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Time Value of Money (Financial Management)
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Time Value of Money (Financial Management)

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  • 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

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