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.