 # Investment Finance: Understanding Present Value

Present value is a term used in financial mathematics, and refers to the present value of the future payments. It is calculated by discounting the future payments. There is also the concept of the actuarial present value, which is a generalization of the present value.

A common application of the present value formula, using the yield on a fixed-rate loan calculates the price. If a bond has a face value (redemption value) of 100 for a period of T years, and pays them an annual coupon of c (in percentage), (the whole number T of years) the present value of the actuarial value of the interest payments and repayment; calculated in the simplest case –

PV = \ frac (100c) ((1 + z)) + \ frac (100c) ((1 + z) ^ 2) +…+ \ frac (100c) ((1 + z) ^ T) + \ frac (100) ((1 + z) ^ T)

If the time until the first coupon payment is less than a year, it contains the present value of pro rata accrued interest on the first coupon and is called the ‘dirty price’. If one of the dirty price from the pro rata interest accrues, this results in the so-called ‘clean price’.

An annuity (or pension) is known in financial mathematics as a constant periodic payment. If such payment is not limited to a period, but runs indefinitely for too long, this is called a perpetuity. Cash flow analysis play a major role in the financial world, including the assessment of the assets of pension funds.

It is sometimes quite complex to calculate the present value of several different periods, using formulas in circulation. The starting point is always the same: a translation of the value of a future amount (its worth). Spreadsheets have a number of built-in formulas to perform cash-flow models.

Present value of amounts payable are calculated in the same way. In this way, the impact of spending and revenues occurring at different times are compared. The present value of costs to be deducted from the cash value of the revenue, creates the net present value (NPV).

For an example, an investment plan provides for the purchase of a machine that takes X years to be paid. And an expected yield of Y per year for five years. And when the machine is worn, the scrap value is probably still Z.

Whether this investment will translate into profits, is a matter determined by relevant calculations, with full considerations of the time aspect. As such, the present value of each cash flow (revenue or expenditure) is calculated, and the balance thereof is the net present value.

During long periods, small changes in the discount rate lead to a big difference in the discounted future value of the same amount. In fact, the uncertainty that exists about future interest and inflation developments is hard a problem to solve. In assessing a present value it is therefore important not only to know the cash value itself, but also the discount rate.

The question of what discount rate is correct, is dependent on the period for which an amount is discounted, and the personal circumstances of the individual or entity making the calculation. An individual can particularly take into account the interest rates on savings deposits for maturities.

An insurance company will (among other things) look at the expected return on investment, assessing the duration and the degree of risk that one wishes to accept in an investment.

While a pension fund takes into considers the expected inflation, and an ordinary commercial enterprise will attach importance to the interest that its bank charges for commercial loans.