How do you calculate the present value
Present value method example calculation - this is how you calculate the current value
In order to be able to decide which investment makes sense, investors need to be able to compare future payouts. So how much is a payout worth today in, say, 2 years?
The present value method is a good decision-making aid. With the present value method, the future amounts of money are discounted using a capital interest rate that corresponds to the interest rate that the investor would have received had an alternative investment.
More on the subject:Use the present value to calculate the pension capital you need.
The present value (PV) is therefore of great importance in the valuation of companies and the determination of the profitability of investments and receivables.
Formula for the present value
Present value formula for one-time payment:
The cash value can be used, for example, to determine how much a payment of 500,000 euros, which will only be due in 5 years, would be worth now.
To do this, it is necessary to set an interest rate (discount rate) for an alternative capital investment. This results in the following parameters for the formula:
PV = present value at the present time
Z = future payment
r = yield (discount rate)
n = investment period
Present value of a one-time payment
In a company with 2 shareholders - Hansel and Gretel - Gretel would like to leave her contract early and receive her full payment that she would be entitled to at the end of the contract.
According to the contract, she would have to work for another 5 years and would then receive a one-off payment of 500,000 euros. Hansel agrees, but is not prepared to pay out the full amount.
Because the 500,000 euros have a different value today than they will have in 5 years. Hänsel assumes a discount rate of 4 percent. The question now is, what should the payout amount be today?
The present value of 500,000 euros is:
PV = 500,000 / (1 + 0.04)5 = 410,963.55 euros
The present value of 500,000 euros in 5 years corresponds to a value of 410,963.55 euros. It is therefore clear to Hansel that he only pays out € 410,963.55 to Gretel immediately.
Present value of multiple payouts
Instead of a one-off payment, investors can also receive multiple payments (called cash flow).
More on the subject:Cash flow - what is it and how is it calculated?
The present value formula can therefore also be used for related cash flows, for example to determine the price of a fixed-interest bond.
The cash values of all payments are to be calculated individually and then added to the repayment (nominal value).
In the following example we assume a coupon (c) or an interest payment of 4 percent per year for a 5-year bond.
The investor can have this paid out annually at the nominal value (N) of 100. The market interest rate (z), on the other hand, is 5 percent.
PV = c / (1 + z) + c / (1 + z)2 +… + C / (1 + z)n + N / (1 + z)n
PV = 4 / (1.05) + 4 / (1.05)2 + 4 / (1,05)3 + 4 / (1,05)4 + 4 / (1,05)5 + 100 / (1,05)5
PV = 95.67 euros
The price of the bond should be 95.67 euros in order to do justice to the usual market interest rate of 5 percent.
How to calculate the present value of zero bonds The present value of zero bonds is quite easy to calculate. With it, an investor can assess the value of his investment. > read more
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