1. Time Value of
Money
 Created By:
 M.i. Jamil
7 April 2018 1

2. Content
 Time Value of Money
 Classification of TVM
 TVM Formula
 Annuity
 Types of Annuity
 Cash Flow Diagram
 Benefits of TVM
 Identifying TVM Problems
7 April 2018 2

3. Time Value of Money (TVM)
 Definition:
In the evolution of time ,the difference in the fundamental difference is
amount of time value of money. Everybody know that, at present any
amount of money is more than valuable from future amount. Time value of
money establish by this time preference.
7 April 2018 3

4. Classification of TVM
 The four basic time value of money concepts are:
 Future value of a sum
 Present value of a sum
 Future value of an annuity
 Present value of an annuity
7 April 2018 4

5. TVM Formula
 FV=Future value of money
 PV=Present value of money
 i = Interest rate
 n = Number of compounding periods per year
 t = Number of year
 TVM: 𝑭𝑽 = 𝑷𝑽(𝟏 +
𝒊
𝒏
)(𝒏×𝒕)
7 April 2018 5

6. Future Value
 Future value is the value of resource at a specific date. This is used in time
value of money calculations.
 Future value = FV
 𝑭𝑽 𝑵 = 𝑷𝑽(𝟏 + 𝑰) 𝑵
7 April 2018 6

7. Present Value
 Value in the present of a total of money, in line to some future value it will
have when it has been invested at compound interest. This is a used in time
value of money calculations.
 Present value = PV
 𝑷𝑽 =
𝑭𝑽 𝑵
(𝟏+𝑰) 𝑵
7 April 2018 7

8. Annuity
 An annuity is a series of equal payments or receipts that occur at evenly
spaced intervals for a specified period. The annuity values are assumed to
occur at the end of each period.
 Examples of annuities:
7 April 2018 8

9. Types of Annuity
 The two basic types of annuities are:
 Ordinary annuity: With an ordinary annuity, the first payment takes place one
period in the future.
 Annuity due: With an annuity due, the first payment takes place immediately.
7 April 2018 9

10. Future Value of An Ordinary Annuity
 The formula for computing the future value of an ordinary annuity is:
 𝑭𝑽𝑨 𝑵 = 𝑷𝑴𝑻
(𝟏+𝑰) 𝑵−𝟏
𝑰
 𝐻𝑒𝑟𝑒,
𝐹𝑉𝐴 𝑁= 𝑓𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎𝑛 𝑁 − 𝑝𝑒𝑟𝑖𝑜𝑑 𝑜𝑟𝑑𝑖𝑛𝑎𝑟𝑦 𝑎𝑛𝑛𝑢𝑖𝑡𝑦
𝑃𝑀𝑇 = 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑒𝑟𝑖𝑜𝑑𝑖𝑐 𝑝𝑎𝑦𝑚𝑒𝑛𝑡
7 April 2018 10

11. Future Value of An Annuity Due
 The future value of an annuity due is computed as follows:
 𝑭𝑽𝑨 𝒅𝒖𝒆 = 𝑭𝑽𝑨 𝒐𝒓𝒅𝒊𝒏𝒂𝒓𝒚 (𝟏 + 𝑰)
7 April 2018 11

12. Present Value of An Ordinary Annuity
 The formula for computing the present value of an ordinary annuity is:
 𝑷𝑽𝑨 𝑵 = 𝑷𝑴𝑻
𝟏−
𝟏
𝟏+𝑰 𝑵
𝑰
 Here, PVA 𝑁 = future value of an N-period ordinary annuity
PMT = the value of the periodic payment
7 April 2018 12

13. Present Value of An Annuity Due
 The present value of an annuity due is computed as follows:
 𝑷𝑽𝑨 𝒅𝒖𝒆 = 𝑷𝑽𝑨 𝒐𝒓𝒅𝒊𝒏𝒂𝒓𝒚 (𝟏 + 𝑰)
7 April 2018 13

14. Cash Flow Diagram
 A cash flow diagram is a picture of a financial problem that shows all cash inflows
and outflows plotted along a horizontal time line.
 Example: You are 40 years old and have accumulated $50,000 in your savings
account. You can add $100 at the end of each month to your account which pays an
annual interest rate of 6% compounded monthly. Will you be able to retire in 20
years?
7 April 2018 14

15. Benefits of The Knowledge of The TVM
 For investment analysis – To decide the financial benefits of projects
 To compare investment alternatives
 To analyze how time impacts business activities such as loans, mortgages,
leases, savings, and annuities.
7 April 2018 15

16. Identifying TVM Problems
 For a financial problem to be solved with time value of money formulas:
 the periods must be of equal length
 payments, if present, must all be equal and be all inflows or all outflows
 payments must all occur either at the beginning or end of a period
 the interest rate cannot vary along the time line
7 April 2018 16

17. 7 April 2018 17