Video Transcript: Time Value of Money

hello, welcome. We're going to be discussing the concept of time value money.  So time value of money. The time value of money is the idea that money  available at the present time is worth more than the same amount in the future  due to its potential earning capacity. So $1 today is worth more than $1  tomorrow, because we can reinvest that dollar today and get a return, instead of  waiting for some time in the future to receive that dollar and then reinvest so we  can gain interest or a return on that dollar if we invest it today, instead of waiting  to invest it sometime in the future. This core principle of finance holds that  provided money can earn interest, any amount of money is worth more the  sooner it is received, because we can reinvest it quicker or that day that we  receive it, we can reinvest it and gain a return. Time value money is also  referred to as present, discounted value. So for time value money, our formula  takes into the account the following variables, future value of money, the present value of money, the interest rate, the number of years or periods of  compounding years and the number of years is T based on these variables, the  formula for time, value of money is future value equals present value times one  plus the interest rate divided by the number of periods, compounding raised to  the number of periods combat compounding times the number of years. Pretty it may seem complicated, but this is actually a very simple calculation. What is  simple interest? Interest is a rental fee to borrow money. So I'm borrowing  money from the bank. They are charging me a fee to borrow the money, and  that is interest. The reason why they charge interest is because they are taking  a risk that you will not be able to pay back that money that is loaned to you. So  your interest rate will correlate, or will be, relative to your credit worthiness. So  the higher the interest rate you have, the less credit worthy you are. The lower  the interest rates you have, the more credit worthy you are. So simple interest is when the interest received or paid is based solely on the amount of money that  was initially invested. Therefore the interest earned each period or year will be  the same. So simple interest formula your initial investment times one plus the  interest rate times the number of periods simple calculation. We'll talk about it  more in a second. Let's discuss compound interest. Compound interest is much  different than simple interest. Compound interest is the kind of interest you  would like to receive in an investment, but definitely would not want to pay. Why  is that? Because the interest rate is based on the balance of the investment,  when it is calculated, not the initial investment. What this means is that interest  is being earned on both the investment and the interest earned from previous  periods. So if I have compounding interest, right? And let's say I receive, I have  a $1,000 corporate bond that I purchased in the market, right, and it offers a  10% return or coupon payment on that $1,000 well, let's say, instead of getting  that coupon, putting it in the bank account and spending it whenever I want, let's say I kept it invested into that same bond, right and now, in year one of the  repayment of this bond, Right now, I left the $100 or the 10% coupon payment 

from the $1,000 bond. I leave it in there, right? So now I have $1,100 so now  with that 10% return, next year, I'll have $110 right? Because I left that $100 in  there that made my balance on my debt, that I let them borrow 1100 so now in  year two, the 10% will be taken from the 1100 which will give me $110 so next  year, in year three, if we leave it in there, right, we'll have $1,210 that will have a  10% bearing coupon. And we'll continue to leave that interest payment into the  pot, so the interest will continue to compound over time. So let's look at it here.  This is exactly what we were talking about. So we have $100 we yield 10% from that $100. So we leave the 100 we leave the $10 in. We don't take it out and  consume it. We leave it reinvested. And then the next year, it grows to $121 and  this will continue to grow exponentially until maturity, right until either the debt is  ready to be repaid, or we decide to settle up our investment and take the cash.  So you'll see that the comp the power of compounding interest is fantastic,  right? The more you leave in, the more it'll compound, and the greater it'll grow,  right? You can see our future value formula. Future value equals present value  times one plus the interest raised to the number of periods in that investment.  So future value equals present value times one plus the interest rate raised to  the number of periods. Let's work this example at the bottom right. Let's say  we've got $100 and we leave it compounded for five years. Okay? So the future  value of 100 right? So we started out our present value is 100 because that was  what our initial investment, right? So your initial investment will always be your  present value when you're calculating future value. So we're going to multiply  this at one plus the interest rate, which is what, 10% right? And now we're going  to raise this right? This is a it's the exponent, right? We're going to raise this by  the number of periods, which is five, right? So let's work this out, right? So we'll  do this equals after we calculate it, right? So this is going to be 100 times 1.10  raised to the fifth, this is going to equal 161 161.05 so if raising it by this  exponent is a really, is a really easy calculation. You just, there's you can denote that on the calculator. You'll see an exponent key, and you hit the exponent key,  and then you'll put in the amount of times it's raised to. So future value is what  $1 today will be worth in the future. This is because of the interest that dollar can earn over time, therefore making it more valuable in the future. So again, future  value. This is the future value of $1,000 corporate bond yielding 10% the  number of periods is 10. Again, we'll work future value equals $1,000 bond times one plus the interest rate at 10% raised to the number of periods is 10. Future  value equals 1000 times 1.10 raised to 10, future value equals 2593.74, so we  bought the bond for 1000 now, this is the power of compounding, right? We've  almost tripled our money on this bond value over time by keeping our coupon  payments invested. We started out with $1,000 investment. Over the 10 years, it grew to 2593.74 that's the power of compounding. That's the power of interest.  Let's talk about annuities. An annuity is a series of equal payments that are  either paid to you or paid from you. Annuities can be cash flows paid, such as 

