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# Time Value of Money (Financial Management)

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### Transcript

• 1. “Don't waste your time with explanations: people only hear what they want to hear.” Paulo Coelho
• 2. Time Value Of Money  The Interest Rate  Simple Interest  Compound Interest  Amortizing a Loan
• 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. 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. Types of Interest INTEREST (Price of Money) Simple Interest Compound Interest Single Amount Annuity Ordinary Annuity Annuity Due Perpetuity
• 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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