Finance: Time Value Concept Of Money
TIME VALUE CONCEPT OF MONEY
In continuation to my earlier post where i tried to explain some of the economy concepts, here i continue with some new concepts..Time value of money.
Time value of money, which serves as the foundation for many concepts in finance, arises from the concept of interest. Because of interest, money on hand now is worth more than the same money available at a later point of time. To understand time value of money and related concepts like Present value and future value,
we need to understand the basic concepts of simple andcompound interest.
Future Value
Future Value is the value that a sum of money invested at compound interest will have after a
specified period.
The formula for Future Value is:
FV = PV*(1 + i)n
Where:
FV : Future Value at the end of n time periods
PV : Beginning value OR Present Value
i : Interest rate per unit time period
n : Number of time periods
Example
If one were to receive 5% per annum compounded interest on $100 for five years,
FV = $100*(1.05)5 = $127.63
Intra-year compounding
If a cash flow is compounded more frequently than annually, then intra-year compounding is being used. To adjust for intra-year compounding, an interest rate per compounding period must be found as well as the total number of compounding periods. The interest rate per compounding period is found by taking the annual rate and dividing it by the number of times per year the cash flows are compounded. The total number of compounding periods is found by multiplying the number of years by the number of times per year cash flows are compounded.
Example
Suppose someone were to invest $10,000 at 8% interest, compounded semiannually, and hold it
for five years.,
Interest rate for compounding period = 8%/2 = 4%
Number of compounding periods = 5*2 = 10
Thus, the future value FV = 10,000*(1+0.04)^10 = $14,802.44
Present value
Present Value is the current value of a future cash flow or of a series of future cash flows. It is computed by the process of discounting the future cash flows at a predetermined rate of interest. If $10,000 were to be received in a year, the present value of the amount would not be $10,000 because we do not have it in our hand now, in the present. To find the present value of the future $10,000, we need to find out how much we would have to invest today in order to receive that $10,000 in the future. To calculate present value, or the amount that we would have to inves today, we must subtract the (hypothetical) accumulated interest from the $10,000. To achieve this, we can discount the future amount ($10,000) by the interest rate for the period. The future value equation given above can be rearranged to give the Present Value equation:
PV = FV / (1+I)^n
In the above example, if interest rate is 5%, the present value of the $10,000 which we will
receive after one year, would be:
PV = 10,000/(1+0.05) = $ 9,523.81
Net Present Value (NPV)
Net Present Value (NPV) is a concept often used to evaluate projects/investments using the Discounted Cash Flow (DCF) method. The DCF method simply uses the time value concept and discounts future cash flows by the applicable interest rate factor to arrive at the present value of the cash flows. NPV for a project is calculated by estimating net future cash flows from the project, discounting these cash flows at an appropriate discount rate to arrive at the present value of future cash flows, and then subtracting the initial outlay on the project.
NPV of a project/investment = Discounted value of net cash inflows – Initial cost/investment.
The project/investment is viable if NPV is positive while it is not viable if NPV is negative. Example An investor has an opportunity to purchase a piece of property for $50,000 at the beginning of the year. The after-tax net cash flows at the end of each year are forecast as follows:
Year Cash Flow
1 $9,000
2 8,500
3 8,000
4 8,000
5 8,000
6 8,000
7 8,000
8 7,000
9 4,500
10 51,000 (property sold at the end of the 10th year)
Assume that the required rate of return for similar investments is 15.00%.
NPV = - 50000 + 9000/(1+0.15)^1 + 8500/(1+0.15)^2 + ….. +51000/(1+0.15)^10 = $612.96
However, if we assume that the required rate of return is 16.00%,
NPV = - 50000 + 9000/(1+0.16)^1 + 8500/(1+0.16)^2 + ….. +51000/(1+0.16)^10 = ($1360.77)
Thus, it can be seen that the NPV is highly sensitive to required rate of return. NPV of a project:
· Increases with increase in future cash inflows for a given initial outlay
· Decreases with increase in initial outlay for a given set of future cash inflows
· Decreases with increase in required rate of return.
Hope it helps,
Regards,
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