1. The Time Value of Money Module 24

2. DISCUSSION!  Major loans in YOUR life?  Where do you get the money to pay them off?  On your phones, find example interest rates for your loans  As a business owner, can you guess what additional loans you may need?  How is international/global finance changing money and your debt? Guesses?

3. Borrowing, Lending, and Interest  Having money now is worth more than the same amount in the future  Ex: $100 in 1913 would be $2,403.48 today  $100 in 1950 would be $987.32 today  $100 in 2014 would be $100.51 today

4. Present Value  Can use interest rate to compare the value of a dollar realized today with the value of a dollar realized later

5. Equations! Amount received one year from now as a result of $X lending today = $X +$X x r = $X x (1+r)

6. Example: $5 received one year from now as result of lending today: $X x (1+r) = $5 Solve for X: $X = $5/(1+r) If r (interest rate) = 0.05 (5%) $X = $5/(1+.05) = $4.76 So you could accept $4.76 today in exchange for every $5 a year from now

7. This works the other way too: If you owe $15 a year from now: $X x (1+r) = $15 Solve for X: $X = $15/(1+r) If r (interest rate) = 0.05 (5%) $X = $15/(1+.05) = $14.29 So you could save $14.29 today in order to have the full $15 a year from now

8. More equations  Also possible to figure out what money would be worth multiple years in the future Amount received n years from now as a result of $V lending today = $V(1+r) n

9. Net Present Value  The present value of current and future benefits minus the present value of current and future costs ProjectDollars Realized Today Dollars realized one year from today Present Value formulaNet present value given r = 0.10 A – Cost nothing and has immediate payoff $100- $100.00 B – Pay $10 today, receive $115 a year from now -$10$115 C – Immediate payoff $119; must pay $20 a year from now $119-$20 -$10 + $115/(1+r) $119 - $20/(1+r) $94.55 $100.82