Annuities II - Annuity Due

What is an annuity due? It is an annuity wherer the first payment is made immediately (think of it as a down-payment). An example might be a long term lease, where the first payment is due at the beginning of the lease term.

You will not encounter annuities due too often in accounting, but they do crop up sometimes and it is necessary to know what to do.

Remember, the only difference between an ordinary annuity and an annuity due is that payments are made at the beginning of the period, not at the end of the period. However, since the end of period 1 is simultaneously the beginning of period 2, it is really only the first payment that causes problems:

Question:

what is the present value of three payments of $100 each. The payments will be received at the beginning of this year (now) and at the beginning of each of the next two years. We want to earn 10% interest on our investment.

Option 1:

We could express this as follows:

	receive	PV	Factor	answer:
beginning of year 1	$100.00	(10%,0)	1	$100.00
beginning of year 2	$100.00	(10%,1)	0.9091	$90.91
beginning of year 3	$100.00	(10%,2)	0.8264	$82.64
				$273.55

Notice what happend: The first payment has a present value of $100 because it is received NOW. The other two payments are discounted as of the end of the first period and second period respectively.

Option 2: (that's what we really want to use)

Using the PV factor for an annuity due (D39, Nikolai): 2.735537

$100 * PVa due (3,10%) = $100 * 2.735537 = $273.55

Note the PV factor for an annuity due (D39, Nikolai): 2.735537. It is determined exactly like ordinary annuity factors by adding up the individual present value factors Because of the fact that payments are received earlier, the present value of an annuity due is always higher than the present value of an ordinary annuity:

Ordinary annuity (payment received a the end of the first period)

$ 100 * PVa (3, 10%) =
$ 100 * 2.486852 = $248.69

Annuity due: Payment received at the beginning of the first period:

$ 100 * PVa due (3, 10%) =
$ 100 * 2.735537= $273.55

What to do if you do not have access to a present value factor table for annuities due (or calculator)? No problem, the factor can easily be calculated as follows: (Using the table on D38)

PVa due (10%,3) = 1 + PVa (10%,3) = 1 + 1.735537 = 2.735537

This is all you need to know of present value for accounting for now. BUT You really, really need to know this. Therefore go on to the examples and then practice, practice, practice.

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