# How to Calculate an Equivalent Cash Price

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An equivalent cash price equals the amount of a down payment plus the present value of a stream of fixed, future payments. An equivalent cash price converts the total payments of a payment plan into a single value in today’s dollars, which you can use to compare payment plans with all-cash purchases. If your business offers a payment plan on a product, you can calculate an equivalent cash price to determine the equivalent amount of cash you would receive if a customer paid upfront for the product instead of making payments over time.

Determine the amount of a down payment you will receive from the sale of a product. Determine the amount of each fixed payment you will receive in the future, the interval at which you will receive them, the number of years for which you will receive them and the rate of interest you could earn if you were to invest the payments. For example, assume you agree to receive a \$200 down payment and a \$1,000 annual payment for two years for selling a car. Assume that you could earn 4 percent interest if you reinvested those payments.

Substitute the values into the present value of an ordinary annuity formula: PMT x [(1 - (1 + r)^-n)/r]. In the formula, PMT represents the amount of each payment, r represents the periodic interest rate and n represents the number of payments you will receive. In this example, substitute the values to get \$1,000 x [(1 - (1 + 0.04)^-2)/0.04].

Solve the numerator in the brackets. In this example, solve 1 - (1 + 0.04)^-2 to get 0.07544. This leaves \$1,000 x (0.07544/0.04).

Divide the numerator by the denominator in parentheses. Then multiply the result by the amount of the payment to determine the present value of the fixed payments. In this example, divide 0.07544 by 0.04 to get 1.886. Multiply 1.886 by \$1,000 to get a present value of \$1,886.

Add together the amount of the down payment and the present value of the fixed payments to calculate the equivalent cash price. Continuing with the example, add \$200 and \$1,886 to get an equivalent cash price of \$2,086. This means that the price of the car would be \$2,086 if the buyer were to pay all cash at the time of the sale.

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