# How to Calculate an Equivalent Cash Price Brand X Pictures/Brand X Pictures/Getty Images

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An equivalent cash price of a product is the amount of the down payment plus the value of all future, fixed-amount payments. Calculate the equivalent cash price to compare the cost of an all-cash purchase with the same product paid for over time.

## Using the Ordinary Annuity Formula

Use the ordinary annuity formula to figure out the cash equivalent price of a product. You're essentially looking at present value versus future value. The cash price formula allows you to convert the future value to a present value so you can, in effect, compare apples to apples.

#### Tips

• An ordinary annuity is a series of equal payments made over a fixed length of time. Ordinary annuities are paid at the end of the specified period, such as monthly or quarterly. An annuity due, by contrast, is a payment that must be made at the beginning of a period.

The ordinary annuity formula is used to calculate the present value. It takes into consideration what your money could be earning if it were available for you to invest. The ordinary annuity formula uses three variables:

• PMT = the amount of each payment
• r = the interest rate per period
• n = the total number of periods

Present Value = (PMT)(r)(n)

You multiply the amount of each payment by the number of payments and then figure the amount of interest you would earn on that money.

If a customer gives you a down payment on an item, that's part of the present value. You don't calculate interest on it because it's money that you already have in hand. You can, of course, invest it, but any interest earned on the down payment is considered part of the future value, not part of the present value.

## Example of Cash Price Formula

As an example, suppose you sell a piece of equipment for \$13,000. You take a down payment of \$1,500. The customer pays the balance of \$11,500 over two years, making four equal payments of \$2,875 each. Assume you could earn 5% interest annually if you reinvested the payments.

• PMT = \$2,875
• r = 5% interest (.05)
• n = 4 total payment periods

Present value = \$1,500 down payment + (\$2,875 x 4 payments)(0.05)

## Calculating Compound Interest

The above formula does not take compound interest into account. If you earn 5% interest annually on payments, you're earning on the amount of the two payments the first year. The second year, you're earning interest on the two payments already made plus the interest they earned; it's essentially interest on the interest. You also earn interest on the second year's payments.

Here's the formula for compound interest:

A = P(1 + r/n)^nt

• A = Accrued amount (principal plus interest)
• P = Principal amount
• I = Interest amount
• r = Interest rate as a decimal
• t = time in years
• n = number of compounding periods

In the above example, A = \$12,678.75. On the principal amount of \$11,500, you'd earn \$1,178.75 in interest over the two-year payment period, when the rate of 5% compounds annually.

The present value of the equipment that you sell is the amount of the down payment plus the amount of equal installment payments and the interest you'd earn. If you sell the equipment for cash, you'd get \$13,000. With the down payment and installment plan outlined in the example, you'd earn \$14,178.75.

## Cash and Cash Equivalents as an Accounting Tool

Cash and cash equivalents is a line item on a balance sheet. It states the amount of cash available along with items that are readily convertible into cash. Cash and cash equivalents are classified as current assets. Analysts sometimes use cash and cash equivalents information to compare a company's current liabilities to its ability to pay its bills in the short term.

Examples of cash include:

• Bank drafts
• Cash in checking and savings accounts
• Coins
• Currency
• Money orders
• Petty cash

Cash equivalents have a short-term maturity date, typically three months or less. Examples include:

• Commercial paper (unsecured, short-term debt instruments such as used to finance payroll and accounts payable)
• Marketable securities
• Money market funds
• Short-term government bonds
• Treasury bills