Interest Rates
(Chapter 14 BH)
Interest Rate
• principle
• interest payment
• interest rate = payment/principle
– (these days often daily, but expressed as a yearly
equivalent)
• Future Value: The future value of 100 at r%
for t years is the amnt of money you will have
in t years if invested at r%: principle*(1+r)^t
• Present Value (PV). Value today of payments
made in the future.
• PV = (1+r) -t * FV
• PV of annual payment of AV starting in one
year is AV/r.
PV of recurring payments starting
in one year
𝑃𝑉 =
𝐴𝑉
1+𝑟
+
𝐴𝑉
1+𝑟 2
𝐴𝑉
+
+. . . .
3
1+𝑟
𝐴𝑉
𝐴𝑉
+
+. . .
2
1+𝑟
1+𝑟
• 1 + 𝑟 𝑃𝑉 = 𝐴𝑉 +
1 + 𝑟 𝑃𝑉 − 𝑃𝑉 = 𝐴𝑉
𝑃𝑉 = 𝐴 𝑉 𝑟
PV of AV starting in 1 year and
ending in T years
PV (T ) 
AV
AV
AV
AV



....

T
1  r 1  r 2 1  r 3
1  r 
PV  AV / r the value of AV for all time
not just till T
PV (T )  PV  (1  r ) T PV
PV (T )  PV (1  (1  r ) T )
PV   AV / r  (1  (1  r ) T )
The Effect of Time on $1,000 in Future
Value. Who cares about climate change?
14-6
© 2011 Pearson Addison-Wesley. All rights
reserved.
Invest and interest
• Obviously high interest and quick depreciation
militate against investments.
– Even socially nice ones.
Why Don’t They Buy…
• Energy efficient appliances, insulation, windows and
so on when they redo their homes?
• additional cost $4K upfront
• utility bill decrease $744
• CO2e saved about 11,800 lbs per year.
– Can this be right? 5 tons? Worth $50-$500.
– Would charging a tax for CO2e work here?
• (hes.lbl.gov)
Back to energy saving
•
•
•
•
•
If interest is 5% and savings last forever
PV of savings is 14,880
Cost is 4047
Present Net Value is 10,833.
On the other hand if the savings only last 5
years the PV of savings is 3221 (look at book
for calc) and PNV = -826.
• Could also try 10% interest rate.
Market interest rates
• Nominal vs. Real
– inflation
– CPI
• If you use real interest rates make sure you are
using real prices for the benefits
– e.g. nominal electric prices rose by 5%/year, but so
did the price of other goods (CPI).
– Use nominal prices and nominal interest rate
– Use real prices (price/CPI) and real interest = r minus
the inflation rate.
– Get same answer either way.
Inflation: Evil or Wrong
• Would a 5% inflation really be bad for the US
right now?
• Would you (students) care
• Should I (a nearly dead) care
• Should China care? (they bought lots of
treasury bills)
• Should I a holder of TIPS and Stocks care?
– Treasury inflation protected securities(acronym)
Borrowing and Saving
• Financial system gets paid to round up your
savings and lend them to someone.
• Difference in rates compensates them for their
work and also the risk of the loan, which they
bare and you do not.
Risk
• Treasury bonds are really as guaranteed as you
can get. You will get your $ back. Hence no risk.
• Corporate bonds—more risk so you get a higher
rate of return to pay you for taking the risk.
• Stocks—S&P 500 is a good index (Russel 2000 is a
little better). Higher rate of return yet, but you
can gain or lose 4% of your money in one day!
Risk Reality
• 1. If you look only at the post war period then
stocks look great relative to bonds. But if you
include pre-war bonds and stocks look more
similar in their returns.
• 2. Your greatest risk is your human capital
risk. Disability is not so uncommon and has a
far greater effect on your lifetime income than
the stock market. (Go to the gym more, study
harder, and stop reading the NYT.)
Price of Risk
• (Advanced Topic)
• Investor can hold the S&P itself. Eliminates
idiosyncratic risk. Intel goes up and AMD
down. Together less risk than alone.
• Stocks are priced based on their tendency to
rise and fall with the market (S&P).
• Ones that go up and down in market cycle
faster than the market have the most risk.
Public Projects
• I want to build a dam. Benefits from
electricity, irrigation and flood control all
come in the future. Costs all come now.
• High interest rate = little PV benefits
• Low interest rate = big PV benefits
• Which interest rate is “right?”
Social Discount Rate
• Pure: I believe that all people are too present
oriented and want my government to
compensate for that. That is, I wouldn’t invest in
the dam, but I think they should.
• Pure: People born in the future can’t vote or buy
today, so their views don’t count in the market.
• Confused: Global warming is an externality. I
want it stopped. I want government to stop it.
Here I don’t see why they should use a lower
interest rate—they should just price the
externality.
Stern v. Nordhaus
• Two economists look at climate change
• Big difference is that Stern thinks low interest
rates are appropriate
• Nordhaus thinks market rates
• Stern: Help! Do something now!
