CHAPTER 1-2
       WEIGHING PRESENT VERSUS FUTURE BENEFITS (AND COSTS)

     Think of time as a measurement.  Indeed, the fundamental 
idea underlying Albert Einstein's theory of relativity is that, 
as he put it, "we understand by the 'time' of an event the 
reading [position of the hands] of...clocks" (Relativity, New 
York: Crown, (1921, p. 24).  
     Indeed, time is the most important measurement because the 
length of the period during which an event takes place measures 
how much pleasure or pain we will experience.  Furthermore, the 
time distance into the future measures how important the upcoming 
event is to us now. 
     John Locke viewed humans' relationship to time as the 
characteristic that most distinguishes us from the animals.  He 
spoke about "the great Creator, who [gave] to man an ability to 
lay up for the future as well as supply the present necessity" 
(CU News Gazette clipping in file).  Indeed, most important 
decisions have consequences in the future as well as in the 
present.  For example: 
     * Should the federal government build a dam in Happy Canyon? 
The difficulty in making such a decision is that the taxes 
required to pay for it would be levied now, while the benefits 
would only gradually accrue over many decades and even centuries. 
     * Should you go to graduate school and postpone earning 
income until two years from now, at which time you could expect a 
higher income than otherwise?  Or would you be better off working 
for the next two years rather than going to school?              
* Should your trucking firm buy a loading device that will cost 
you a pretty penny this year, but which will reduce labor costs 
for at least five years? 
     * Should you tell a lie which may get you out of a jam for 
the moment, but which will may have ill consequences on your 
reputation and conscience in coming months and years? 
     In each of these cases, the decision requires weighing 
benefits and costs that occur in different years.  A given amount 
of money does not have the same value when you possess it now 
versus only getting it in some future year.  Nor do non-monetary 
consequences have the same value for us if they will occur far in 
the future as if they were to occur now.  If this idea is not 
immediately obvious to you, ask yourself whether you would be 
willing to lend a hundred dollars to me now, and then get back 
from me the same amount five years from now.  (If the answer is 
yes, please express the money to me as soon as possible)  
     Please notice that your reluctance to lend me money and get 
back the same amount later has nothing to do with inflation; we 
could easily modify the arrangement to allow for inflation.  
Rather, you will not consider this a good deal because having the 
use of the money for the next five years has a value for you as 
well as for me, just as having the use of a farm for the next 
five years has value and the renter therefore pays for the right 
to do so.  
    The concept of time discounting enables us to handle all the 
above examples.  With the discounting device we can appropriately 
weigh the incomes and outgoes in various future periods, and then 
add the set of them into a single overall sum which is called the 
present value of the stream of future incomes and outgoes. This 
is the core idea in making decisions about investments and other 
actions taken in the present that will have ramifications long 
into the future.  Time discounting is the single most important 
and powerful idea in all of managerial decision-making. 
     Now let's get specific about how time discounting operates. 
The full name of the concept is "discounted net present value."  
The discount factor is the proportion of a sum next year that 
makes it equal in value to a smaller sum today.  That is, if the 
appropriate one-year discount factor is .80, a dollar one year 
from now is worth 80 cents today, and a dollar two years from now 
is today worth .64 (that is, .8 x.8) of a dollar.  The cost of 
capital (sometimes confusingly called the "discount rate") is the 
opposite side of the coin from the discount factor.  It is the 
proportion of the sum this year that you must pay to have the use 
of the money until next year.  If the price of using 80 cents for 
a year is 20 cents, so that you will pay back a dollar next year, 
the cost of capital is 25 percent. That is, a cost of capital of  
discount factor of .80.  These are two names for the same idea. 
The definition of present value:  Present value of a given 
alternative equals
(Expected revenue from the given alternative in the first year)

     minus

(Expected expenditures on the given alternative in the first 
year)

     plus

(Expected revenue in the second year, multiplied by the one-year 
discount actor)

     minus

(Expected expenditure on the given alternative in the second 
year, multiplied by the one-year discount factor)

     plus

(Expected revenue from the alternative in the third year, 
multiplied by the two-year discount factor--i.e., the one-year 
discount factor multiplied by itself)

     minus

(Expected expenditure in the third year, multiplied by the two-
year discount factor)

     plus

(Expected revenue in each subsequent year, each multiplied by its 
appropriate discount factor)

     minus

(Expected expenditure in each subsequent year, each multiplied by 
its appropriate discount factor)

     plus

(The expected market value of nonmonetary assets at the end of 
the decision horizon, discounted to the present)

     minus

(Market value of nonmonetary assets at present)

