1. Finance Chapter 6 Time value of money

2. Time lines & Future Value Time Lines, pages 218-219 Time: 0 1 2 3 4 5 Cash flows: -100 Outflow ? Inflow 5%

3. Time lines & Future Value  Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when compound interest is applied.  Future value (FV) the amount cash flow(s) will grow over a given period of time when compounded at a given interest rate.

4. Time lines & Future Value  PV=present value (beginning amount). PV = $100  i = interest rate for one year i = 5%, or i = 0.05  INT = dollars of interest earned during the year INT = $100(0.5) = $5  FV n = the value n years into the future n = number of periods in the analysis, n = 1  FV n = FV 1 = PV + $105

5. Time lines & Future Value Future value, pages 219-223 Time: 0 1 2 3 4 5 Cash flows: -100 FV 1 =? …………………………… FV 5 =? Interest earned: 5.00 5.25 5.51 5.79 6.08 Amount at the end 105.00 110.25 115.76 121.55 127.63 of each period 5%

6. Time lines & Future Value  FV N = PV(1 + i) n  The equation has 4 variables. If we know any 3 we can solve for the 4 th.  Problem format: Time: 0 1 2 3 4 5 5% -100 FV=? FV N = PV(1 + i) n = $100(1.05) 5

7. Present Value  Opportunity cost rate  The rate of return on the best available alternative investment of equal risk, or  the rate of return you could earn on an alternative investment of similar risk.  Present Value (PV) The value today of a future cash flow or series of cash flows  The $100 is defined as the present value (PV) of $126.63 due in 5 years when the opportunity cost rate is 5%.  If an alternative security is less than $100, buy it  If an alternative security is more than $100, ignore it

8. Present Value  Fair (Equilibrium) Value The price at which investors are indifferent between buying or selling a security  Discounting The process of finding the present value of a cash flow or a series of cash flows; discounting is the reverse of compounding

9. Present Value  The present value of a cash flow due in n years is the amount, if in hand today, would grow to equal the future amount Time: 0 1 2 3 4 5 5% PV = ? 127.63

10. Present Value  Discounting equation Start with the future value equation and solve for PV: FV N = PV(1 + i) n PV = FV N / (1 + i) n Time: 0 1 2 3 4 5 5% -100= 105.00 110.25 115.76 121.55 127.63 /1.05 /1.05 /1.05 /1.05 /1.05

11. Annuities  Annuity A series of payments of an equal amount (PMT) at fixed intervals for a specified number of periods  Ordinary (deferred) annuity PMT occur at the end of each period  Annuity due PMT occur at the beginning of each period  Perpetuities a stream of equal payments expected to continue forever

12. Interest rates  Nominal (Quoted, Stated, APR) interest rate The contracted, or quoted, or stated interest rate  Effective (Equivalent) annual rate (EFF% or EAR) The actual rate of interest actually being earned, as opposed to the quoted rate. Also called “equivalent annual rate.”  Used to convert any nominal rate to an equivalent annual rate  These two rates may differ.

13. Amortized loans  Amortized* loans A loan that is repaid in equal payments over its life.  Amortized schedule A table that shows how a loan will be repaid, showing how much is interest and how much is principal repayment  Example: $1,000 loan, 6% interest on loan balance $1,000 represents the PV of an annuity of PMT dollars per year for n years, discounted at 6%  Partial amortization with a balloon payment page 248 *mors = Latin for “kill”