Explanation

The PV function is a financial function that returns the present value of an investment. You can use the PV function to get the value in today’s dollars of a series of future payments, assuming periodic, constant payments and a constant interest rate. An annuity is a series of equal cash flows, spaced equally in time

In this example, an annuity pays 10,000 per year for the next 25 years, with an interest rate (discount rate) of 7%. The PV function is configured as follows in cell C9:

=PV(C5,C6,C4,0,0)

The inputs to PV are as follows:

  • rate - the value from cell C7, 7%.
  • nper - the value from cell C8, 25.
  • pmt - the value from cell C6, 100000.
  • fv - 0.
  • type - 0, payment at end of period (regular annuity).

With this information, the present value of the annuity is $116,535.83. Note payment is entered as a negative number, so the result is positive.

Annuity due

With an annuity due, payments are made at the beginning of the period, instead of the end. To calculate present value for an annuity due, use 1 for the type argument. In the example shown, the formula in F9 is:

=PV(F7,F8,-F6,0,1)

Note the inputs (which come from column F) are the same as the original formula. The only difference is type = 1.

Explanation

In this example, the goal is to calculate the required recovery rate (or gain) to complete offset a loss expressed as a negative percentage. This is not a difficult problem, but you must pay attention to the sign of the loss and be sure to format the result with the percentage number format .

Background

One of the most important aspects of investing is the math of gains and losses. A 50% loss does not require a 50% gain to recover the loss, it actually requires a 100% gain . Put simply, as a loss gets larger (as a percentage), the recovery rate (or gain), required to offset the loss increases at an increasing rate :

  • A loss of 10% requires a gain of 11.1%
  • A loss of 20% requires a gain of 25%
  • A loss of 50% requires a gain of 100%
  • A loss of 80% requires a gain of 400%

Formula

With a loss expressed as a percentage, you can calculate the required gain or recovery rate with a formula like this:

=1/(1-%loss)-1

The formula above assumes the loss is given as a positive percentage. If the loss is given as a negative percentage (as in the worksheet shown), use the modified formula below:

=1/(1+%loss)-1

In the worksheet shown, the loss percentages are in column C. The formula in F5, copied down, is:

=1/(1+C5)-1

This formula evaluates like this:

=1/(1+-0.05)-1
=1/(0.95)-1
=1.0526-1
=0.0526
=5.3%

The result is a decimal value that should be formatted with the percentage number format .

Formula check

To check the calculated recovery rate for each loss, the formula in G5, copied down, is:

=D5*(1+F5)

This formula simply multiples the result in column D by 1 plus the recovery rate. In all cases, it should return the initial value in column B, proving that the recovery rate will completely offset the loss.