     Let us work an illustration showing how the present value is 
computed.  Please notice how the choice of the discount factor 
can affect which alternative should be chosen as best.  
     Consider a situation in which an owner of a new patented 
item has a choice of selling the item gradually over a period of, 
say, three years (after which time we assume demand falls to zero 
because this is an item people buy only once), or of tooling up 
in a hurry, selling them all at once in the first year, and then 
closing up the business.  Assume that the revenues and 
expenditures under the two alternatives are as follows: 
                   TABLE 2-1 (FROM AME P. 17)

where Pt=0 is the price of Qt=0 is the quantity that is expected to 
be sold.
     If the appropriate discount factor is .95, the present 
values of the two alternatives will be as follows:

     V1,T=0 = ($50,000 - $20,000 = $30,000
     V2,T=0 = ($20,000 - $13,000) + ($20,000 - $5,000)
     + (20,0002 - $5,0002)
       = ($20,000 - $13,000) + [($20,000 * .95) - (5,000 * .95)]
     + [($20,000 * .952) - ($5,000 * .952)]
       = $7,000 + (15,000 * .95 + (15,000 * .952) =       $34,787

With a .95 discount factor, alternative 2 is clearly better, 
yielding the higher present value.  But now consider the results 
if the appropriate yearly discount factor is .50 rather than .95: 

     V1,T=0 = $50,000 - $20,000 = $30,000
     V2,T=0 = $7,000 + ($15,000 * .5) + ($15,000 * .502) = $18,250.

If a .50 discount factor is appropriate, the first alternative is 
clearly better and should be chosen. 
     The unrealistically high and low discount factors for the 
examples in Table 2-1 were chosen to bring out the point that the 
appropriate choice often depends upon the discount factor used in 
the calculation.  
     Another example:  Fenster says that if you will lend him 
$10,000 to help start a print shop, he will pay you back $1,800 
per year for the next ten years.  He will pledge his house as 
security and (based on his character, as well as on the value of 
the house), you figure that there is almost as little risk of not 
getting the money back as with a U.S. government bond.  You want 
to decide: Is the loan a good deal for you? 
     If you discount the future at 90 per cent from year to year, 
then the $1,800 payment one year from now is presently worth 
(.9 x $1,800) = $1,620, the second year's payment is presently 
worth (.9 x .9 x $1,800) = $1,448, third year's is presently 
worth (.9 x .9 x .9 x $1,800) = $1303, and so on.  The sum of 
these discounted payments is $10,551.  And if you subtract your 
original $10,000 investment, the net present value of the deal, 
figured at a 90% discount factor, is $551.  Since the present 
value is positive, you should accept the offer if the 90% 
discount factor -- equivalent to a 11.1 percent "rate of return" 
or "cost of capital" -- is appropriate.       Consider still 
another example, comparing the alternatives of buying versus 
renting a machine as seen in Table 2-2.  The present value of 
purchasing is $-10,000 at any discount factor, because the 
purchase takes place immediately.  The present value of renting, 
however, depends upon the discount factor.  With a discount 
factor of .8, purchasing is the better alternative.  With a 
discount factor of .5, however, purchasing is the better 
alternative. 
                            TABLE 2-2

Rent versus Buy (Zero Salvage Value)

     Present value of buying:
           PV of $10,000 Today= -$10M

     Present value of renting: 

     PV of $4,000 Each Year For 4 Years =

          - $4,000 + (-$4,000d + (-$4,000d2) + (-$4000d3)

