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Question 1085878: Mike has the opportunity of $200,$350 and $400 respectively at the end of one through three years. Calculate the Pv of this stream of each inflows if interest is 9%
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Fv1 = the future value of cash (in dollars) one year into the future
Fv2 = the future value of cash (in dollars) two years into the future
Fv3 = the future value of cash (in dollars) three years into the future
Pv1 = present value of cash that corresponds to the future value value Fv1
Pv2 = present value of cash that corresponds to the future value value Fv2
Pv3 = present value of cash that corresponds to the future value value Fv3
We'll use the formula
FV = PV*(1+r)^t
where we compound the money annually (n = 1). If the compounding amount is different, then let me know.
Solve for the present value PV to get
FV = PV*(1+r)^t
PV = FV/[ (1+r)^t ]
We'll use that formula to compute the present values for each given future value. The given future values are:
Fv1 = 200
Fv2 = 350
Fv3 = 400
The time values are respectively t1 = 1, t2 = 2, t3 = 3. The interest rate is held constant at r = 9% = 9/100 = 0.09 (we'll use the decimal form for r).
So,
PV = FV/[ (1+r)^t ]
Pv1 = Fv1/[ (1+r)^(t1) ]
Pv1 = 200/[ (1+0.09)^(1) ]
Pv1 = 183.48623853211
Pv1 = 183.49
and,
PV = FV/[ (1+r)^t ]
Pv2 = Fv2/[ (1+r)^(t2) ]
Pv2 = 350/[ (1+0.09)^(2) ]
Pv2 = 294.587997643296
Pv2 = 294.59
and finally,
PV = FV/[ (1+r)^t ]
Pv3 = Fv3/[ (1+r)^(t3) ]
Pv3 = 400/[ (1+0.09)^(3) ]
Pv3 = 308.873392024426
Pv3 = 308.87
Now add up the present values (Pv1 through Pv3) to get
Pv1 + Pv2 + Pv3 = 183.49+294.59+308.87
Pv1 + Pv2 + Pv3 = 786.95
The sum of the present values is 786.95 dollars
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