Created 7/1/1996
Go to
Brad DeLong's Home Page



Business Administration 130

Brealey and Myers, chapter 6: Making Better Investment Decisions with Net Present Value





What To Discount:

Now we are going to expand each of these principles

Only Cash Flow Is Relevant:

Largely ignore what accountants tell you. Accountants "accrue" things and "depreciate" things; they use a set of rules that were developed from the 15th to the early 20th centuries largely for purposes of control.

Count the money instead.

If taxes are relevant, be sure to count after tax cash flows. And be sure to take account of taxes only when they are paid, not when they hit the balance sheet.

Estimate incremental cash flows:

Include all incidental effects

Do not confuse average with incremental payoffs

Do not forget working capital requirements

Ignore sunk costs

Include opportunity costs (Storrow Drive in Boston; FDR Drive in NY; places where opportunity costs not considered).

Beware of allocated overhead costs (relevance lost, again); talk about Relevance Lost. Save on materials; but it shows up in quality control (or in returns and maintenance).

Treat Inflation Consistently:

(1 + r(nominal)) = (1 + r (real))(1 + inflation rate)

Do everything in one or the other (usually it doesn't matter which you use).

You cannot avoid making projections of all 3 rates--nominal, real, and inflation--and if you think you can avoid making projections of any one of them, you probably have missed something in your problem.


Brealey and Myers go through a long example, IM&C, with investment, depreciation, working capital impacts, salvage values, taxes and tax shields, and so forth. Let me skip over it here; but let me urge you to spend a lot of time on it--because it is a good thing to read to try to assess what you have missed at the end of this, the first unit of the course.

Project Interactions

Optimal timing of investment...

 Year 1 2 3 4 5 6 7 thereafter
 "Harvest" Now: $1000 $900 $810 $729 $656 x.9 x.9 x.9
 Build a road: -$100 $1300 $1170 $1053 $948 x.9 x.9 x.9
 Build and wait: -$100 0 $1500 $1350 $1115 x.9 x.9 x.9
 Build and wait 2 years:  -$100 0 0 $1600 $1440 $1296 x.9 x.9

with a discount rate of 10%, what do you do? Future value. Opportunity cost--should be defined to include the value of waiting, because then you can do something else...



Choosing between a long-lived and short-lived investment (discount rate of 6%):

 Machine  C(0) C(1) C(2) C(3) PV @ 6%
 A  -15 -5 -5 -5  -28.37
 B  -10 -6 -6  -21

Machine B has the lower cost, properly discounted; so you should buy machine B, right?

Wrong. What do you do in year 3? You have to convert a cost into a cost-per-year

Perhaps the best thing to do is to say that there are actually two things going on: first, you are in the machine purchase and rental business; second, you are in the business of producing goods and hence need to rent a machine...

Suppose that you are in the machine purchase-and-rental business. You need to set a rate X that earns you a fair return--a 0 NPV investment at the margin.

What is this rental price? Use your annuity formula: $10.61 for machine A; $11.45 for machine B;

Machine A looks cheaper, but:

Deciding when to replace an existing machine (at 6% interest)...

 C(0) C(1) C(2) C(3)
 Old Machine $4,000 $4,000 0 0
New Machine (Now) -$15,000 $8,000  $8,000 $8,000
New Machine (wait a year) -$15000 $8,000 $8,000, and same in year 4
New Machine (wait two years) -$15,000 $8,000, and same in 4 and 5

What do you do if you cannot use both the old machine and the new machine at the same time

(New machine now an NPV of $6,380, an equivalent 3-year annuity of $2,387)

Costs of using up excess capacity--and thus of accelerating machine replacement; even though it looks like all you are doing is using excess capacity, to the extent that you are imposing incremental costs they should be charged.

So to our three rules:

Add a fourth rule:

Perhaps this "recognize project interactions" is already contained in the idea of "opportunity cost" but it often isn't properly unpacked.

Possible interactions:


Adam Smith
Send e-mail to Brad DeLong

Return to Brad DeLong's Home Page

Return to Business Administration 130 Home Page