At.8
     = -$4,000 - $3,200 - $3,560 - $2,048  = -$11,708

At.5
     = -$4,000 - $2,000 - $1,000 - $500 = $7,500

     One more illustration:  In many business situations the 
price in the present period has an effect upon sales in future 
periods as well as upon sales in the present period.  For 
example, customers may be induced by a low price now to begin a 
long-continuing habit of purchasing for a given brand of beer.  
Or, a low price of natural gas now may bring some customers to 
buy gas dryers and refrigerators which will lock them into buying 
natural gas during the life of those appliances.  This is the 
case of a supermarket chain entering the prescription drug 
market:
     Giant...keep[s] low on many popular drugstore items and on      
prescription, all to build market share.  The higher market      
share is expected to pay off in the long run for Giant      after 
new shopping habits are established and some of its      prices 
are raised. (Washington Post, July 30, 1990, Business      
section, p. 28)     Trial offers similarly cause sales in the 
future to be higher than they would otherwise be at the 
prevailing future prices.  
     More specifically:  say you are considering a low 
introductory price for your newly-opening pizza shop -- $6.95 for 
your basic pizza in contrast to the $8.95 you expect to charge 
after the first two-month introductory period.  The purpose of 
the introductory price is to acquaint a large number of customers 
with your excellent product.  You estimate the number of 
customers in the first two months with the $6.95 price, and then 
you estimate the number you expect in the rest of the first year, 
in the second year, and so on, at your $8.95 price.  Each sub-
period has a separate set of columns in your table.  Then you 
also make estimates of customers for the first year, second year, 
and so on assuming you do not set a low introductory price; the 
number of customers after the first two months will be lower (at 
least for a while), in the no-introductory-price alternative, 
because you will have brought in fewer customers in the first two 
months.  The question is, will the extra revenue from the extra 
customers later on outweigh the cost of getting then with the low 
introductory price?  Computation of the profit for each 
alternative will reveal which is preferable.  
     In all these cases, the tabular analysis presented in 
Chapter 1 is expanded to contain sets of columns not only for the 
present year but also for several future years.  And the incomes 
and outgoes in those future years must be discounted so that the 
alternative with the highest present value may be correctly 
chosen.  
     The concept of present value is the appropriate definition 
of profit in business decision-making.  The accounting concept of 
profit is another matter altogether, because the aim of 
accounting is to assess what happened in the past rather than to 
make choices for the future.  Only in the simplest case -- when 
everything happens in a single period and the activity being 
analysed is the only activity of the firm -- is accounting profit 
equal to present value.       The computation of the present 
value of an investment has a long history.  English and Dutch 
lenders, and insurors such as those at Lloyds in London, have for 
hundreds of years used the technique to adjudge how much to 
charge for loans and insurance.  Indeed, calculating the net 
present value of each alternative is the appropriate way to 
compare any two courses of conduct whose consequences will 
continue to be felt into the future.  Other examples include 
deciding whether to give up the pleasure of smoking now in order 
to extend the likely length of your life, and figuring whether it 
makes sense to buy aluminum siding for the house in order to 
avoid the need for painting in the future.  The fundamental 
notion of discounting future incomes and outgoes, and then 
summing these discounted flows to calculate a present value for 
each alternative, is always at the heart of the matter.  This big 
idea is indispensable in making almost any decision that has 
economic ramifications, and for many non-economic decisions, too.      
         HOW SHARPLY SHOULD YOU DISCOUNT FUTURE EVENTS?

