Download Determinants of loan rates

Risk factors in loans
Discount rate
• Discount rate is the main tool governments
and central banks use to fine tune
economic activities.
• Lending rate is the main reflection of loan
risk.
• We will study how banks determine
lending rate.
• Some general observation.
Risk Factors
• We will examine some risk factors that
affect loan rate.
– Salvage ratio
– Ratio of self funding
– Uncertainty
Salvage ratio and discount rate
• Banks charge interest rate based on risk of
loans. Assume the bank’s borrowing rate is 1%
per annum. 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+1%+2%
• 1% is the bank’s cost of borrowing. 2% is
the bank’s required rate of return on its
loans
• Solving the equation to get
• X = 12.71%
• Discount rate is a reflection of downward
risk
Discussion
• If the salvage ratio is increased to 80%,
the interest rate will decline to 9.88%.
• If the credit and judicial systems can
increase the ratio of salvage value, the
discount rate will decline.
Bonds and Stocks
• Bond owners have higher priority in
claiming assets over stock owners. Bonds
have higher salvage values than stocks.
• So cash flows from bonds are discounted
at lower rates than cash flows from stocks.
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=0.918
• 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.
Discussion
• How much trading in banks is funded by
traders themselves or by banks?
• Should banks enjoy such low rate in their
own trading activities?
• It is often said the causes of financial crisis
are “complex”. Are they really that
complex?
Multiyear project
• A business plans for a natural gas project, which will
require 40 million initial investment. The business will
supply 8 million funding itself. It will apply for 32 million
dollar loan from a bank and plan to repay the loan in two
years. A loan officer estimates the payoff from the
project will be 80 million with 90% probability and 24
million with 10% probability, depending on future natural
gas prices. If a loan defaults, on average, a bank can get
70% of the salvage value. Assume the bank’s financing
cost is 2% per annum. If the bank requires 2.5% per
annum return on its loans, what would be the loan rate?
If the business will supply 16 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
• 0.9*32*(1+x)^2+0.1*24*0.7
• =32*(1+2%+2.5%)^2
amount of initial investment
40million
40million
self funded part
8
16
amount of loan
32
24
2.00%
2.00%
risk free rate
probability
0.9
0.1
0.9
0.1
expected payoff
80
24
80
24
average
34.94
26.21
70%
70%
required return on loans
2.50%
2.50%
required payback
34.945
26.209
loan rate
7.47%
6.56%
salvage ratio
Uncertainty and discounting
• There are two projects. Each require 1
million dollar funding. Each project will be
liquidated in one year’s time. There is a
60% probability that the liquidation value
will be exp(S) and a 40% probability that
the liquidation value will be exp(-S). Where
S =0.3 for the first project and S =0.4 for
the second project.
• Suppose both projects are 20% self
funded and need to take 80% loan from a
bank. Assume the bank’s funding cost is
3%. The required rate on its loans is 2%.
When the project could not make loan
payment in full, the bank will take over the
asset of the project. What are the loan
rates for the two projects?
Solution
• For the first project
• 0.6*0.8*(1+x) +0.4*exp(-0.3)
=0.8*(1+3%+2%)
• X = 13.27%
• Similarly, for the second project, the loan
rate is 19.14%.
• Projects with higher uncertainty are
charged with higher loan rate.
Uncertainty and discounting
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 3%, which project you will choose? If projects
are forced to close down after three years due to unexpected
circumstances, what would be the realized value for both
projects, discounted at 3%? If the discount rate is 10%, which
project you will choose? With the benefit of hindsight, what
discount rate one should use to value two potential projects?
How should the choice of discount rate be related to
uncertainty and our capacity in information processing?
Solution
• When discounted at 3%
– NPV of project 1 = 15.59 million
– NPV of project 2 = 19.86 million
– Choose project 2
• If projects have to close down after three
years
– Realized value of project 1 = -1.51 million
– Realized value of project 2 = -10.65 million
Solution (Continued)
• When discounted at 10%
– NPV of project 1 = 8.43 million
– NPV of project 2 = 7.27 million
– Choose project 1
• Choosing project 1 avoid possible heavy
losses due to uncertainty.
Discussion
• Some people claimed that since future is
unpredictable, one should not be held
responsible for losses due to uncertainty.
• However, if we acknowledge future is highly
uncertain, one should discount future at a higher
rate. This will help you reduce the amount of
losses due to uncertainty.
• Policymakers often attribute bad economic
performance to uncertainty but at the same time
keep discount rate low. Are they being
consistent?
Discounting, long term forecasting
and fraud
• Low discount rate makes expected
earning in distant future more valuable.
This encourages long term forecasting.
• Since we are less capable to forecast
distant future, aggressive optimism and
downright fraud often flourish in low
discount rate environment.