• Nordhaus: Go slow and phase in avoidance
measures
Risk in Public Projects
• There is a way of stopping global climate
change. (a hypothetical)
• It’s expected costs are a little larger than its
expected benefits at the market rate of
interest (around 10%, the return, nominal, on
the s&p 500)
• Would you do it anyway?
– Do you insure your house against fire?
– Would you buy planet fire insurance?
Vexed Question: Is there a social
rate of interest?
• I hold with the conservatives:
• for the same type of project, the gov’t and the
private sector should be using the same rates
Socially Responsible Investing
• A bet against dirty companies.
– Tobacco; nuclear; alcohol; defense;
•
•
•
•
Loses diversification
Costs money to do the “screens”
Gives investors a “warm glow”;
When would it accomplish something?
Benefit Cost Analysis (BH 15)
• “if the benefits to whomsoever they may
accrue are in excess of the estimated costs.”
• Criteria for public projects
Tellico Dam
•
•
•
•
•
Outline of story: (Chapt 15)
Dam was mostly built
Snail darter discovered
ESA invoked
G_d squad—interagency group to determine
whether to allow extinction.
• Found defect in BCA
• Dam built and darter survived
• Development benefits never happened.
We know that B - C
• Is benefits to consumers, willingness to pay,
less costs to all, C.
• Reasonable thing to maximize
• Two common cases:
– 1. There is as much money for capital costs as one
wants. One or many potential projects
– 2. Limit on funds that can be invested.
Two problems
• 1. Maximize B – C with no restrictions
• 2. Maximize B – C with C = C* a fixed amount.
– Each potential project has a Bi and Ci.
• Rank by ratio: Bi / Ci
• Choose by highest rank till money is gone
• This gets most benefits for given Cost.
Ratio or Absolute?
When a limited number of projects, for instance 10 places to put a dam, pick
the projects with the biggest B-C. When limited funds, then pick projects with
highest ratio. With 100million is 10 small better than 5 large? (Not far fetched–
a bond to fund water saving projects in CA—projects ranked by BCR)
Benefits
• Area under demand
– could be market good, like corn
– could be non-market good like whales
costs
• usually engineering estimates for structures
• got to get all costs
– drowned land
– drowned Indian villages and historic sites
– endangered species
– and so on.
costs
• DWL of taxation
– Feldstein goes for 30% DWL; large estimate
– Means that projects that are tax funded, like
welfare, need large B-C so that B-C*1.3 > 0
Alternatives
• Big or little dam?
– Max concrete s.t. B-C > 0
– Max B-C
• When?
– Now
– Later
– Is there an uncertainty that will be resolved if you
wait? Is the project marginal with 10 years ago
energy prices? Would it be a go now?
Nuclear Power
• $5.46b for 1,000 MW plant
– Big deal: this figure includes the interest cost
from day 1 until the day that the plant opens.
– Most analysis don’t include the interest before
opening day and miss a good fraction of costs
– As the time to build goes to large because of
delays for permitting, modification, sloppy work,
etc the 5.46 will go towards gargantuan.
Other costs
• Important that decommissioning happens in
year 40 or more (more these days) so that its
present value at 10% is $40m though it costs
1.8b in future value.
Fuel is PV at .58 billion
• Total of all costs is 6.41 billion.
Levelized cost per kwh
• Find the price per kwh of the electricity produced so
that Revenue – costs = 0.
• It is 10cents/kwh in this study.
• Nat gas is 7.8cents/kwh
• It takes a carbon price of $50/ton to even them out.
• So if you think that carbon should be priced high, you
favor nukes.
• Not entirely fair comparison as there ought to be a
small but positive glow in the dark fee
Older Nukes
• US went out of nuclear industry because the
levelized costs were higher than the costs of
coal/gas/and in those days oil.
• The expected costs were low, but the realized
costs were high.
• Newer reactors may well avoid these
problems and minaturized nukes built in
factories could completely overcome the big
delay/hard to build problems.
Nukes and Grids
• Nukes need a place to put their power. Can’t
turn on and off all the time. Can’t do this with
coal either.
• Power demand has sharp peak in evening and
then falls to nearly nothing in late night.
• Limits how much nuke could be done without
pumped storage.
Nukes and heat
• Nukes were placed away from people
therefore their waste heat could not be used.
• Indian point cycles 2.5 billion gallons per day
through its cooling system. Makes the Hudson
hotter (bad for fish) and catches fish in the
screens. Uses about as much water as NYC.
– Antiquated system but hard to replace.
To BCA or Not to BCA
•
•
•
•
It is a screen to get rid of truly awful projects.
Like an EIS/EIR it can be manipulated.
If permitted it could be litigated.
Requiring a BCA for environmental regulations is
controversial. In practice we do that here in CA
and still have the toughest environmental laws.
• Perhaps it is an important part of being able to
have tough environmental laws—efficient ones
are cheaper.