consistent right so this is a monthly rate a monthly number of period no problem and that is 632 well the question of course is how much can you borrow well how much you can borrow you're going to calculate the present value of the 632 dollars per month for 48 months at 1% so again you can play with the formula if you want to but as I mentioned earlier we are going to use the calculator okay so in my calculator I will introduce a number of periods and equal to 48 is 48 payment and period the rate that the bank has quoted is 1% per period per month so when put why are the payment is minus 632 you're going to spend six hundred and sixty-two dollars and then you can compute PV the present value and you should obtain twenty three thousand nine hundred and ninety nine let's say twenty four thousand so that's how much you can borrow today another illustration here we are going to look at the number of payment you are running a little bit short on your spring break vacation so you put a thousand dollars on your credit card so right now you're borrowing your thousand minus a thousand and you know that you will only be able to afford the amount minimum monthly payment of twenty so twenty twenty twenty twenty twenty twenty now on your credit card your the rate you paying is 1.5 percent per month okay and the question is how many months will it take for you to repeat one thousand so the question is what is end how long now let's make sure we consistent this is a monthly rate perfect those are we payment and of course I will find a monthly number of period so what will you put in your calculator a rate of one-point-five a present value of minus a thousand payment of twenty and you're going to compute and and will be equal to ninety three point eleven but again remember that this is monthly this is monthly also then you answer is a certain number of map so if you want to know in years well since there is 12 months per year you can always divide 93 by twelve so it's a long time seven point seven close to eight years put it this way okay now I mentioned earlier perpetuity perpetuity is also called council and you know when we will talk about securities later on we will talk about the first stock and you will remember a preferred stock is a perpetuity so what did we agreed upon earlier what we agreed to calculate the present value of a perpetuity we are going to take the cash flow the payment and divide by our so that's how we are going to calculate the present value see the cash flow divided by R or C so so the payment now a perpetuity does not have a future value does not exist because the cash flow never end it goes until infinity now suppose company a wants to sell prefer stock at $100 per share so this is what they want has the present value this will be how much we will spend also assume that Company B a similar prefer stop and they're selling at $40 per share this is also the present value would be the value present value now B is providing a dividend of $1 every quarter while the dividend is the payment it is the cash flow it is the see what dividend should company a have to offer if the preferred stock is going to sell well let's see what people expect when they pay $40 and receive one so in the first two first stock the present value is 40 the dividend is $1 divided by R the rate so we can solve for R it is 2.5% per quarter so investors or purchasing prefer stock from company a expect the rate of return of 2.5% so what should be the dividend that the other company is going to pay in order for investors to have the same rate of return so remember PV 100 equal to C which we are solving for the dividend divided by the rate point 0 to 5 so if you solve for C you will obtain 2 point 2 dollars and 50 cents per quarter so if you want to sell you the first stock which is way more expensive than the others but you're gonna have to provide a way higher dividend and the dividend will have to be two point five dollars two dollars and 50 cents per step two let's compare rate and understand better the impact of compounding there is different rates sometimes you will talk we will talk about the quarry trade the quarry trick is a nominal rate this is always going to be an annual rate sometimes we are going to talk about the periodic rate is the rate per period per month per day and ei R is the effective annual rate now we are also going to introduce the a P R so I will complete this later so let's illustrate if a red is quoted so that's the nominal as 10% but then we say compounded semi-annually this means the investment is going to pay 5% every six months so the question is 5% every six months the same as 10% per year no so your nominal rate the quality rate is 10% the periodic rate is of every six month so it's 10% / - right Sousa manually there is - so my annual period per year the green and there is also for quarterly periods per year so the number of period per years is M so the first case M is equal to 2 in the second cases M will be equal to 4 right quarterly so when we calculate the periodic rate what did we do well we took the nominal rate and we divide by M please look to calculate the periodic rate we took the nominal rate 10 that was given we divide by the number of semiannual period per year which is true - and that's five so we did nominal divided by M so if your rate so same problem so 10% nominal 5% periodic what is the AAR but to calculate you EA are you will use the formula that is given here so the EA are equal one plus the periodic rate exponent M minus one and remember the periodic rate is the nominal rate divided by M we'll put it here as well so we have everything in front of us so this is nominal divided by M this is exactly what we just did here nominal divided by M ma and that's the periodic right periodic rate is the nominal rate divided by M so the formula works both ways so in this case ten percent per year is five percent semi-annually so the EA r is one plus five percent again point oh five in a formula square minus one and that will give you ten point twenty five percent so this ei R is very important when we want to be able to compare various type of investment so I'm going to illustrate this imagine that you're looking at three banks Bank a gives me fifteen percent but compounded daily so every day I'm adding money in my account B is fifteen five compounded quarterly and c16 scamper compounded annually which one of the Joe's account will allow me to earn more interest well since those rates a compounding differ to compare you need to calculate a are so I did it here for Bank a dar is one plus the rate exponent M minus one I have the formula here on top in case so the AR is 1 plus the periodic rate exponent M minus one so for Bank be August bank see okay I make the change in the following slide and we order think to make sure it's clearer okay so a pay fifteen percent compounded daily so this is the nominal rate if I wanted to calculate for this specific Bank the periodic rate the periodic rate is my fifteen percent which is point fifteen divided by how many days per year 365 so this is the periodic rate for Bank B what will my periodic rate be well my periodic rate will be point fifteen five divided by the number of quarter per year and there is four core appears and then Bank C what will be my periodic rate well it's sixteen percent but since its annually divided by one so that my periodic rate so I'm going to use those numbers in the formulas point fifteen divided by three sixty five point two one five five divided by four and point sixteen divided by one yeah so bank a my ei R is 1 plus the periodic rate remember the periodic rate is the rate divided by 365 so I copied it here again just in case and that is point zero zero zero four so exponent M M is number of periods per year 365 minus one for B the rate is one five five divided by four quarterly that is point zero 3875 exponent for the number of quarter per year for and subscribe 12.16 point forty two and you're the bank what is one point sixteen exponent 1 minus 1 and that 16 percent so clearly in this case bank beats you better choice one the rate is a little bit higher in B than India look back now in United States do is a law which is called truth in landing and think there is a lot of laws behind as a body so close to the truth in lending laws requires that Lander disclose the AP are a PR stand for annual percentage rate and the annual percentage rate is the interest rate per period multiplied by the number of period per year so adding this as I mentioned earlier on our first slide just in case you want everything together so this is the annual percentage rate and we just agreed this is the rate that is multiplied by 12 order by the number of periods sorry so here let's illustrate here's that's what I was thinking 12 but that's fine so for example a bank is charging 1.2 percent per month on the car well since there is 12 month per year the APR is 14.4 if you wanted to calculate e AR we're going to use the formula that we had before so observe that here we say 1 plus a PR divided by 12 exponent 12 minus 1 and that will give me a rate of 15 point 39 percent so the banks can quote 14 for the real rate is still 15 3 for now I want you to take a look here this formula and then notice that here we use a PR divided by 12 you agree while the APR divided by 12 is indeed the periodic rate that is the periodic rate now you can review that and the last section here is pure discount loan or amortized known as the last section in this review so I will stop the video here and then start a new one this is long enough