# Present Value

Question: Does the application of present value change substantially if cash is paid each year rather than as a

lump sum at the end of the term? What reporting is appropriate if an intangible asset is purchased by making a

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down payment today followed by a series of payments in the future?

To illustrate, assume a company acquires a copyright from an artist by paying \$10,000 on January 1, Year One,

and promising an additional \$10,000 at the beginning of each subsequent year with the final payment on January

1, Year Five. The total amount is \$50,000. No separate interest is paid. What is the historical cost to be reported

for this intangible asset and what interest should be recorded on the liability over these future years?

Answer: Although cash is conveyed over an extended period of time in this purchase, a reasonable rate of interest

is not being explicitly paid. Thus, once again, a present value computation is necessary to pull out an appropriate

amount of interest and leave just the cost of the asset. The present value of the payments (the principal) is the cash

paid after all future interest is mathematically removed. That process has not changed. Here, cash is not conveyed

as a single amount but rather as an annuity—an equal amount paid at equal time intervals. An annuity can be

either an ordinary annuity with payments made at the end of each period or an annuity due with payments starting

immediately at the beginning of each period.

The specific series of payments in this question creates an annuity due pattern because the first \$10,000 is

conveyed when the contract is signed. As before, a mathematical formula can be constructed to determine the

applicable present value factor6.

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