CHAPTER 10: TIME VALUE OF MONEY

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  • A ringgit that received today are more worth than a ringgit that received tomorrow.

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Basic Concept

-Future value

-Present value

-Annuities

i)Future value of lump sum
-future value determine the amount that a sum of money invested today will grow to in a given period of time.
-"compounding" is the process of finding a future value.

iii)Future value of a multiple Cash Flow :

-Calculation for Future Value (lump sum)
-By using formula

  • FVn = PV (1+i)n
    -By using table
  • FVn = PV (FVIF i%,n)
  • Cash flow is a set of payments that an investor will receive or invest over time
  • The future value of cash flows equals the sum of the future cash flows of an individual.
  • Calculation:
    i) Using the formula
  • FVn = PV (1+i) n-1 + PV (1+i) n-2 + PV (1+i) n-3 + PV (1+i) n-4
    ii) Using the table
  • FV = PV(FVIF i%,n-1)+PV(FVIF i%,n-2)+PV(FVIF i%,n-3)+ PV(FVIF i%,n-4)
  • FV = PV(FVIF 10%,3)+PV(FVIF 10%,2)+PV(FVIF 10%,1)+ PV(FVIF 10%,0)
  • Present Value of a Multiple Cash Flow
  • The cash flow PV equals the present value of each individual cash flow in the stream.
  • Cash flow of PV can also be found by taking FV cash flow and depositing the amount at the appropriate discount rate for the appropriate period of time.
  • Calculation:
    i) Using formula
  • PV = [FV1/(1+i)1]+[FV2/(1+i)2]+[FV3/(1+i)3]+[FV4/(1+i)4]
    ii) Using table
  • PVn = FV (PVIF 10%,1)+ FV (PVIF 10%,2)+ FV (PVIF 10%,3)+ FV (PVIF 10%,4)
  • Present Value of a Lump Sum

-Calculation:
i) Using the fomula

  • PVn = FV [1 / (1+i)n ]
    ii) Using table
  • PVn = FV (PVIF i%,n)
  • Current value calculation determines what future cash flows will be received today (time 0).
  • Interest rates used to reduce cash flow are generally referred to as discount rates

i) Future Value of ordinary annuities calculation:
i) Using formula

  • FVA - PMT (1+i)n-1/i
    ii) Using table
    FVA = PMT (FVIFA i%, n)

iv) Present Value of Annuities Due

  • An annuity is a cash flow in which cash flows are all equal and occur on a regular basis.
  • Normal annuity - cash flow occurs at the end of the period
  • Annuity Due -cash flow occurs at the beginning of the period.

ii) Future value of Annuities Due:

iii) Present Value of Ordinary Annuities

  • Calculation:
    i) Using formula
  • FVA = PMT(1+i)n -1 / i x(1+i)
    ii) Using table
  • FVA = PMT (FVIFA i%, n) X (1+i )
  • Calculation:
  • PVA = PMT (PVIFA i%, n)
  • Calculation:
    i) Using formula
  • PVA = PMT1 - (1+i)-n / i x (1+i)
    ii) Using table
  • PVA = PMT (PVIFA i%, n) X (1+i)
  • INTERPOLATION
  • The process of determining the right interest rate (i) or the exact timeframe (n).
  • Interest (before) + (factor value (before) - calculated factor value) / (factor value (before) - factor value (after) X difference between interest after and before.