Future Value Annuity (FVA)
Future value of an annuity is the future value of a stream of payments, presuming the payments are invested at a given rate of interest.
If an investor select an option say A and invest the total amount at a simple annual rate of 4.5%. The future value of the investment at the end of the first year is $10,450. This value is computed by multiplying the principal amount by the interest rate and adding the interest gained to the principal amount as mentioned below:
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Future value of investment at end of first year:
= ($10,000 x 0.045) + $10,000
= $10,450
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Investor can also compute the total amount of a one-year investment with a simple modification of the above defined equation:
The original equation is : ($10,000 x 0.045) + $10,000 = $10,450
The modification is: $10,000 x [(1 x 0.045) + 1] = $10,450
Here investor can see the final equation: $10,000 x (0.045 + 1) = $10,450
The modified equation is merely a removal of the alike-variable $10,000 by dividing the complete original equation by $10,000.
Computation of future value of investment at end of second year
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Future value of investment at end of second year:
= $10,450 x (1+0.045)
= $10,920.25
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The above computation is equivalent to the following equation:
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Future Value = $10,000 x (1+0.045) x (1+0.045)
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Internal Rate of Return (IRR)
The internal rate of return is the rate of return employed in capital budgeting to evaluate and equate the profitable of investments. It is also referred as the discounted cash flow rate of return or DCFROR. In the case of loans and savings it is also referred as the effective interest rate. The term internal cites to that the computation does not comprise environmental factors such as the rate of interest or inflation.
The internal rate of return on an investment is the annualized effective compounded return rate or also referred as rate of return. It makes the net present value (Net Present Value as NET*1/(1+IRR)^year) of all cash flows for both positive and negative from a particular investment equivalent to zero.
In more particular terms, the internal rate of return of an investment is the discount rate at which the net present value of costs with negative cash flows of the investment is equal to the net present value of the gains i.e positive cash flows of the investment.
Internal rates of return are normally employed to evaluate the desirableness of investments. The higher the internal rate of return, it is desirable to undertake the project to a greater extent. It is assumed that all projects require the equivalent amount of up-front investment. The project with the highest internal rate of return would be regarded as best and undertaken first.
A firm or an individual should, undertake all investments or projects available with the internal rate of return that surpass the cost of capital. Investment may be fixed by:
i) Available of funds to the firm
ii) The capacity or power of a firm to manage numerous projects.
The internal rate of return is a rate quantity, it act as an indicator of the, quality, yield and efficiency of an investment. This is in direct contrast with the net present value. Net present value indicates the value or magnitude of an investment.
An investment is regarded acceptable if its internal rate of return is greater than an demonstrated minimum acceptable cost of capital or rate of return. In a play script where an investment is regarded by a firm that has equity holders. The minimum rate is the cost of capital of the investment which may be decided by the risk-adjusted cost of capital of mutually exclusive investments. This guarantees that the investment is backed up by equity holders. In general, since an investment whose internal rate of return surpasses its cost of capital adds value for the company and is economically profitable.
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