Fundamentals of Financial Management (Concise 6th Edition)

140 Part 2 Fundamental Concepts in Financial Management

N I/YR PV PMT FV

6 0 –1200 10000 End Mode

6.96

With these smaller deposits, it would take 6.96 years to reach the $10,000 target. If

you began the deposits immediately, you would have an annuity due and N would

be a bit less, 6.63 years.

5-10c Finding the Interest Rate, I

Now suppose you can save only $1,200 annually, but you still want to have the

$10,000 in 5 years. What rate of return would enable you to achieve your goal?

Here is the calculator setup:

N I/YR PV PMT FV

5 0 –1200 10000 End Mode

25.78

You would need to earn a whopping 25.78%. About the only way to earn such a

high return would be to invest in speculative stocks or head to the casinos in Las

Vegas. Of course, investing in speculative stocks and gambling aren’t like making

deposits in a bank with a guaranteed rate of return, so there’s a good chance you’d

end up with nothing. You might consider changing your plans—save more, lower

your $10,000 target, or extend your time horizon. It might be appropriate to seek a

somewhat higher return, but trying to earn 25.78% in a 6% market would require

taking on more risk than would be prudent.

It’s easy to! nd rates of return using a! nancial calculator or a spreadsheet.

However, without one of these tools, you would have to go through a trial-and-

error process, which would be very time-consuming if many years were involved.

SEL

F^ TEST Suppose you inherited $100,000 and invested it at 7% per year. How much

could you withdraw at the end of each of the next 10 years? How would your

answer change if you made withdrawals at the beginning of each year?

($14,237.75; $13,306.31)

If you had $100,000 that was invested at 7% and you wanted to withdraw

$10,000 at the end of each year, how long would your funds last? How long

would they last if you earned 0%? How long would they last if you earned the 7%

but limited your withdrawal to $7,000 per year? (17.8 years; 10 years; forever)

Your rich uncle named you bene! ciary of his life insurance policy. The insur-

ance company gives you a choice of $100,000 today or a 12-year annuity of

$12,000 at the end of each year. What rate of return is the insurance company

o# ering? (6.11%)

Assume that you just inherited an annuity that will pay you $10,000 per year for

10 years, with the! rst payment being made today. A friend of your mother of-

fers to give you $60,000 for the annuity. If you sell it, what rate of return would

your mother’s friend earn on his investment? If you think a “fair” return would

be 6%, how much should you ask for the annuity? (13.70%; $78,016.92)