Fundamentals of Financial Management (Concise 6th Edition)

146 Part 2 Fundamental Concepts in Financial Management

Finding the interest rate for an uneven cash " ow stream such as Stream 2 is a

bit more complicated. First, note that there is no simple procedure—! nding the

rate requires a trial-and-error process, which means that a! nancial calculator or a

spreadsheet is needed. With a calculator, we enter the CFs into the cash " ow regis-

ter and then press the IRR key to get the answer. IRR stands for “internal rate of re-

turn,” and it is the rate of return the investment provides. The investment is the

cash " ow at Time 0, and it must be entered as a negative. As an illustration, con-

sider the cash " ows given here, where CF 0! $$1,000 is the cost of the asset.

Periods 0 1 2 4

Cash "ows

3 5

!$1,000

IRR $ I $ 12.55%

$100 $300 $300 $300 $500

When we enter those cash " ows into the calculator’s cash " ow register and press

the IRR key, we get the rate of return on the $1,000 investment, 12.55%. You get the

same answer using Excel’s IRR function. The process is covered in the calculator

tutorial; it is also discussed in Chapter 11, where we study capital budgeting.

SEL

F^ TEST An investment costs $465 and is expected to produce cash " ows of $100 at

the end of each of the next 4 years, then an extra lump sum payment of $200

at the end of the fourth year. What is the expected rate of return on this in-

vestment? (9.05%)

An investment costs $465 and is expected to produce cash " ows of $100 at

the end of Year 1, $200 at the end of Year 2, and $300 at the end of Year 3.

What is the expected rate of return on this investment? (11.71%)

5-15 SEMIANNUAL AND OTHER COMPOUNDING PERIODS

In all of our examples thus far, we assumed that interest was compounded once a

year, or annually. This is called annual compounding. Suppose, however, that you

deposit $100 in a bank that pays a 5% annual interest rate but credits interest each

6 months. So in the second 6-month period, you earn interest on your original

$100 plus interest on the interest earned during the! rst 6 months. This is called

semiannual compounding. Note that banks generally pay interest more than once

a year; virtually all bonds pay interest semiannually; and most mortgages, student

loans, and auto loans require monthly payments. Therefore, it is important to

understand how to deal with nonannual compounding.

For an illustration of semiannual compounding, assume that we deposit

$100 in an account that pays 5% and leave it there for 10 years. First, consider again

what the future value would be under annual compounding:

FVN! PV(1 " I)N! $100(1.05)^10! $162.89

We would, of course, get the same answer using a! nancial calculator or a

spreadsheet.

How would things change in this example if interest was paid semiannually

rather than annually? First, whenever payments occur more than once a year, you

must make two conversions: (1) Convert the stated interest rate into a “periodic

rate” and (2) convert the number of years into “number of periods.” The

Semiannual

Compounding

The arithmetic process of

determining the final

value of a cash flow or

series of cash flows when

interest is added twice a

year.

Semiannual

Compounding

The arithmetic process of

determining the final

value of a cash flow or

series of cash flows when

interest is added twice a

year.

Annual Compounding

The arithmetic process of

determining the final

value of a cash flow or

series of cash flows when

interest is added once a

year.

Annual Compounding

The arithmetic process of

determining the final

value of a cash flow or

series of cash flows when

interest is added once a

year.