Theory of discounting and
• The concept of a “discount rate” is central to
economic analysis … Because of this centrality,
the choice of an appropriate discount rate is one
of the most critical problems in all of economics.
And yet, to be perfectly honest, a great deal of
uncertainty beclouds this very issue. … The
most critical single problem with discounting
future benefits and cost is that no consensus
now exists, or for that matter has ever existed,
about what actual rate of interest to use.
(Weitzman, 2001, p. 260)
• The main problem in the theory of
discounting is that “an economist who
knows the literature well” is “able to justify
any reasonable social discount rate by
some internally consistent story”.
Some puzzles (Puzzle 1)
• The borrowing rates for banks are very low. But
the credit card interest rates that banks can
charge their customers are very high. How can
the large interest rate differential be maintained
over a long time?
• From another perspective, individuals can obtain
a line of credit or mortgage at much lower
interest rate than the credit card interest rate.
Why do so many people still maintain a large
amount of credit card debt, without replacing it
with a line of creditor or mortgage refinaning?
• Most economists are staunch proponents on the
efficiency of markets, especially when a market is very
liquid and transparent. The short term money market is
among the most liquid and transparent markets in the
• Yet, most economists support that the short term
discount rate, possibly the most important factor
affecting economic performance, should be determined
by a small group of “independent” professionals from
• Does that mean the market is only capable of being
efficient on minor issues and not on major issues?
• In general, yield curves slope upward. Loans with
longer maturity pay higher interest rates than loans
with shorter maturity. At the same time, empirical
evidence suggests that humans discount the long
term future at lower rates than the short term future.
This pattern is called hyperbolic discounting. Many
policy papers also advocate discounting long term
projects at lower rates than short term projects.
• Why do market discount rates and psychological
and policy discount rates move at different directions
with the increase of project duration?
Human discounting rates
– Depending on the designs of the experiments,
– If showed pictures of beautiful ladies before
surveys, discount rates can be extremely high
• Credit card rates can be 30%.
What determine human
psychological discount rates?
• For human beings, it is from our
• In old times, the probability of death is
• Hence the high discount rate.
• People feel high interest rate charge is
natural. So they are willing to pay high
interest rate on credit card debts.
• This resolves the first puzzle.
Government bond yields
• Currently, 10 year Canadian bond yield is
• Similar yields for many other government
The role of government
• Government is the largest equity holder of the
• Housing: Privately owned?
• What happened if you do not pay property tax
for three years?
• Private housing can be more precisely
understood as long term leasing from the
government. Property tax is the rent.
• There is really no chasm between public and
• As equity owner, the government prefer
high rate of economic growth and high
equity value so it can generate more tax
revenue and other types of revenues.
• From our earlier calculation, low discount
rate environment increase equity value
and encourage economic growth.
• So government prefer low discount rate
• Government preferred discount rate is
lower than human psychological discount
rate. Hence low discount rate needs to be
actively managed by central banks instead
of directly determined by financial markets.
• This resolves the second puzzle.
A consequence of low discount rate
• Low discount rate policy benefit borrowers
instead of lenders.
• As a result, saving rates in countries of low
discount rates, which are all the wealthy
countries, are low.
• A company has a choice to select one of the two
projects. The first project requires an initial spending of
10 million dollars. For the next ten years, the project
will generate 3 million dollar profit each year. The
second project requires an initial spending of 20 million
dollars. The project will generate 3 million dollar profit
the first year. The profit from the project will increase
10% from each previous year. The project will last ten
years. The criterion of selection is NPV of a project. If
the discount rate is 12%, which project you will
choose? If the discount rate is 5%, which project you
• Tax base is the total net profit over the
project’s life. Calculate tax bases for both
• If the government attempts to maximize
tax base, which discount rate the
government will choose?
