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# Time value 1

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time value of money

time value of money

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• 1. ACCT 302 by Professor Hsieh Chapter Time Value of Money Concepts
• 2. 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
• 3. Time Value of Money Concepts 3 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%. \$10,000 x (1+i)2 = \$12,100
• 4. Time Value of Money Concepts 4 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% \$12,100 / (1+10%)2 = \$10,000
• 5. Time Value of Money Concepts 5 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 0 End of Year 1 End of Year 2 End of Year 3 First payment \$10,000 2nd payment \$10,000 3rd payment \$10,000
• 6. Time Value of Money Concepts 6 C.Annuity (contd.) Case 1 (contd.) The future value of these payments (an ordinary annuity) is: Payment FV of \$1, i=10% Future Value (at the end of year 3) n First Payment \$10,000 x 1.12a = \$12,100 2 Second Payment \$10,000 x 1.10b = \$11,000 1 Third Payment \$10,000 x 1.00 = \$10,000 0 Total 3.31 = \$33,100 The future value annuity factor The future value
• 7. Time Value of Money Concepts 7 C.Annuity (contd.) Case 1 (contd.) A short cut: FVA = \$10,000 x 3.31 the future value annuity factor (Table 6A-3 under 10%, n=3) a=(1+10%)2 =1.21 b=(1+10%)1 =1.10
• 8. Time Value of Money Concepts 8 C.Annuity (contd.) Case 2: Future Value of An Annuity Due Diagram of this annuity 0 End of Year 1 End of Year 2 End of Year 3 2nd payment \$10,000 3rd payment \$10,000 future valueFirst payment \$10,000 Note: This annuity is similar to that of Case 1 except that the first payment was made at the beginning of year 1.
• 9. Time Value of Money Concepts 9 C.Annuity (contd.) Case 2: (contd.) Future value of these payments: Payment FV of \$1, i=10% Future Value (at the end of year 3) n First Payment \$10,000 x (1+10%)3 =1.331 = \$13,310 3 Second Payment \$10,000 x (1+10%)2 =1.21 = \$12,100 2 Third Payment \$10,000 x (1+10%) = \$11,000 1 Total 3.641 = \$36,410 A short cut: \$10,000x3.641=36,410 (Table 6A-3, the factor under 10%, 4 period minus one. or Table 6A-5, under 10%, n=3)
• 10. Time Value of Money Concepts 10 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 0 End of Year 1 End of Year 2 End of Year 3 First payment \$10,000 2nd payment \$10,000 3rd payment \$10,000 Present Value ?
• 11. Time Value of Money Concepts 11 C.Annuity (Contd.) Case 3: (contd.) The Present value of these payments (an ordinary annuity) is: Payment PV of \$1, i=10% Present Value (at the end of year) n First Payment \$10,000 x 0.90909a = \$9,091 1 Second Payment \$10,000 x 0.82645b = \$8,264 2 Third Payment \$10,000 x 0.75131 = \$7,513 3 Total 2.48685 = \$24,868 a=1/(1+10%)=0.90909 b=1/(1+10%)2 =0.82645 A short cut: \$10,000 x 2.48685=24,868 The present value annuity factor(Table 6A-4,under 10%, n=3)
• 12. Time Value of Money Concepts 12 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. 0 End of Year 1 End of Year 2 End of Year 3 First payment \$10,000 2nd payment \$10,000 3rd payment \$10,000 Present Value ?
• 13. Time Value of Money Concepts 13 C.Annuity (contd.) Case 4 : (contd.) The present value of these payments: Payment PV of \$1, i=10% Present Value (at the beg.of year 1) n First Payment \$10,000 x 1.000 = \$10,000 0 Second Payment \$10,000 x 0.90909 = \$9,091 1 Third Payment \$10,000 x 0.82645 = \$8,264 2 Total 2.73554 = \$27,355 A short cut: \$10,000 x 2.73554=\$27,355 (Table 6A-4, the factor under i=10%, n=2 plus one. Or Table 6A-6, factor under i= 10%, n=3)