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Mastering Time Value of Money Concepts

Learn the principles of Time Value of Money - calculating future value, present value, annuity payments, and more. Enhance your financial knowledge with practical examples and shortcuts.

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Mastering Time Value of Money Concepts

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  1. Chapter Time Value of Money Concepts

  2. Time Value of Money • The dollar amount cash flows difference between the present value of an amount and its future value. The difference is also referred to as the interest. • Example: • The time value of $100 for one year at i = 10%. • Present value=$100 • Future value=$100 x (1+10%)=$110 • The time value of one year for this $100 • =$110-$100=$10 Time Value of Money Concepts

  3. $10,000 x (1+i)2 = $12,100 A.Future Value of A Single Amount • FV= I x ( 1 + i)n • Where:FV = Future value of the invested amount; • i = Amount invested at the beginning of the • period; • n = the number of compounding periods. • Example: The future value of $10,000 invested on • 1/1/x1, at the end of year 2 (i.e.;12/31/x2) • with i=10%. Time Value of Money Concepts

  4. $12,100 / (1+10%)2 = $10,000 B.Present Value of A Single Amount • FV = I x (1 + i)n • I = FV / (1 + i)n • Where: I = Present value of a single amount. • Example: The present value of $12,100 to be • received two years from now with i =10% Time Value of Money Concepts

  5. End of Year 2 End of Year 3 End of Year 1 0 First payment $10,000 2nd payment $10,000 3rd payment $10,000 C. Annuity • The cash flows of a constant amount to be received or paid each period. • Case 1: Future value of an ordinary annuity • FVA: Annuity amount x future value annuity factor • Example:The future value of paying $10,000 every year • for the following three years at i= 10%. The first • $10,000 is to be paid one year from today (n=0). • Diagram of these payments Time Value of Money Concepts

  6. The future value annuity factor The future value C.Annuity (contd.) Case 1 (contd.) • The future value of these payments (an ordinary annuity) is: Time Value of Money Concepts

  7. the future value annuity factor (Table 6A-3 under 10%, n=3) C.Annuity (contd.) Case 1 (contd.) • A short cut: • FVA = $10,000 x 3.31 a=(1+10%)2=1.21 b=(1+10%)1=1.10 Time Value of Money Concepts

  8. End of Year 3 End of Year 2 End of Year 1 0 future value First payment $10,000 2nd payment $10,000 3rd payment $10,000 C.Annuity (contd.) Case 2: Future Value of An Annuity Due • Diagram of this annuity • Note: • This annuity is similar to that of Case 1 except that the first payment was made at the beginning of year 1. Time Value of Money Concepts

  9. (Table 6A-3, the factor under 10%, 4 period minus one. or Table 6A-5, under 10%, n=3) C.Annuity (contd.) Case 2: (contd.) • Future value of these payments: • A short cut: $10,000x3.641=36,410 Time Value of Money Concepts

  10. End of Year 3 End of Year 2 End of Year 1 0 First payment $10,000 2nd payment $10,000 3rd payment $10,000 Present Value ? C.Annuity (contd.) Case 3:Pre. Val. of An Ordinary Annuity • PVA=annuity amount x present value annuity factor • Example: The present value of paying $10,000 • every year for the following three years at • i=10%. The first $10,000 is to be paid • one year from today (n=0). • Diagram of these payments Time Value of Money Concepts

  11. The present value annuity factor(Table 6A-4,under 10%, n=3) C.Annuity (Contd.) Case 3: (contd.) • The Present value of these payments (an ordinary annuity) is: • a=1/(1+10%)=0.90909 • b=1/(1+10%)2=0.82645 • A short cut: $10,000 x 2.48685=24,868 Time Value of Money Concepts

  12. End of Year 3 End of Year 2 End of Year 1 Present Value ? 0 First payment $10,000 3rd payment $10,000 2nd payment $10,000 C.Annuity (contd.) Case 4: Pre. Value of An Annuity Due • Diagram of this annuity • Note: • This annuity is similar to that of Case 3 except that the first payment was made at the beginning of year 1. Time Value of Money Concepts

  13. (Table 6A-4, the factor under i=10%, n=2 plus one. Or Table 6A-6, factor under i= 10%, n=3) C.Annuity (contd.) Case 4 : (contd.) • The present value of these payments: • A short cut: $10,000 x 2.73554=$27,355 Time Value of Money Concepts

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