     Just how much allowance you should make for having the 
dollar now, rather than in one or ten years, is a very tough 
question.  The answer must depend upon your circumstances.  If 
the decision concerns an individual rather than an organization, 
the appropriate discount factor also depends upon personal 
preferences.  
     A discount factor represents the combination of two 
elements: 1) An adjustment for "pure" time preference, which 
allows for the fact that a dollar in hand now is worth more to 
you than even a sure-fire dollar a year from now.  This is shown 
by the interest paid on even a "risk free" government-guaranteed 
bond when there is no inflation.  2) An adjustment for risk, 
because financial markets as well as individuals value 
opportunities inversely to their risk.  Risky loans pay a higher 
rate of interest than otherwise-similar risk-free loans, and 
risky stocks sell for lower prices relative to their expected 
payouts than do less risky stocks. 
    For a corporation whose stock is traded in a public market, 
the appropriate discount factor is an average of the prices that 
the firm has to pay for the various classes of capital it uses in 
the business.  For example, if half of the firm's funds come from 
bonds that pay lenders 10 percent a year, and half comes from 
stocks that return 20 percent a year to stockholders, the overall 
cost of capital is 15 percent, and the discount factor is 
roughly .87.1     
     There is continuing controversy about whether or not government programs should attribute a lower value to a given benefit to 
be received by a citizen a century from now in the future, say, than to the same benefit received by a citizen now.  That is, 
should a discount factor be used in calculating the value of government investment in a dam or a recreation area?  Whatever the 
morality of the matter, discounting is universal practice; it is woven into the fabric of all our governmental decision-making, 
and will certainly continue so in the future.  Less settled is what the government discount factor should be. 
     The appropriate discount factor for government agencies and non-profit organizations cannot be established as objectively as 
for a business, however.  Politics may enter in, as well as subjective judgments.  My own belief - which many economists share - 
is that government and non-profit institutions should use the same investment criteria -- that is, the same discount factor -- as 
do private business activities with the same degree of risk. 
     The most difficult choice of a discount factor arises when making personal decisions.  For activities that affect your 
economic situation, you can sometimes find guidance in the cost for you to borrow money.  For example, when you reflect on the 
decision about whether to postpone earning and continue in school, you can ascertain how much the bank would charge you for a loan 
to go to school.  (And indeed, you should always consider the possibility of borrowing to finance such activities, rather than 
limiting yourself to waiting until you have saved the necessary money.  Too often I have seen students err by working for several 
years at the minimum wage to fund schooling, instead of borrowing and later being able to repay out of much higher income and 
therefore less cost in work time.)  Interestingly, individuals usually can obtain capital at lower rates than can businesses, 
suggesting that loans to individuals are generally less risky than business loans.  
     For decisions about activities that do not mainly affect your economic situation -- for example, comparing the pleasure of 
smoking now versus the possible shortening of your later life due to the smoking -- taking future events into account in a 
reasonable fashion is extremely difficult.  Even if you can estimate the expected shortening of life - about 5 years for the 
average smoker, or 5-9 minutes per cigarette smoked - you are faced with a complicated risk assessment; a particular person might 
lose 20 years of life or none.  For comparison, is the pleasure of 10 minutes smoking worth 10 minutes of non-life in the present?  
If it is, you might ask yourself at what rate you would have to discount lost life in the future to make a balance against 10 
minutes of smoking now.  If that discount would be very high, you might say to yourself that the loss then does not mean enough to 
you now to quit smoking.  But this sort of analysis is so difficult that one is not likely to actually do it.  Indeed, I have 
never seen a satisfactory analysis for such issues.  
     This much is clear and obvious:  The older you get to be, the larger the weight it is sensible to assign to the present 
relative to the future.  Also, the greater the risk you presently face -- in wartime battle, for example -- the lower the weight 
you are likely to place upon possible future consequences. 
     It sometimes is useful to imagine what you would think then of the calculation you are making now if you were to reach a 
point, say, at which you are told that you are about to die from lung cancer due to smoking.  Perhaps the greatest contribution of 
the concept of time discounting in such situations is to help you think explicitly about how much weight you wish to put now upon 
a given event that will occur well into the future. 
     People sometimes make choices that seem inconsistent in light of time discounting.  The most dramatic example is having a 
house painted, or going to the dentist, and then committing suicide a week later.  The likeliest explanation is not a gross 
inconsistency in present-value calculation, but rather the presence of several conflicting desires which are only alternately in 
the person's mind and are never brought into mental relationship with each other.  We will discuss such cases later with the help 
of the concept of multiple selves. 
     Also interesting is when people pay to be compelled to do something -- for example, when they pay a bank to force them to 
save -- or when they do things tonight that they will hate themselves for tomorrow.  Both kinds of cases are explained by people 
applying a much lower discount factor from the immediate present to the near future than from one future period to another.  
(Whether or not it is sensible to have such a "kinked" structure of discount factors is another matter.)  These interesting cases 
will be discussed in Chapter 00. 
     Of course there are great difficulties in factually assessing the likely far-off consequences of today's decision.  How will 
you like being a physician if you make the investment of going to medical school?  How good a musician will you be if you 
undertake long training to be a concert pianist?  We will tackle these problems of prediction in Part II. 