0 1 2 3 4 5 6 7 8 9 10 tax base
-10 3 3 3 3 3 3 3 3 3 3 20
-20 3 3.3 3.63 3.99 4.39 4.83 5.31 5.85 6.4 7.1 27.8
• Lower discount rate generates more
• The government will choose the lower
On the third puzzle
• Discounting and uncertainty
• For the same project, longer duration,
• For different projects, only low uncertainty
projects are designed to last long.
Relation between discounting and
• fixed cost
Resolution of the third puzzle
• Low discount rate is associated with low
uncertainty, long duration systems
• This resolves the third puzzle.
• One should not force low discount rate on
long term issues if uncertainty is high.
– Massive funding for climate change related
– The excuse is that these projects will have
massive long term benefits.
– How do you know?
Preconditions for low discount rate
• Economic growth has to be possible
– The key constraint is the availability of natural
• Effective selection and monitoring systems have
to be developed to distinguish projects with
genuine high growth potential and project with
low probability of high growth potential. These
systems will be highly expensive and prone to
errors in long term forecasting.
• Examples: Various green energy projects
Past, Present and Future
• In the most time of past several hundred
years, low discount rate, high fixed cost
societies are more competitive and spread
out. However, in the last several decades,
the trend has reversed. High discount rate,
low fixed cost societies are spreading out.
It is time reconsider low discount rate
Limits to low discount rate
• The biological value of a low discount rate is limited by
its requiring the organism to detect which one of all the
events occurring over a preceding period of hours or
days led to a particular reinforcer. As the discounting
rate falls, the informational load increases. Without
substantial discounting, a reinforcer would act with
nearly full force not only on the behaviors that
immediately preceded it, but also on those that had been
emitted in past hours or days. The task of factoring out
which behaviors had actually led to reward could exceed
the information processing capacity of a species. (Ainslie
and Herrnstein, 1981)
High discount rate environment
• While low discount rate environment require
active policy and institutional support, high
discount rate environment require less active
policy or institutional support. Hence it is a
passive and low cost environment from
institutional point of view. However, at this
moment, we may not to wish the discount rate to
be as high as human nature deems it to be.
Institutions and policies will still work to keep
interest rate lower than the pure market rate.
• Higher interest rate than now
• How much higher?
• Let the market take on more active roles.
Governments only insure small depositors.
Interest rate will increase to reflect the risk.
• In countries with two tier financial systems, such
as in China, where it is often difficult for private
businesses to obtain loans. Illegal but common
practice is to set up private credit unions to
attract deposits and make loans.
• Deposit rates are much higher than official rates
from banks. This shows that discount rate
without government guarantees are much
• But doesn’t higher discount rate lower the
rate of economic growth?
• If the amount of fuel is unlimited, driving at
a higher speed will get you further.
• If the amount of fuel is limited, driving at
70km/hour will get you further than driving
• Low discount rate does stimulate
economic growth over short term.
• However, with little growth prospect in real
economy in most parts of the world,
money, which is made abundant under low
interest rate environment, is concentrated
in real estates and commodity speculation.
• This is what caused eventual collapse of
the financial system in 2008
• From our theory, we should adjust policy
measures to adapt to the level of resource
• This means we should stimulate economy
when resource is abundant and slow down
economy when resource is scarce.
• WACC is the standard method we have
learned in the classes. So we will discuss
• Definition of WACC:
• WACC is the weighted average of the cost
of debt and the cost of equity.
• Cost of debt is the bond yield. Can we define the
cost of equity as the dividend yield?
• It will make the definition of the cost of equity
consistent with that of the cost of debt.
• Potential problem
– Price change of equity.
• But bond price change as well, especially long
• Do mortgage rates based on WACC?
• What is mortgage rate right now?
• What is WACC for banks?
• Why such big difference between
mortgage rate and WACC?
What is capital?
• Capital is long term funding.
• But bank cash flows are mainly short term
• This illustrate the importance of duration in
• There is a continuation from short term to
long term funding. No chasm between
• Banking industry illustrate this clearly.