CHAPTER 14 (final exam) Flashcards
(29 cards)
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?
- we value future payments less than if we received them today
- present payments are valued higher than future payments because money received today could be invested and earn a return (there is an opportunity cost)
- therefore, we have to discount the future value in order to bring it back to present terms and account for the opp.cost of not investing that money)
How?
- we use interest rates that could be earned on current payments
Define Interest
Define interest rate
Define 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
**interest calculated on principal and interest
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 interest rates observed in the market 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
