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					Discounting
• 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”.
                 WACC
• WACC is the standard method we have
  learned in the classes. So we will discuss
  more
• 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
  bond.
             Mortgage rate
•   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
  funding.
• This illustrate the importance of duration in
  funding processes.
• There is a continuation from short term to
  long term funding. No chasm between
  them
• Banking industry illustrate this clearly.
              Some puzzles
• 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 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
  credit?
• 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
  world.
• 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
  central banks.
• 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
• Experiments
  – Depending on the designs of the experiments,
    results vary.
  – If showed pictures of beautiful ladies before
    surveys, discount rates can be extremely high
    for men
• Credit card rates can be 30%.
       What determine human
    psychological discount rates?
• For human beings, it is from our
  evolutionary past.
• In old times, the probability of death is
  high.
• Hence the high discount rate.
• People feel high interest rate charge is
  natural.
• This answers the first puzzle.
     Government bond yields
• Currently, 10 year Canadian bond yield is
  below 3%
• Similar yields for many other government
  bonds
       The role of government
• Government is the largest equity holder of the
  society.
• 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
  private ownership.
• As equity owner, the government prefer
  high rate of economic growth so it can
  generate more tax revenue and other
  types of revenues.
                      Exercise
•   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
    will choose?
• Tax base is the total net profit over the
  project‟s life. Calculate tax bases for both
  projects.
• If the government attempts to maximize
  tax base, which discount rate the
  government will choose?
                         Solution


                                                        tax
                                                              ba
 0    1    2    3    4     5   6    7    8    9   10          se



-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 6.43 7.07   27.81
                Solution
• The government will choose the lower
  discount rate
              Discussion
• Government preferred discount rate is
  lower than human psychological discount
  rate. Hence low discount rate needs to be
  actively managed.
• This answers the second puzzle.
Preconditions for low discount rate
              policy
• Economic growth has to be possible
  – The key constraint is the availability of natural
    resources
• Effective selective 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
         Alternative scenario
• Suppose the market size is constrained by
  resource availability. If the profit does not
  grow as expected in the second project
  and remain flat during the project life,
  what is the tax base for the second
  project?
   Further resource constraint
• Suppose the sums of the cost of building
  the project and the subsequent revenues
  are constant at 80 million for different
  possible projects. The first project requires
  10 million initial cost and generates 25%
  marginal profit. The second project
  requires 20 million initial cost and
  generates 30% marginal profit. What are
  the net profits for both projects?
• 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
  policy.
High discount rate environment
• While low discount rate environment require
  active policy and institutional support, high
  discount rate environment require no active
  policy or institutional support. Hence it is a
  passive and costless 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.
         On the third puzzle
• Discounting and uncertainty
• For the same project, longer duration,
  higher uncertainty.
• For different projects, only low uncertainty
  projects are designed to last long.
• One should not force low discount rate on
  long term issues if uncertainty is high.
  – Massive funding for climate related projects.
financial discounting and biological
             discounting
• People borrow at 30% on credit card. Why
  the pattern does not disappear in a
  competitive world?
• 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)
• Low discount: Wealthy, high fixed cost,
  low fertility and low mortality.
• Advantageous in a high overall mortality
  environment. Disadvantageous in low
  overall mortality environment .
                   From Darwin,
•         A most important obstacle in civilized countries to an
    increase in the number of men of a superior class has
    been strongly urged by Mr. Greg and Mr. Galton,
    namely, the fact that the very poor and reckless, who are
    often degraded by vice, almost invariably marry early,
    whilst the careful and frugal, who are generally otherwise
    virtuous, marry late in life, so that they may be able to
    support themselves and their children in comfort. Those
    who marry early produce with a given period not only a
    greater number of generations, but, as shewn by Dr.
    Duncan, they produce many more children. The children,
    moreover, that are born by mothers during the prime of
    life are heavier and larger, and therefore probably more
    vigorous, than those born at other periods.