monthly rent payments, car payments, or they can be money received, such as  semi annual coupon payments from a bond. Just remember, for a series of cash flows to be considered an annuity, the cash flows need to be equal. So an  annuity due, an annuity due is when payments, when a payment is made at the  beginning of the payment period. And then, let's say it's rent, for example, where you are usually required to pay rent in advance at the first month, first of the  month, so that I'm kind of pre paying for that service with my rent, right? I'm  paying at the first of the month, so I can rent for the for the rest of the month,  ordinary annuity. An ordinary annuity is a pay. That is paid or received at the end of the period. An example of an ordinary annuity would be a coupon payment  made from bonds. Usually, bonds will make semi annual coupon payments at  the end of every six months. All right, now, let's discuss present value in a little  more depth. Okay, present value is the current worth of a future sum of money  or stream of cash flows, given a specified rate of return, future cash flows are  discounted the discount rate, and the higher the discount rate, the lower the  present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing cash flows in the future, whether they be earnings  or debt obligations. Present value is also referred to as the discount value. The  basis is that receiving $1,000 now is worth more than $1,000 5 years from now,  because if you've got the money now, you can invest it and receive an additional return over the five years. The money today is worth more than the same money tomorrow, because the passage of time has financial value attached to it, and  rewards or costs are demanded for owning or using today's money. Future value can relate to future investment cash inflows from investing today's money or  future payments or outflows from borrowing money today, present value  provides a basis for assessing the fairness of any future financial benefit or  liability. For example, future cash rebate discounted to present value may or  may not be worth having a potentially higher purchase price, the same financial  calculation applies to 0% financing when buying a car, paying some interest  instead of a lower sticker price, may work out better for the buyer than paying  zero interest on a higher sticker price, paying mortgage paying Mortgage points  now in exchange for lower mortgage payments in the future makes sense only if the present value of the future mortgage savings is greater than the mortgage  payments paid today. So let's look at present value. So present value in a simple form, right? Where we're just going to estimate out what I'll receive in a year,  right? So receive the $100 in a year, right? We received $100 in a year. We want to know what is the present value of that $100 that we're going to receive in a  year? What is that $100 that we're going to receive in a year worth today, right?  And our discount rate, or interest rate, is going to be 10% so let's look at the  present value formula. Present Value equals future value divided by one plus the interest rate raised to the number of times. Now we know the future value is 100 we're going to receive that in the future. We're going to divide that 100 by one 

plus the 10% raised to one year. We're going to receive our $100 a year from  now. So let's see. Let's calculate this, right? 100 divided by 1.10 gives us $90.91 right? So now we want to decide, okay, is this going to be better for us to take  this at 10% or can we find an investment that is going to yield us a greater return than a 10% so if we have the same scenario, but with a different interest rate.  So the future value is 100 now instead of 10% let's say we're going to get 12%  one plus point one two raised to one year, present value equals 100 divided by  1.12 so we will find that the calculation 89.29 so now if we compare the two at  12% the present value of this $100 investment will be 89.29 whereas at 10%  90.91 what would we take? Now? We want the greater present value so we.  Would elect to go with this route. So future value of a series of cash flow  payments. So let's assume we have $100 payments for three years at 5%  interest. What is the present value of the annuity? You will need to solve the  present value of each payment individually. So let's take a look. So our annuity  pays $100 at the end of the next three years in a fund that pays 5% interest. So  now in year one, we have to calculate 100 Okay, divided by one plus the rate of  return, as we know, is .05 or 5% raised to the time, right? One year. This our first period. This our first payment. So year 190 $5 it'll generate $95.24 that's the  present value of the $100 in year one, year two, $100 divided by one plus .05  raised to two. It's the second period. So we're going to raise to two. Present  value of the $100 and year two is $90.70 now let's look at year three, 100  divided by one plus .05, 5% so three is the third period of the annuity. Let's look  at year three. Year three, our present value, $86.38 we add these together the  present value of our annuity now $272.32 this means that if you invested  $272.32 in a fund that earned 5% interest, you would withdraw $100 for the next three years. So we want to find out, okay, if I have a certain number, a certain  objective, a certain amount of money that I need to make, this will be very handy to figuring out your initial investment to earn, excuse me, to earn the amount of  money that you need in the future.