When a fixed stream of payments is received at the beginning of each period, you would utilize the concept of the present value of an annuity due; to solve such a problem, you would multiply the present value factor by (one plus the discount rate) and then multiply that by the amount of the annuity. When a fixed stream of payments is received at the end of each period, just use the present value of annuity factor.
Here's a problem that I use for one of my classes when we cover time value of money (first using present value of an annuity, and then present value of an annuity due):
PRESENT VALUE OF AN ANNUITY: On January 1, Year 1, Harry Dunne won the state lottery, with a grand prize of $10,000,000 (tax effects not considered in this problem). However, this amount cannot be claimed in a “lump sum” but will be distributed to Mr. Dunne over a twenty year period at the end of each year. Mr. Dunne meets with a financial advisor, who believes that the time value of money is 7%. How much is Harry Dunne’s grand prize actually worth today?
1) What is the question asking?
How much are annual payments (an annuity) of $500,000 for twenty years actually worth today?
2) How to solve?
First, calculate the annuity ($10,000,000 / 20 = $500,000 per year). Second, note when the amount will be paid (beginning or end of the period; in this case it is the end). Then find the factor to use from the present value of an annuity table for twenty periods at a rate of 7%.
3) Solve the problem:
$500,000 * 10.5940 = $5,297,000
PRESENT VALUE OF AN ANNUITY DUE: Use the same information as before, except assume that the amounts will be paid at the beginning of each year (period) instead of the end).
In this case, you still use the present value of an annuity table, but you must multiply the given factor by (1 + i), where “i” is the interest rate (time value of money). For this problem, it would be as follows:
10.5940 * (1 + 0.07) = 10.5940 * 1.07 = 11.33558
Then, use this figure to solve:
$500,000 * 11.33558 = $5,667,790
Obviously your present value of an annuity due should always be greater than that of a present value of an annuity, as you are receiving the amount at the beginning of the period as opposed to the end, and hence have the entire period in which your discount rate is applied to the principal amount.
.