1. Time Value of MoNey - business applications
Present value of 1, future value of 1, present value of ordinary annuity (or annuity due), future value of ordinary annuity (or annuity due)

2. What is the time value of money and why is it important?
Compensate for risk, delay in payment/receipt, and inflation
Values of some items on financial reports – determined by TVM
Lendors and other creditors use in determining pay back on loans, etc.
Investors expect returns to tie up their funds with a company
Discounting – converting future cash flows to the present value
Compounding – converting current period cash flows to the future value
Examples – investing in PPE using loans or mortgages, estimating fair values of assets/liabilities, valuing certain assets/liabilities known for future cash flows

3. Types of Interest – simple versus compound
Simple interest
Compound interest
Only calculated on original principal received or paid
No matter how many periods, no interest is accrued on from the past interest
Beneficial if borrowing
Detrimental if investing
Principal X interest rate (usually annual*) X time
Time – if note expressed in days, time will be days/360 or days/365
Example – 2 year $1000 note with 10% interest………… $1000 X .10 X 24/12 = 200
Calculated on original principal received or paid plus interest previously accrued
Beneficial if investing
Detrimental if borrowing
(Principal + accumulated interest) X rate* X time
Time – if note expressed in days, time will be days/360 or days/365
Example – 2 year $1000 note with 10% interest... … 1st year $1000 X .10 X 12/12 = $100, 2nd year 1100 X .10 X 12/12 = 110, interest is $210
Example – if compounded semi-annually, above note would be: $1000 X .10 X 6/12 = $50 (1st 6 months), $1050 X .10 X 6/12 = $52.50 (2nd 6 months), $ X .10 X 6/12=55.13 (3rd 6 months) and finally X .10 X 6/12 (4th 6 months) = $57.86, interest is $215.49

4. Future value versus present value of a single sum
Future value (FV)
Present value (PV)
One amount in the present plus compound interest on future periods until a specified time period is reached
Example -- $1000 now with 4% interest and how much is there in three years (3 periods)?
1st year X = 1040
2nd year (1000 X 1.04) X 1.04 =
3rd year (1000 X 1.04) X 1.04 X 1.04 =
FV = PV X (1 + i) n n=number of periods, i=interest rate
Future value of 1 table based on equation
Factor table amount (3,4%) = PV X (1.04)3 =
1000 * =
One amount in the future at a specified period of time brought back to the present
Example -- $ three years from now – how much is it worth in today’s dollars?
PV = FV X 1/(1 + i)n
Present value of 1 Table based on equation
Factor table amount = FV X 1/(1.04)3
Factor table amount = 1/ =

5. Future value Ordinary Annuity (FVOA) versus Future value annuity Due (FVAD)
Future value ordinary annuity – determined immediately after the last cash flow in the series
Annuity – series of equal cash flows (rents-- deposits, receipts, payments or withdrawals)
Ordinary annuity –cash flow occurs at end of period
Fvo = C X [(1+i)^n – 1)/i]
C = cash flow FV?
R R R R
/ / / /
Future value annuity due – Determined one period after the last cash flow in the series
Annuity – series of equal cash flows (rents-- deposits, receipts, payments or withdrawals)
Annuity due – cash flow occurs at the beginning of period
Fvad = C X ((1+i)^n – 1)/i) X (1+i)
FVOA earns one extra interest period
R R R R FV?
/ / / / /

6. Present value ordinary annuity (PVOA) versus present value of annuity due (PVAD)
Present value of ordinary annuity – the 1st rent occurs one period after the beginning of the problem
PVo = C X [(1-1/(1+i)n)/i]
Table approach –present value of ordinary annuity of 1 --example for 10 periods, 5% interest [1-1/(1.05)10 /.05 =
PV? R R R R
/ / / /
Present value of annuity due – the 1st rent occurs right away at the beginning of the problem
PVD = C X [1- 1/(1+i)n-1 /i + 1]
Table approach- present value of annuity due of 1 – example for 10 periods, 5% [1-1/(1.05)9 / ]
PV?
R R R R
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