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Present Value of Single / Multiple Cash Flows

Assignment / Homework Help
The Present Value concept is also called as discounting technique. In this approach, the money received in some future date will be worth lesser now at the present date because the corresponding interest is lost during the period. Given a positive rate of interest, the present value of future amount will always be lower, and thus this procedure is called as discounting.


Present Value Single Cash Flows

The Present Value of a future single cash flow can be calculated by the following formula:
PV = FVn  x     1    
(1 + r)n
Where
PV = Present Value
FVn = Future value at nth year
r = discount rate and
n = number of years after which the future value would be received.

Example: Let us calculate the present value of $10,000 to be received in 9 years when discounted at 11%.

Here,

FV   =  $10,000;
n     =  9 and
r      =  11% or 0.11
PV  =   $10,000 x [1/(1 + 0.11)9]
      => $3,909.25


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Present Value Multiple Cash Flows

In many cases, especially in Capital Budgeting decisions, we will come across a series of cash flows that would be received in future dates that are different from each other. In such cases, we need to calculate the present value of all such future cash flows discounted with their respective years and discount rate and then add up them together to find out the sum of the present value. It would be then compared with the initial investment required for the project. If the net present value is positive, the project would be considered for acceptance. The formula for calculating the present value of a series of cash flows is:
PV = C1 C2 Cn

+
+ ........
(1 + r)1 (1 + r)2 (1 + r)n
Where
PV = Sum of all the PVs of future cash inflows
C1, C2...Cn = represents cash inflows in period 1,2 to .... n respectively
r = discount rate and
The above formula will be applied for both even and uneven cash inflow series.

Example: Let us calculate the present value of the following stream of cash inflows, if discounted at 12%.

Year 1 - $5,000; Year 2 - $4,000; Year 3 - $3,000; Year 4 - $2,000 and Year 5 - $1,000. All the cash inflows would be received at the end of the respective years.

Year Cash inflows Present Value factor @ 12% Present value of Cash inflows @ 12%
 1 $ 5,000 0.8929 $ 4,464.50
 2 $ 4,000 0.7972 $ 3,188.80
 3 $ 3,000 0.7118 $ 2,135.40
 4 $ 2,000 0.6355 $ 1,271.00
 5 $ 1,000 0.5674 $ 567.40
Total PV $ 11,627.10

(The PV factors at 12% have been worked out thus: 1/(1 + 0.12)1 = 0.8929; 1/(1 + 0.12)2 = 0.7972 and so on for 5 years period. These factors will also be provided in the Present value table.)

Thus, the sum of all the present value works out to $11,627.10. If this sum exceeds the initial investment, the project would be considered for acceptance.


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