Discounting and Valuation
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
• 30*12 = 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
adjustable rates mortgage
• A house is bought for 500,000 dollars. The mortgage
rate is 3% per annum. The buyer chooses the adjustable
rates mortgage that last for 25 years. In the first 5 years,
the buyer only needs to pay the interest part. In the next
20 years, the buyer will pay back interest and principle
with an equal monthly payment. What is the monthly
payment for the first 5 years? What is the monthly
payment for the next 20 years? Why people often default
on adjustable rate mortgages? Suppose the housing
price appreciates 15% over one year. If the capital
investment is measured as the first 12 month’s mortgage
payment, what is the rate of return from this investment?
House price
mortgage rate
monthly rate
monthly interest payment
duration for payment in principle and interest
payment period
monthly payment for the last 25 years
percentage of capital gain
total capital gain
capital invested
rate of return
500,000
3% per annum
0.0025
1250
20 years
240
2772.988
15%
75000
15000
4.00
Discussion
• Many ARMs were initiated after 2001.
• Housing market peaked at 2006.
• Defaults occurred in a large scale from
2007 to 2008.
• Any relations?
Short term benefits and long
term harm
• To a drug addict, a shot in the arm will
stimulate him over a short period. But it
will also put him on long term dependency.
• However, this type of policies and
activities are very common in our society.
Low discount rate policy after
2000
• After the burst of internet bubble, discount
rate was lower to stimulate economy.
• Housing prices rose rapidly.
• Commodity prices rose rapidly.
• Financial crisis occurred in 2007, 2008.
Low discount rate after the
financial crisis
• During the financial crisis, central banks
dropped the discount rate sharply to
stimulate economy.
• But easy money flows to commodity
speculation, driving oil prices from 20s to
near 100 over a short period of time.
• High commodity prices increase the
overall cost of economic activities, stifling
recovery.
• Global economic slowdown, together with
geopolitical maneuvers, caused sharp
drop in oil prices.
• Canadian central bank drop its rate again
at Jan. 2015
• Overall, low discount rate policy generate
great uncertainty in economic life
Some examples of long term
tradeoff
Increase of pension premium
• Benefit: seniors can get higher
Women’s participation in labor
market and labor shortage
• When there is a labor shortage, women
are encouraged to join the labor market.
This relives labor shortage over short
term. But the increased labor participation
of women reduces fertility rate, which will
intensify labor shortage in the future.
Senior care: Short term and long
term
• Increased input to senior care improves its
quality. But it reduces resources for next
generation. With less resource to next
generation, less next generation is
produced. With less future workforce, the
quality of senior care is threatened over
long term.
Social safety net and savings rate
• We all try to avoid uncertainty. Social safety nets
are established to countervail negative shocks.
• But with extensive social safety nets, there is
little incentive to save. In most countries with
highly developed social safety nets, saving rates
are near zero or negative for most people.
• The reduction of uncertainty at individual level
increases uncertainty at social level.
• In many rich countries, governments accumulate
large amount of debts.
Pain Killer
• Many athletes use Advil as pain killer.
• Advil, as an anti-inflammation drug, reduce the
inflammation, and hence the healing, of athletes
involved in heavy exercises, which damage
muscle tissues.
• Over short term, athletes are less painful and
can endure more strenuous exercises, which
helps improve their performances.
• Over long term, tissue damage accumulate.
Cellar Phone use
• Many people check cell phone regularly in
classrooms
• This greatly reduces the effectiveness of
learning
• Many even check cell phone regularly
while driving
• This is the cause of many accidents.
• Short term satisfaction and long term
consequences
Concluding remarks
• The choice of discount rate has long term
consequences.
• Many central banks fine tune discount rates to
improve short term economic performances.
• However, short term monetary policies have
long term consequences, which often do not
concern policy makers and general public as
much.
• They don’t fully understand the precise relations
among the various factors in social and
economic activities.
WACC and asset valuation
• WACC is often used in corporate finance
to value assets and projects.
• We will make a closer look at valuation
process.
An Example
• A company will distribute coupon amount
to 3 million dollar and dividend amount to
3 million dollars next year. The market
value of bond is 100 million dollars and the
market value of the equity is 100 million
dollars as well. So the yield of the
perpetual bond is 3% and the dividend
ratio is 3%. Assume the growth rate of the
dividend is 4% per year.
• What is the cost of equity?
• What is WACC?
• What is asset value calculated from
discounting by WACC?
• What is the asset value as the sum of debt
and equity?
• Is it the same as the sum of debt and
equity?
Solution
• The cost of equity
• Dividend yield + growth rate =
3%+4%=7%
• WACC = 0.5*3% + 0.5*7% = 5%
Asset value
•
𝑖−1
∞ 3+3 1+4%
𝑖=1
1+5% 𝑖
•
∞
=
𝑖=1
3
+
𝑖
1 + 5%
∞
𝑖=1
3 1 + 4% 𝑖−1
1 + 5% 𝑖
•
3
3
=
+
= 60 + 300 = 360
5% 5% − 4%
• The sum of debt and equity is
• 100+100 = 200
• So the asset value calculated from WACC
is 1.8 times the value of debt plus equity.
• What is the problem?
Risk free rate
• 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.