• Thus the reckless, degraded, and often vicious
  members of society, tend to increase at a
  quicker rate than the provident and generally
  virtuous members. Or as Mr. Greg puts the
  case: “The careless, squalid, unaspiring
  Irishman multiplies like rabbits: the frugal,
  foreseeing, self-respecting, ambitious Scot, stern
  in his morality, spiritual in his faith, sagacious
  and disciplined in his intelligence, passed his
  best years in struggle and in celibacy, marries
  late, and leaves few behind him.
• Given a land originally peopled by a thousand
  Saxons and a thousand Celts --- and in a dozen
  generations five-sixths of the population would
  be Celts, but five-sixths of the property, of the
  power, of the intellect, would belong to the one-
  sixth of Saxons that remained. In the eternal
  „struggle for existence,‟ it would be the inferior
  and less favoured race that had prevailed --- and
  prevailed by virtue not of its good qualities but of
  its faults.”
             Today's world
• Rich country.
  – Low discounting, long education, late
    marriage, low fertility.
• Poor country
  – High discounting, short education, early
    marriage, high fertility.
    Inside a rich country such as
                Canada
• Mainstream: Low fertility.
• Nonmainstream such as aboriginal: High
  fertility
advantages of high discounting
• We normally notice many disadvantages
  of high discounting, such as poverty.
• Advantages:
  – Enjoy now,
  – More children,
  – In the current social system, little
    consequences for being high discounting rate.
  – More government support, more subsidy, less
    tax.
    Relation between discounting and
              other factors
•   fixed cost
•   duration
•   uncertainty
•   growth
      Policy recommendations
• Higher interest rate than now
• How much higher?
• Slowly but steadily raise until fertility rates
  reach two.
• 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
  at 150km/hour.
•
• 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 speculation.
• This is what caused eventual collapse of
  the financial system in 2008
• In our theory, we should not attempt to
  “stimulate” economy. Instead, we should
  adjust policy measures to adapt to the
  level of resource bases.
• What are the main parameters we should
  use to gauge the health of our society?
             A Water Tank
• Suppose you heat water in an enclosed
  water tank and use the thermometer to
  monitor the water condition. After some
  time of heating, the thermometer reaches
  100 degree and stay there. From the
  reading of the thermometer, you realized
  that water inside the tank has reached
  equilibrium condition. So you don‟t have to
  worry about the water tank anymore.
• The water tank is on the verge of
  explosion and yet we feel it is completely
  safe from the constant reading of the
  thermometer.
• What we need is a pressure meter.
• Economists mostly use GDP as the
  measure of health of the society.
• We believe fertility rate, which is the return
  on human investment, is a much more
  fundamental parameter.
               Examples
• If fertility is used as a measure of social
  health in Japan, you can recognize its
  eventual decline in early 70s.
• However, even today, economists are still
  arguing about how past policy mistakes
  wreck Japanese economy and how a good
  policy can revive Japanese economy.
• If fertility is used as a measure of social
  health in Europe, you would be much less
  ambitious about expansive social
  engineering such as Euro zones. Instead
  various countries will prepare for
  maintaining and reducing their social
  structures.
• If fertility is used as a measure of social
  health in China today, policy makers would
  attempt to slow down instead of speed up
  economic growth, to avoid future
  economic collapse.
• If fertility is used as a measure of social
  health in Canada today, we would stop
  further burdening ourselves with things like
  carbon tax; we would stop worrying for the
  impacts to future generations for we have
  already stopped producing future
  generations.
• Historically, the sharp decline of fertility is
  always the harbinger of decline of highly
  developed civilizations.
• However, there is a time lag between the
  decline of fertility and the decline of
  economic output.
• The initial decline of fertility reduces the
  ratio of dependents over workers, which
  actually speed up economic growth.
