The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

579

CHAPTER 14

SUMMARY

Topic Key Ideas, Formulas, and Techniques Examples

The Present Value

Method, p. 565

• To compare two different streams of future
  payments, calculate their present values and
  choose the higher present value.


• Which choice will be preferred depends on the
  interest rate used for the calculation.

Using present values and an 8.5%

rate, would you prefer a business

opportunity that could be expected

to earn $5,000 per year for 5 years

or an investment that would pay

$32,000 all at once at the end of

5 years?

(Example 14.1.1)

Perpetuities, p. 566 • The present value of a stream of payments that

continues indefi nitely is given by:

PV 
 PMT_____i

Find the present value of a $7,500

per year perpetuity assuming an

interest rate of 8%.

(Example 14.1.2)

The Present Value

Method with Increasing

Payments, p. 568

• Calculate the present value, using a rate equal
  to the required rate of return less the projected
  growth rate.

An investment in a bowling alley is

expected to return $8,000 in the

fi rst year, growing at a 2% annual

rate. An investment in a solar

installation business is projected

to return $5,000 in the fi rst year,

growing at an 8% rate. Which

option has the higher present value

assuming an 18% required rate of

return?

(Example 14.1.4)

Net Present Value, p. 569 • To fi nd the net present value, subtract the

present value of the investment payments from

the present value of the projected income.

At a 12% rate of return, we

determined that the present value

from the bowling alley would be

$80,000 and the present value

from the solar installation business

would be $125,000.

Suppose that you can buy this

share of the bowling alley business

for $65,000, while the solar

installation business would require

a $175,000 up-front investment.

Which investment option is more

attractive?

(Example 14.1.5)

Payback Period, p. 572 • P 
 __I

R^

• Payback period is the time required for
  investment to provide a return equal to its costs.

To dd has a no-contract cell phone.

He pays no monthly or annual

fee, but pays a fl at 20 cents per

minute used. He is considering

signing up for a contract that offers

800 minutes per month and costs

$47.99 per month. He knows that

he will never actually use the full

800 minutes, but wonders how

many minutes he would need to

use for it to be worth signing up for

the new plan.

(Example 14.2.2)