Present Value of Single / Multiple Cash Flows
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
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 PV’s 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 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.
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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