Copyright © 2008, The McGraw-Hill Companies, Inc.
14.1 The Present Value Method 569The rate for the bowling alley would then be 18% 2% 16%. The rate for the solar
business would be 18% 8% 10%.Bowling alley: PV _____PMTi
$8,000
___0.16 $50,000
Solar business: PV _____PMTi
$5,000
___0.10 $50,000
A higher expectation of profits means that future profits are discounted more heavily. So in this
case, the much higher rate of return that I demand on my investment means that the higher prof-
its in the near term count more heavily in my thinking. Note, though, that, with a higher required
rate of return, the amount I would be willing to put up today for each business is also quite a bit
lower. While the 18% required rate of return equalizes the present value of these two opportuni-
ties, it also means that neither one of them would be worth the $100,000 up-front investment.
Spreadsheets (covered in Chapter 5) can also be used as a tool for finding present values.
While we will not discuss their use here, the Additional Exercises for this section present
a few examples where spreadsheets may be the preferable means of evaluation.Net Present Value
So far, we have assumed that any two business opportunities we are comparing have the
same up-front costs, so whichever one offers the higher present value is preferable. What
if the two options have different costs?
The net present value of a series of payments is the difference between the present
value of the expected income less the present value of the expected investment. The fol-
lowing example will illustrate how net present value may be used.Example 14.1.5 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?The bowling alley’s investment of $65,000 is less than the present value of its projected
profi ts. This is refl ected in a positive net present value of $80,000 $65,000 $15,000.The solar business’s investment of $175,000 is greater than the present value of its pro-
jected profi ts. This is refl ected in a negative net present value of $125,000 $175,000
$50,000.On the basis of this assessment, the bowling alley is the more fi nancially attractive investment
option.Calculations and interpretations of net present values can become quite involved. If a busi-
ness opportunity requires both an initial investment and also additional future investments,
for example, we would need to calculate the present value of the investments as well as
the present value of the projected income. If the future investments and/or future projected
income varies, the present value calculations can require quite a bit of effort.
The net present value can also be a bit misleading. While the solar business had a negative
net present value, this does not mean that it is a losing proposition. It only means that with
a 12% required rate of return, the projected cash flows do not justify the $175,000 invest-
ment. The investment may still be profitable, but just does not produce a 12% rate of return.
The actual rate of return that it does produce is referred to as the projected rate of return.
Projected rates of return are another useful tool in evaluating business opportunities.
The mathematics of these sorts of evaluation is both challenging and interesting, and of
great importance in the business world. A more thorough treatment of these methods lies
beyond the scope of this book, however. Students who wish to study this in greater depth
may want to pursue reading and/or course work in finance.