• Write a 200- to 300-word description of the four time value of money concepts: present value, present value of an annuity, future value, and future value of annuity. Describe the characteristics of each concept and provide an example of when each would be used.
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DESCRIPTION OE THE FOUR TIME VALUE OF MONEY CONCEPTS
Present value is the value of a cash flow today.
Usage when a single cash flow is to be discounted to today’s value.
Formula PV = FV / ((1+i) ^n))
Where, PV = Present value
FV = Future Value
i= interest rate per compounding period
n=period
PVIF = Present Value Interest Factor = (1/ ((1+i) ^n))
Example Mr A would receive $1,100 from Mr B after 1 year. Find the present value of the cash flow if Mr A’s interest rate is 10% p.a.
PV = 1100 / (1.1^1) = $1,000
Thus, the present value of cash flow to be received after 1 year is $1,000 today.
Present value of annuity is the value of a series of equal cash flow received in equidistant period, today.
Usage when a series of cash flow is to be discounted to today’s value.
Formula PV = (a/i) (1-(1/ ((1+i) ^n)))
Where, PV = Present value
a = equal cash flow (annuity)
i= interest rate per compounding period
n=no. of annuities
PVIFA = Present Value interest factor of annuity = (1/i) (1-(1/ ((1+i) ^n)))
If cash flow occurs at the beginning of period then the above formula is to be multiplied by (1+i)
Example Mr A would receive $1,000 from Mr B every year for 5 years. Find the present value of the cash flow if Mr A’s interest rate is 10% p.a.
PV = (1000/.1)(1-(1/((1.1^5))) = $3,791
Thus, the present value of cash flow to be received every year for 5 years is $3,791 today.
Future value is the value of a cash flow in future.
Usage when value of a single cash flow is to be computed in future’s date.
Formula FV = PV ((1+i) ^n))
Where, PV = Present value
FV = Future Value
i= interest rate per compounding period
n=period
FVIF = Future Value Interest Factor = ((1+i) ^n))
Example Mr A would receive $1,000 from Mr B today. Find the future value of the cash flow if Mr A’s interest rate is 10% p.a.
FV = 1000 * (1.1^1) = $1,100
Thus, the future value of cash flow after 1 year is $1,100.
Future value of annuity is the value of a series of equal cash flow received in equidistant period, on a future date.
Usage when future value is to be computed for a series of cash flow.
Formula FV = (a/i) (((1+i) ^n)-1)
Where, FV = Future value
a = equal cash flow (annuity)
i= interest rate per compounding period
n=no. of annuities
FVIFA = Present Value interest factor of annuity = (1/i) (((1+i) ^n)-1)))
If cash flow occurs at the beginning of period then the above formula is to be multiplied by (1+i)
Example Mr A would receive $1,000 from Mr B every year for 5 years. Find the future value of the cash flow if Mr A’s interest rate is 10% p.a.
FV = (1000/.1) ((1.1^5)-1)) = $6,105
Thus, the future value of cash flow to be received every year for 5 years is $6,105.
Present value is the value of a cash flow today.
Usage when a single cash flow is to be discounted to today’s value.
Formula PV = FV / ((1+i) ^n))
Where, PV = Present value
FV = Future Value
i= interest rate per compounding period
n=period
PVIF = Present Value Interest Factor = (1/ ((1+i) ^n))
Example Mr A would receive $1,100 from Mr B after 1 year. Find the present value of the cash flow if Mr A’s interest rate is 10% p.a.
PV = 1100 / (1.1^1) = $1,000
Thus, the present value of cash flow to be received after 1 year is $1,000 today.
Present value of annuity is the value of a series of equal cash flow received in equidistant period, today.
Usage when a series of cash flow is to be discounted to today’s value.
Formula PV = (a/i) (1-(1/ ((1+i) ^n)))
Where, PV = Present value
a = equal cash flow (annuity)
i= interest rate per compounding period
n=no. of annuities
PVIFA = Present Value interest factor of annuity = (1/i) (1-(1/ ((1+i) ^n)))
If cash flow occurs at the beginning of period then the above formula is to be multiplied by (1+i)
Example Mr A would receive $1,000 from Mr B every year for 5 years. Find the present value of the cash flow if Mr A’s interest rate is 10% p.a.
PV = (1000/.1)(1-(1/((1.1^5))) = $3,791
Thus, the present value of cash flow to be received every year for 5 years is $3,791 today.
Future value is the value of a cash flow in future.
Usage when value of a single cash flow is to be computed in future’s date.
Formula FV = PV ((1+i) ^n))
Where, PV = Present value
FV = Future Value
i= interest rate per compounding period
n=period
FVIF = Future Value Interest Factor = ((1+i) ^n))
Example Mr A would receive $1,000 from Mr B today. Find the future value of the cash flow if Mr A’s interest rate is 10% p.a.
FV = 1000 * (1.1^1) = $1,100
Thus, the future value of cash flow after 1 year is $1,100.
Future value of annuity is the value of a series of equal cash flow received in equidistant period, on a future date.
Usage when future value is to be computed for a series of cash flow.
Formula FV = (a/i) (((1+i) ^n)-1)
Where, FV = Future value
a = equal cash flow (annuity)
i= interest rate per compounding period
n=no. of annuities
FVIFA = Present Value interest factor of annuity = (1/i) (((1+i) ^n)-1)))
If cash flow occurs at the beginning of period then the above formula is to be multiplied by (1+i)
Example Mr A would receive $1,000 from Mr B every year for 5 years. Find the future value of the cash flow if Mr A’s interest rate is 10% p.a.
FV = (1000/.1) ((1.1^5)-1)) = $6,105
Thus, the future value of cash flow to be received every year for 5 years is $6,105.
Solve, using the Rule of 72: rate =6%, pv=$7,000, fv= $56,000. Solve for years.
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