CHAPTER 14 (final exam) Flashcards
What can we use PDV for. Define PDV in terms of what you’re finding with the formula
PDV = present discounted value
Allows us to compare costs and benefits over time in a way that puts all present and future financial values on equal footings
PDV is the original principal amount that makes us indifferent between payment today and payment in a year/periods
Why do we have to discount future payments and how should we do this?
Why?
- present payments are valued higher than future payments because money received today could be invested and earn a return (there is an opportunity cost)
How?
- we use interest rates that could be earned on current payments
Define Interest
Define interest rate
Dfine principal
Interest = a periodic payment tied to an amount of assets borrowed or lent
Interest rate = amount of interest paid - interest expressed as a fraction or percentage of the principal (deposit)
Principal: the amount of assets on which interest payments are paid (the deposit - ex. $100 in a savings account)
What is compound interest? What is the formula?
Compound interest: a calculation of interest based on the sum of the original principal and the interest paid over past periods > happens when payments occur more than one period in the future
*when interest paid in one period is added to the principal, and the interest rate in the next period is applied to the sum
Vt (value in any peiod) = A x (1+r)^t
A=initial principal amount
r=interest rate
t= number of periods
How are PDV and compounding interest concepts related?
PDV adjusts expenditures and payoffs that happen at different times to they can be compared on a consistent basis - does this by using the compounding of interest rates in reverse
compounding interest: how large will an initial principal value grow to be if compounded at a given interest rate?
PDV: takes a future dollar value and asks how large the initial principal would have to be today in order to grow at a given interest rate to that future value
PDV of a given future value is always ________ related to the interest rate. explain
inversely
- the higher the interest rate, the smaller the initial principal needs to be to grow to the same value
- higher interest rates reduce the initial value necessary to grow to future value Vt
Explain the PDV formula
PDV = Vt / (1+r)^t
*reverse of Vt = Ax(1+r)^t
Vt = future payment that needs to be expressed in present value terms
PDV = (A) the initial principal - present discounted value
PDVs are _________ to the future value being discounted
proportional
If Vt was twice as high, its PDV would be too
As time goes on, compounding interest leads to an _________ growth of savings
accelerating
- as the interest rate rises savings rise even faster
What is simple interest?
Interest that is only calculated on the initial sum borrowed or deposited
What is the Rule of 72?
A simple rule of thumb that allows us to compute the time it will take for a principal amount to double when it is earning a positive interest rate
- divide 72 by the annual interest rate
- ex. 4% interest rate > (72/4=18) - principal should double every 18 years
How would you calculate the present discounted value of payment streams?
Payment streams are collections of payments that happen at different times - ex. a scholarship that pays $1000 in four installments today and the next 3 years
- to calculate this, simply apply the PDV for each payment and add them together
PDV = 1000 + (1000/1+r) + (1000/1+r^2) + (1000/1+r^3)
*the 1000 is worth less and less today as more and more years pass
What is the formula for calculating the PDV special case > identical payments that occur every period over an indefinite period
M / r
M = fixed payment
r = interest rate
*this won’t give you the actual nominal #, just the present discounted value
When an investment stream has payments and costs, how do we value it and calculate it?
We use the net present value (NPV)
- use the PDV to evaluate the expected long-term return on an investment
- allows us to determine whether the benefits of an investment exceed the costs
Literally just subtract your costs from the PDV formula
*if you end with a positive number, that means your benefits exceed the costs and you should go forward with the investment/purchase
What is a payback period? What’s the downside of this method
You can use payback periods to evaluate investment projects
- it calculates the amount of time required for an investment’s initial costs to be recouped in future benefits WITHOUT discounting future flows
(ex. initial cost of $500 and you gain $200 after every year? > takes 3 years to gain back the money)
Downside is that it does not include forgone interest on the money spent > future payments are treated the same as current payments > doesn’t include the discount affect over time
*this is why NPV is the better method
What 2 effects do the market interest rates capture?
- Price changes in the broader economy
- The real rate of return to capital
Define the nominal interest rate and the real interest rate?
Nominal interest rate: the rate quoted in the market
- a rate of return expressed in raw currency values without regard for how much purchasing power those values hold
- doesn’t adjust for inflation
Real interest rate: the rate of return in terms of purchasing power
- also called the inflation-adjusted interest rate
- as long as inflation is not wildly high, the real rate = the nominal rate minus inflation rate
*should use real interest rate in PDV and NPV calculations
Explain how uncertainty is a factor of many investment projects and how we calculate that into the payouts
Uncertainty with respect to outcomes is a feature of many investment projects
- we use expected value calculations > the probability-weighted average payout
Expected value = (p1xM1) + (p2xM2) …
p = probability
M = associated payout
expected value = the overall return considering the different possible outcomes - it’s like the average expected return because we can’t guarantee anything
*p’s must sum to 1
Explain the Option Value of Waiting
Investments are risky because we can’t forsee what will happen to them for sure
BUT, as time goes on, some uncertainty is resolved
- implies that there is an informational value associated with delaying investment decisions
- option value of waiting = the value created if an investor can postpone the investment decision until the uncertainty about an investment’s return is wholly or partially resolved
*BUT there is also a cost of waiting > your money isn’t being used, it’s just sitting there
What do we assume of economic agents in terms of risk preference? why?
We assume that economic agents have a preference for less risk > that they are risk averse
Why?
- based on the assumption of the declining marginal utility of income
- as income continues to rise, utility increases at a decreasing rate
The same expected payoff can give different amounts of utility depending on what?
Depending on the riskiness of the underlying income levels > if one is guaranteed and the other is only expected
(other ex. a guaranteed income that is slightly less than an expected income can both give you the same utility levels even though guaranteed is a bit less than the other)
The utility of guaranteed income is _____ than the utility of expected income
higher
An economic agent who is willing to pay to reduce risk is _________
risk-averse
- they would expect a utility loss from uncertainty or they are willing to pay for a risk reduction
What is a risk premium?
It is the amount an investor must be compensated for bearing risk without taking a loss in expected utility
- ex. the amount of expected income you are willing to give up in order to have a certain income with the same utility as before
- as the variability of potential income increases, the risk premium increases
What is the certainty equivalent?
The guaranteed income level at which a potential investor would receive the same expected utility as from an uncertain income (the amount of income in between these levels is the risk premium)
Explain the use of insurance
What is complete/full insurance compared to partial insurance
Insurance is a payment to reduce a risk facing the payer (useful because we are risk-averse)
- shifts risk from the insured to the insurer
Insurance offers compensation if an undesired outcome occurs
Complete/full insurance leaves the insured individual equally well off regardless of the actual outcome > different from partial insurance, which is still valuable but not quite as valuable because it doesn’t eliminate risk completely (ex. a deductible that must be paid by the insured)
How do insurers avoid massive losses when they insure people?
DIVERSIFICATION - reduces risk by combining investments with uncertain outcomes
- insure different types of risk (flood, fire, auto) > make sure risks are not too closely correlated
ex. don’t provide fire insurance for every house in a neighbourhood
What does it mean for an insurance policy to be actuarially fair?
It is actuarially fair when the expected payouts or loss from a policy are equal to the expected premiums
- expected net payments equal to zero
- in competitive insurance markets, the premiums will adjust downward toward the actuarially fair level, thereby reducing insurer’s profits
How is the degree of risk aversion reflected in the shape of the utility curve?
The more concave/curved the utility curve, the more risk-averse the person is - will be willing to pay a larger risk premium
Flatter = less risk-averse
