PART 1: INTRODUCTION
The future value of the annuity due is greater because its cash flow occurs at the beginning of each
period, not at the end. In our illustration, by shifting each saving date one year earlier, you earn about
$400 more with the annuity due and could enjoy a somewhat more luxurious vacation.CONCEPT REVIEW QUESTIONS 3-5
8 Why is the future value of an ordinary annuity generally less than the future value of an identical
annuity due?9 Once you know the future value of an ordinary annuity, it is easy to calculate the future value of an
identical annuity due. Explain.3-6 PRESENT VALUE OF CASH FLOW
STREAMS
Many decisions in corporate finance require financial managers to calculate the present values of cash
flow streams that occur over several years. In this section, we show how to calculate the present values
of mixed cash flow streams and annuities. We also demonstrate the present-value calculation for a very
important cash flow stream known as a perpetuity.3-6a FINDING THE PRESENT VALUE OF A MIXED STREAM
The present value of any cash flow stream is merely the sum of the present values of the individual cash
flows. To calculate the present values of all kinds of cash flow streams, we can apply the same techniques
we used to calculate present values of lump sums.Shortly after graduation, you receive an inheritance
that you use to purchase a small bed-and-breakfast
hotel. Your plan is to sell the hotel after five years.
The hotel is an old mansion, so you know that
appliances, furniture and other equipment will wear
out and need to be replaced or repaired on a regular
basis. You estimate that these expenses will total
$4,000 during year 1, $8,000 during year 2, $5,000
during year 3, $4,000 during year 4 and $3,000
during year 5, the final year of your ownership. For
simplicity, assume that these expenses will be paid at
the end of each year.Because you have some of your inheritance
left over after purchasing the hotel, you want to
set aside a lump sum today from which you can
make annual withdrawals to meet these expenses
when they come due, as shown on the time line in
Figure 3.10. Suppose you invest the lump sum in a
bank account that pays 9% interest. To determine
the amount of money you need to put into the
account, you must calculate the present value of
the stream of future expenses, using 9% as the
discount rate.example