L1 | Present Values Flashcards
What is the net present value (NPV)?
the present value of sum of all future cash flows minus the required investment
How long is a perpetuity for?
forever
How long is an annuity for?
a specified number of years
How do we calculate the IRR?
the IR value when NPV = 0
What is the present value formula for a perpetuity?
What is the present value formula for a perpetuity when the first payment is made in year t+1?
What is the present value formula for an annuity?
What is the present value formula for a perpetuity with growth?
What is the present value formula for an annuity with growth?
What is meant by the budget constraint?
Level of consumption in second period is a function of the amount of income spent in first period
What is the budget constraint?
the inequality formula
Level of consumption in the second period is a function of…
amount of income spent in first period
When does an individual lend?
if C0 < M0 and C1 > M1
When does an individual borrow?
if C0 > M0 and C1 < M1
Optimal Consumptionb
If IR increases, what happens to the CML and what is the result to the individual?
- slope increases
- CML pivots around the endowment point
- beneficial to consume less today because what is left will be inflated more by r
- so consume more next period
How are consumer preferences for current and future consumption represented?
utility function (C0,C1) and associated set of indifference curves
What does the slope of the indifference curves represent?
Marginal Rate of Substitution (MRS) = rate at which consumers will trade of consumption today for consumption tomorrow
Where does an individual’s consumption package lie on the graph?
where the slope of the highest indifference curve is tangential to the CML
Optimal Investment
What is meant by the production possibility frontier?
a curve showing maximum output possibilities of consumption good in 2 periods
What is meant by the slope of the Production Possibility Frontier?
Marginal Rate of Transformation (MRT) = rate at which it is technically feasible for one unit of C0 to be transformed into units of C1
What is the solution to optimal investment?
where CML is tangential to PPF
Where MRT = (1+r)
How do we combine optimal investment and optimal consumption?
- Optimal consumption requires MRS = 1+r
- Optimal investment requries MRT = 1+r
- Optimal investment and consumption when MRS=MRT
In the absense of capital markets, the condition for optimal consumption/investement is given by…
MRS = MRT
In the absence of capital markets, if MRT < (1+r) and MRS < (1+r), how can utility be increased?
if capital markets introduced by lending and increasing next period’s consumption
In the absence of capital markets, if MRT > (1+r) and MRS > (1+r), how can utility be increased?
if capital markets introduced by borrwing and increasing the present period’s consumption
What is the Fisher Separation Theorem?
a firm’s choice of investment is separate from its owners’ investment preferences and therefore the firm should only be motivated to maximize profits.
What is the power of the Fisher separation result?
even if entrepreneur and consumer are different:
all shareholders and managers agree on the optimal investment policy
unanimity with respect to the firm’s objectives.