 Salvage ratio and discount rate
• Banks charge interest rate based on risk of
  loans. For simplicity, assume the risk free rate to
  be zero. A business applies for 1 million loan for
  a project and plans to repay the loan in one
  year. A loan officer estimates the payoff from the
  project will be 2 million with 85% probability and
  0.8 million with 15% probability. If a loan
  defaults, on average, a bank can get 60% of the
  salvage value. If the bank requires 2% return on
  its loans, what would be the loan rate?
                     Solution
• If the project payment is 0.8 million, the
  company will declare bankruptcy and the
  bank will receive
     • 0.8*0.6 = 0.48 million
• If the project payment is 2 million and the
  loan rate is x, the bank will receive
     • 1+x million
• Overall, the bank is expected to receive
     • (1+x)*0.85+0.48*0.15 = 1.02
• 2% is the bank‟s required rate of return on
  its loans
• Solving the equation to get
     • X = 11.53%
• Discount rate is a reflection of downward
  risk
               Discussion
• If the salvage ratio is increased to 80%,
  the interest rate will decline to 8.71%.
• If the credit and judicial systems can
  increase the ratio of salvage value, the
  discount rate will decline.
         Further discussion
• To protect rental tenants, landlords are not
  allowed to evict tenants even when
  tenants failed to pay rents for several
  months. Will this increase rent or decrease
  rent over the long term?
  Ratio of self funding and discount
                  rate
• A business plans for a project, which will require 1 million
  initial investment. The business will supply 0.1 million
  funding itself. It will apply for 0.9 million loan from a bank
  and plans to repay the loan in one year. A loan officer
  estimates the payoff from the project will be 1.3 million
  with 85% probability and 0.7 million with 15% probability.
  If a loan defaults, on average, a bank can get 60% of the
  salvage value. Assume the risk free rate to be zero. If
  the bank requires 2% return on its loans, what would be
  the loan rate? If the business will supply 0.2, 0.3 million
  funding itself and apply a loan for the remaining amount
  of capital, what will be the loan rates? What conclusion
  you can draw?
                     Solution
• The amount of loan
     • 0.9 million
• The required payback
     • 0.9*1.02= 0.918
• Assume the loan rate is x
     • 0.9*(1+x)*0.85+0.7*0.6*0.15=0.919
• Solving the equation to obtain x
     • X = 11.76%
• When the part of self funding are 0.2
  million or 0.3 million, the required loan
  rates are 10.74% and 9.41%.
• This shows that the higher the percentage
  of self funding, the lower the discount rate.
• When you put in your own money, others
  trust you more.
• There are two types of projects. Each project
  require an initial investment of 1 million dollar.
  For the first type of projects, there is a 65%
  chance that the project will generate 1.3 million
  dollar payoff after one year and there is a 35%
  chance that the project will generate 0.7 million
  dollar payoff after one year. For the second type
  of projects, there is a 85% chance that the
  project will generate 1.3 million dollar payoff
  after one year and there is a 15% chance that
  the project will generate 0.7 million dollar payoff
  after one year. (Continued on next page.)
• Each prospective project operator may
  apply for a loan from the bank. As a rule,
  the bank will require the project operator to
  supply 30% funding and provide 70%
  loan. From past statistics, the bank knows
  that 60% of the projects are of type 1 and
  40% of the projects are of type 2. But the
  bank cannot distinguish between type 1
  and 2 projects without additional cost.
  (Continued on next page.)
• The bank require 2% return on its loans. If the
  risk free rate is 4%, what is the loan rate the
  bank would offer to prospective project
  operators? The prospective project operators
  will accept the loan only if the expected payoff is
  positive. We assume the interest rate the
  prospective operator will earn is the risk free rate
  if he decided not to start the project. Will the
  prospective operators of projects of type 1 and 2
  accept the loans? (Continued on next page.)
