Chapter 4,5 Time Value of Money. Learning Goals. 1. Understand the concept of future value, their calculation for a single amount, and the relationship of present to future cash flow.
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Time Value of Money
1. Understand the concept of future value, their calculation for a single amount, and the relationship of present to future cash flow.
4. Calculate the present value of a mixed stream of cash flows.*
5. Understand the effect that compounding more frequently than annually has on future value and the effective annual interest rate.
Would it be better for a company to invest $100,000 in a product that would return a total of $200,000 after one year, or one that would return $220,000 after two years?
It depends on the interest rate!
With simple interest, you don’t earn interest on interest.
With compound interest, a depositor earns interest on interest!
Algebraically and Using FVIF Tables
You deposit $2,000 today at 6% interest. How much will you have in 5 years?
$2,000 x (1.06)5 =
$2,000 x 1.3382 = $2,676.40
EAR = (1 + k/m) m -1
EAR = (1 + .18/12) 12 -1
EAR = 19.56%
Algebraically and Using PVIF Tables
How much must you deposit today in order to have $2,000 in 5 years if you can earn 6% interest on your deposit?
$2,000 x [1/(1.06)5]= $2,000 x 0.74758 = $1,494.52
PV = Annuity/k
PV = $1,000/.08 = $12,500
Using the FVIFA Tables
FVA = 100(FVIFA,5%,3) = $315.25
Year 1 $100 deposited at end of year = $100.00
Year 2 $100 x .05 = $5.00 + $100 + $100 = $205.00
Year 3 $205 x .05 = $10.25 + $205 + $100 = $315.25
=FV (interest, periods, pmt, PV)
=FV (.06, 5,100, )
Using PVIFA Tables
PVA = 2,000(PVIFA,10%,3) = $4,973.70
=PV (interest, periods, pmt, FV)
=PV (.10, 3, 2000, )