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# Time Value of Money (Financial Management)

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### Time Value of Money (Financial Management)

1. 1. “Don't waste your time with explanations: people only hear what they want to hear.” Paulo Coelho
2. 2. Time Value Of Money  The Interest Rate  Simple Interest  Compound Interest  Amortizing a Loan
3. 3. Time Value Of Money The Interest Rate Which would you prefer -- \$10,000 today or \$10,000 in 5 years? Obviously, \$10,000 today. You already recognize that there is TIME VALUE TO MONEY!!
4. 4. Time Value Of Money Why TIME? Why is TIME such an important element in your decision? TIME allows you the opportunity to postpone consumption and earn INTEREST.
5. 5. Types of Interest INTEREST (Price of Money) Simple Interest Compound Interest Single Amount Annuity Ordinary Annuity Annuity Due Perpetuity
6. 6. Types of Interest  Simple Interest Interest paid (earned) on only the principal amount, or principal borrowed (lent). Formula: SI =(Po)(i)(n)  Assume that you deposit \$1,000 in an account earning 7% simple interest for 2 years. What is the accumulated interest at the end of the 2nd year? SI = (Po)(i)(n) = \$1000(0.07)(2) s = \$140
7. 7. Types of Interest  Simple Interest (FV)  What is the Future Value (FV) of the deposit? FV = Po+SI = \$1000+\$140 =\$1140 Future Value is the value at some future time of a present amount of money, or a series of payments, evaluated at a given interest rate.
8. 8. Types of Interest  Simple Interest (PV)  What is the Present Value (PV) of the previous problem? The Present Value is simply the \$1,000 you originally deposited. That is the value today! Present Value is the current value of a future amount of money, or a series of payments, evaluated at a given interest rate.
9. 9. Types of Interest Compound Interest Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent). Example: Assume that you deposit \$1,000 at a compound interest rate of 7% for 2 years. 0 7% 1 2 \$1,000 FV2
10. 10. Types of Interest Future Value Single Deposit FV1 = P0 (1+i)1 = \$1,000 (1.07) = \$1,070 Compound Interest You earned \$70 interest on your \$1,000 deposit over the first year.This is the same amount of interest you would earn under simple interest.
11. 11. Types of Interest Future Value Single Deposit FV1 = P0 (1+i)1 = \$1,000 (1.07) = \$1,070 FV2 = FV1 (1+i)1 = P0 (1+i)(1+i) = \$1,000(1.07)(1.07) = P0 (1+i)2 = \$1,000(1.07)2 = \$1,144.90 You earned an extra \$4.90 in Year 2 with compound over simple interest.
12. 12. Types of Annuities Annuity: A series of equal payments or receipts occurring over a specified number of periods. Ordinary Annuity: In an ordinary annuity payments or receipts occur at the end of each period. Annuity Due: In an annuity due payments or receipts occur at the beginning of each period.
13. 13. Types of Annuities Ordinary Annuity (FV): FVA= R(FVIFAi,n) FVA= R[(1+i)ᵑ-1/i] Activity: If R=\$1000, i= 8%, n= 3 years. Calculate future value of ordinary annuity? FVA= R[(1+i)ᵑ-1/i] FVA= \$1000[(1.08)³-1/(0.08)] FVA= \$3246
14. 14. Types of Annuities Ordinary Annuity (PV): PVA= R(PVIFAi,n) PVA= R[1-[1/(1+i)ᵑ]/i] Activity: Periodic receipts of \$1000 at the end of each year , discount rate= 8%, n= 3 years. Calculate present value ordinary annuity? PVA= R[1-[1/(1+n)ᵑ]/i] PVA= \$1000 [1-[1/(1.08)³]/(0.08)] PVA= \$2577
15. 15. Types of Annuities Annuity Due (FV): FVAD= R(FVIFAi,n)(1+i) FVAD= R[(1+i)ᵑ-1/i](i+i) Activity: R=\$1000, i= 5%, n= 5 years, Calculate future value of annuity due?. FVAD= R[1-[1/(1+n)ᵑ]/i] (1+i) FVAD=\$1000 [1-[1/(1.05)^5]/(0.05)](1.05) FVAD= \$5802.3
16. 16. Types of Annuities Annuity Due (PV): PVAD= (1+i) (R) (PVIFAi,n) PVAD= (1+i) (R) [1-[1/(1+i)ᵑ]/i] Activity: R=\$1000, i= 8%, n= 3 years, Calculate present value of annuity due?. PVAD= (1+i) (R) [1-[1/(1+i)ᵑ]/i] PVAD=(1.08) (\$1000) [1-[1/(1.08)³]/(0.08)] PVAD= \$ 2783.16
17. 17. Types of Annuities Perpetuity: An ordinary annuity whose payments or receipts continue forever. PVA oo = R/I Activity: R=\$1000, I = 5%,Calculate Perpetuity annuity? PVA = R/I PVA = \$1000/0.05 PVA = \$20000 oo oo oo
18. 18. Amortizing A Loan A table showing the repayment schedule of interest and principal necessary to pay off a loan by maturity. Activity: PV= \$10,000, i= 14% compounded annual, n= 4 years, R=? PV= R (PVIFAi,n) \$10,000= R (PVIFA14%,4) \$10,000 = R (2.914) R= \$10,000/2.914 R= \$3432
19. 19. Amortizing A Loan End of Year Installments Interest Principal 0 Amount Owing At Year End \$10,000 1 \$3432 \$10000x 14% =\$1400 \$2032 \$7968 2 \$3432 \$7968x 14% =\$1116 \$2316 \$5652 3 \$3432 \$5652x 14% =\$791 \$2641 \$3011 4 \$3432 \$3011x 14% =\$421 \$3011 - \$13,728 \$3728 \$10,000
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