• If the risk free rate is 6%, what is the loan
  rate the bank would offer to prospective
  project operators? Will the prospective
  operators of projects of type 1 and 2
  accept the loans? If only prospective
  operators of projects of type 2 will apply
  for loans, what will the bank charge for its
  loans? Is this rate higher or lower than
  when the risk free rate is 4%? What
  conclusion you can draw?
                    Solution
• First we assume the risk free rate is 4%.
• Assume the interest rate bank will charge
  is x.
• For type 1 projects, the payoff is
     • (1.3-0.7*(1+x))*0.65-0.3*1.04
• For type 2 projects, the payoff is
     • (1.3-0.7*(1+x))*0.85-0.3*1.04
• For the bank, the expected payoff is
     • (0.7*(1+x)*0.65+0.7*0.8*0.35)*0.6+
       (0.7*(1+x)*0.85+0.7*0.8*0.15)*0.4 =
       0.7*(1+0.04+0.02)
• Solving for x to get
     • X = 15.74%
• Plugging into the equations for expected
  returns for projects of type 1 and 2, we find
     • Type 1: 0.0064
     • Type 2: 0.1044
• Both operators will accept the loans.
• Then we assume the risk free rate is 6%.
• Following the same procedure, we find
     • X = 18.36%
• The expected returns for projects of type 1
  and 2 are
     • Type 1: -0.0115
     • Type 2: 0.0828
• Operators of project type 1 will not accept
  the loans.
• As a result, only projects of type 2 will actually
  start.
• This shows that higher risk free interest rate
  reduce information cost for financial systems.
• Is high interest rate bad for economy?
• When resource is abundant, waste of resources
  will not be reflected in human society.
• When resource is scarce, waste of resources will
  accelerate the decline of human society.
    Interest rate and housing price
•    Suppose a house is bought for 400,000 dollars. The required
     down payment is 5% of the house price. The rest of the money is
     borrowed through a 30-year mortgage with monthly payments.
     What is the amount of down payment and what is the amount of
     borrowing? The annual percentage rate on the mortgage loan is
     6%. Calculate the monthly payment. Now suppose the
     government tries to making housing more affordable. It reduces
     the interest rate to 3%. What is the new monthly payment on the
     mortgage? Does the government policy improve the affordability
     of housing market over the short term? If the housing supply
     doesn‟t increase, those who can afford the monthly payment of
     the original 400,000 dollar house will likely to buy the same kind
     of house. What will be the new price of the house which was
     originally sold for 400,000 dollars, if monthly payment is kept at
     the same level when interest rate was at 6% and down payment is
     5% of the housing price? What is the new down payment? Over
     the long term, will lowering the interest rate alone improve or
     deteriorate the affordability of housing market?
                     Solution
• Down payment
     • 400000*5% = 20000
• Amount remaining
     • 400000 – 20000 = 380000
• Number of payment
     • 30812 = 360
• Monthly interest
     • 6%/12 = 0.0005
• Monthly payment
     • 2278.292
• Formula for calculation

                                 1 
                             1
                             (1  r ) n 
          PV ( A, r , n)  A            
                               r        
                            
                                        
                                         
• When the interest rate is reduced to 3%, redo the
  calculation to obtain the new monthly payment: 1602.095
• Over the short term, the low interest rate policy improves
  the affordability of housing.
• To maintain the original monthly payment of 2278.292
  with the 3% interest rate, the present value becomes
  540386.7, which represent 95% of the housing value,
  which is 568828.1.With this housing price, the new down
  payment will be 28441.4
• Over the long term, low interest rte policy will deteriorate
  the affordability of housing market
       Le Châtelier principle
• Any change in status quo prompts an
  opposing reaction in the responding
  system.
         Concluding remarks
• The choice of discount rate has consequences.
• Many central banks believe they can fine tune
  discount rates to optimize economic
  performances.
• They don‟t fully understand the precise relations
  among the various factors in social and
  economic activities. They especially don‟t
  understand the relation between discount rate
  and fertility rate, the return on human
  investment.

				
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