Time Value of Money. Ex: How much a bond, which can be cashed out in 2 years, is worth today
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1 Time Value of Money The time value of money is the idea that money available now is worth more than the same amount in the future - this is essentially why interest exists. Present value is the current value of a sum that you are expecting to be paid in the future Ex: How much a bond, which can be cashed out in 2 years, is worth today Future value is the value of an asset or cash at a specified date in the future, based on its value now, and interest Ex: How much $100 will be in 2 years, if earning 5% interest Grab a whiteboard- let s practice!
2 Future Value Review: How much will a current interest-earning investment be worth in the future? Sally can put $1000 into a CD earning 4% compounded interest for 5 years What is the future value of her investment? Show your work!
3 Future Value Review: How much will a current interest-earning investment be worth in the future? Sally can put $1000 into a CD earning 4% compounded interest for 5 years What is the future value of her investment? $1000(1 +.04) 5 = $
4 Future Value Review: How much will a current interest-earning investment be worth in the future? Rupert buys a $500 bond earning 2% compounded interest for 20 years What is the future value of his investment? Show your work!
5 Future Value Review: How much will a current interest-earning investment be worth in the future? Rupert buys a $500 bond earning 2% compounded interest for 20 years What is the future value of his investment? $500(1 +.02) 20 = $742.97
6 Present Value vs Future Value Scenario: You win $1 million in the lottery. Choices: Get the whole $1 million in two years, OR a smaller sum right now. Which do you choose? In order to make an informed decision, we would need to determine the present and future values.
7 Money Now or Later? It depends on the present and future value of the money. We know the future value: $1 million (in 2 years) However, what is the minimum amount we would be willing to accept right now? Need to know the interest rate! Let s say that the expected interest rate is 5% and officials are offering you $910,000 now. Do we take the offer?
8 Formulas PV = present value R = interest rate FV = future value n = number of years Future Value Formula FV = PV(1 + r) n Present Value Formula PV = FV/(1 + r) n Now calculate the present value of the $1 million dollar deal on your whiteboard. Should we take the deal?
9 Yes take the deal! PV = 1,000,000/(1+.05) 2 PV = $907, Money Now or Later? Present values is less than what they are offering, $910,000. So, take the deal! Another way to look at it: If we take the $910,000 now and invest it at 5% interest for two years, we will have more than $1 million dollars. $910,000(1+.05) 2 = $1,003,275.00
10 Let s Practice! #1. The Federal Reserve issues a $1,000, one year T-Bill (Treasury Bill) paying 5%. The buyer receives the $1,000 at the date of maturity, which is 1 year from now. You pay the present value of the T-Bill upon purchase. What is your purchase price? Show your work!
11 Let s Practice! #1. PV = 1000/(1 +.05) 1 PV = $952.38
12 Let s Practice! #2. Suppose you want to get a lump sum payment of $100,000 two years from now. If the current interest rate is 10%, how much will you need to invest now, in order to meet your goal? In other words, what is the present value of $100,000 two years from now? Show your work!
13 Let s Practice! #2. PV = $100,000(1 +.10) 2 PV = $
14 #3. You lend this jabroni $500, and he promises to pay you back in 2 years. You agree to have him pay you back with a compound interest rate of 3% at the end of two years. How much does he owe you in two years? Let s Practice!
15 Let s Practice! #3. FV = $500(1 +.03) 2 FV = $530.45
16 Let s Practice! #4. You are planning to move out of your parents house in 3 years and want to start saving now for your first month s rent and deposit. You ve calculated that you ll need $3,000. How much money would you need to save now, if you can get an interest rate of 2%, in order to have the money for your new place?
17 Let s Practice! #4. PV = $3000/(1 +.02) 3 PV = $
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