                             SUMMARY
     Explicitly allowing for time differences in events is hard mental work.  But it is all-important.  The present-value concept 
is the appropriate technique to use.
                       ADDITIONAL READING
     Chapters 00 and 00 in my Applied Managerial Economics contain more lengthy discussion of the subject matter of this chapter.
                            EXERCISES     1. What are your thoughts about the following newspaper clipping in light of the concept 
of present value? 
          We know what the Redskins would do.  They have done it      16 of the last 19 years, counting the 1987 draft.  They'll      
trade the pick, take the player and run.

          "Traditionally, a second-round pick this year is work a      first-rounder next year," Gibbs said.


     2. And about this clipping from a Sunday supplement story:
          It is my Social Security number.

          I got it in 1941, four years after the program began,      when I went to work as a copyboy for the Associated Press in      
Chicago. 

          Since then, I have paid $20,490.63 in payroll taxes.       If I retire at age 67, I'll get at least $9480 a year.  That      
means that, in a bit more than two years, I'll get back all      the money I put in during 43 working years. (I was in the      
Army in World War II and paid no taxes then.)  What's more,      I'll keep collecting $9480 or more each year until I die.       
With a life expectancy of 79, I can figure on getting a sort      of bonus of at least $142,200.  All gravy.  Not a bad deal.

     3. And this news report:

          BIRMINGHAM, June 21 - Heisman Trophy winner Bo Jackson,      the No. 1 pick in the NFL draft, announced today that he 
had      signed with baseball's Kansas City Royals, shunning reported      $7 million deal with the Tampa Bay Buccaneers.

          Jackson said that one consideration in his decision was      the possibility of injury in football.

          "My knees are my bread and butter," he said. "They have      never been injured, and I don't feel like going under      
anybody's scalpel."

     4. How would you compare the two following modes of auto purchase? 
          In a lease, the customer's monthly payments are lower      than they would be for the same car bought on credit.  But      
the lessee doesn't own the car, which is returned to the      dealer when the lease expires - normally after four years.

          Consider a moderate equipped Pontiac Grand Am that      would sell for $11,288.  GM calculates that the standard      
lease on the car would be $229 a month for 48 months, or a      total of $10,992.  With a 5% tax on the monthly payments,      the 
cost would total $11,542.

          If a person were to buy the car with the standard      minimum down payment of 13%, or $1,481, and finance the      rest 
at 11% for 48 months, the monthly payments would be      $253, or a total of $12,144.  Including the down payment and      lost 
interest earnings on that amount, as well as 5% sales      tax, the buyer's cost would be $14,840, compared with the      lessee's 
$11,542.


     5. Do the ideas in this chapter cast any light on the common observation that it is easier to get a commitment from a person 
to give a talk half a year or a year in advance, than it is a week in advance?  And that a person often accepts an invitation a 
long time in advance and later comes to wish it had not been accepted? 

                            FOOTNOTE

     1 This is not strictly true.  The discount factor for a 
particular decision hinges on the extent of the risk involved in 
the activity being analysed.  Even more precisely, the analysis 
should consider the change in risk for the enterprise as a whole, 
and not just for the single activity.


***do calculations p. 6***

Page # thinking prsvl12%