Lecture 7 - The Time Value of Money

Main Concept of the Time Value of Money

A dollar received today is worth more to you than a dollar received one year from today. Why? Not because of inflation. Even if there is no inflation because you can take the dollar, invest it and have more money at the end of the year.

Evaluating scenarios in which cash flows are generated at different points in time require us to put a value on having money for some amount of time.

The Four Tables

There are four tables (aka annuity tables) that are used to assess the value of money.

1. The future value (FV) of a dollar received today if I could earn i% per period for n periods.

Formula: FV = PV(1+i)ⁿ (Don't worry about the formulas for the exam.)

Example 1: 10 yrs at 10% = 2.594. Multiply that by 386,000 for the final answer.

Don't worry, tables will be provided for the exam.

2. The future value of a dollar received at the end of each period if I could earn i% per period for n periods. (aka future value of an annuity)

Formula: FVa = (PV(1+i)^-1)/r

The table assumes annuity is "in arrears" (not annuity "due") - payments are made at the end of the period.

The table can be worked forward (example 2) or backward (example 3).

3. The present value (PV) of a dollar to be received n periods from now. This is essentially the inverse of table 1.

4. The present value of an annuity. This is the inverse of table 2. Do you take the lump sum today or the timed payments?

As the interest rate goes up, the value of the timed payments goes down. And current cash becomes more valuable.

Time Value Quiz has "oddball" questions - non-traditional context.

1. Use table 4 to get present value of the mortgage. 10% for 30 yrs is 9.427. multiply by 10,000 monthly payment = 94,270.

2. How much would remain on the mortgage after the first year? make the same calculation with 29 periods = 93,700. principle went down by 570, rest was interest. uggh!

3. Joe the plumber makes $50k. He can buy his business for $150k. Only consider the excess $100k. 10% for 5 yrs has a present value of 3.791. He should only pay $379,100.

4. Amt of Payment = FV / Factor = 200,000/15.94 (from table 2 - 10% for 10 yrs)
could this be calculated using table 4??

5. we need the present value of an annuity - table 4. use 20 years since it's semiannually (twice a year), but only 5% interest.

6. this is a problem for table 1 - FV of a single sum. ~7-8 years to double your money at 10%. ~14 yrs @ 5%. Shortcut: 72/%rate (x100)
why does this work??