Chapter 16 - Capital Flashcards
Financial capital (Definition)
Money or other paper asset that functions like money
Real capital (Definition)
physical capital.
productive equipment that generates a flow of services
general equation for C(2)
- consumption in the future
C2 = Present value of lifetime income - i(C1)
Real vs Nominal equation
i= (n-q)/ 1+ q
n = nominal q = inflation rate
i= n-q if inflation rate is v small
Marginal rate of time (MRTP)
∆c2/∆c1
definition = the number of units of consumption in the future of a consumer would exchange for 1 unit of consumption in the present
if > 1 then positive time preference and consumes more in the future (patient)
if < 2 then negative and consumes more today (impatient)
Milton Friedman’s primary determinant of current consumption
Primary determinant of current consumption is =
Permanent income
Permanent income = PV of lifetime income
Effect of a fall in IR on consumers who are:
1) saver
2) borrower
Saver
- future consumption decreases!
- current consumption (? ambiguous)
Borrower
- future consumption (? ambiguous)
- current consumption increases!
Demand for REAL capital
- constant rental rate
(MRP)
MRP(k) = MP * MP(k) = r
Value of marginal product of capital
VMP(k) = P* MP(k)
Bond (definition)
A contract in which the borrower agrees to pay the bondholder a stream of money
Perpetuity (type of bond or also known as Consol)
A bond that pays out a fixed amount each year forever
example: endowments
- face value doesn’t matter
Pc = X /I (derived through PV equation)
Technological obsolescence (Definition)
a good loses value (not due to depreciation) but due to improvements in technology, making substitute products more attractive
Retail price of a unit of real capital
r = i + m + depreciation
I = IR m = maintenance cost
PV equation
R-M/(1+i) + R-M/(1+i)^2 … R-M/(1+i)^n + S/(1+i)^n
Firm should buy machine if Pv > Pk
Pk = price of machine (physical capital)
Interest rate determination
Demand:
1) Firm - how much capital it has and how much it would like to have
2) Consumers - borrow finance for house or other goods
3) Government - funding
Supply:
1) Consumer savings
2) International lenders (growing importance)
- upward sloping supply curve
Risk Premium (definition)
a payment differential necessary to compensate the supplier of a good or service for having to bear risk
Trade-off between safety and expected return
Cautious investors invest in safer stocks (with lower returns)
Less cautious investors give up safety for a higher expected return
Economic rent (definition)
Difference between what a factor of production is paid and the MIN necessary to indue it to remain in its current use
Exhaustible resources
Cannot be replenished by people.
owner of stock must decide: how much to sell of current stock and how much to keep for sale in the future
For market equilibrium:
- Price must be increasing at precisely the rate of interest
Pt = Po (I + i)^t ——> price after t years
Stock exhaustion path: plotting the quantity of a good remaining at each moment
- downward sloping curve
if ∆Pt > i then no one would sell (& if MB to someone using the resource today > Pt then they will bid up current price)
if ∆ Pt < i then everyone would sell (& if MB to someone of last unit of resource today is < Pt thy will not purchase and current price must fall)
Example: Solar and oil
- lowering price of solar = price path of oil shifts downwards
- more demand for oil and oil being depleted earlier
Deriving Perpetuity bond equation
Use PV
PV = X/(1 + i) + X/(1+i)^2 + X/(1+i)^3
y = 1/1+I + 1/(1+i)^2 (multiply both sides by 1+i)
y(1+i) = 1 + 1/(1+i) + 1/(1+i)^2
RHS is function of Y
y = 1/ i
PV = X/i
If P > PV then no one would buy
If P < PV then P would bid up till the point P = PV
Annual Return for Stock (equation)
R = (P1 - Po + d)/Po = (∆P + d)/ Po Po - initial price P1 - end price d - dividends
Risk Averse investors
Rm > Rf
Rm = expected return on stock market
Rf = Return on risk free asset
Expected Value of Portfolio
Rp
Rp = Rf + (Rm - Rf)/σm (σp)
- tradeoff between expected payout and risk
- since Rf, Rm and σm are constants
Intercept = Rf
Slope = (Rm-Rf)/σm
- price of the risk
- the increase in return needed to offset the higher risk
- difference in return from risk free and risky assets and variance on return of risky assets
Question of finding effective yield
effective yield is the interest rate for which PV = P
so set P = PV and find IR
What happens to price in the LR if IR was lower than the effective yield (P=PV) of the bond
If IR < Effective yield then purchasing would be a good investment
- as PV > IR
- Firms would realise this and bid up price till PV = P
Alternatively more firms can enter market & increase competition
- this would result in lower price of product sold by firm and decrease return generated
- essentially excess profits will be eroded through competition
Calculating Float
Dell question from tutorial.
APR = annual percentage rate
- e.g. making suppliers wait 37 days to get paid when paid by consumers immediately
- Annual IR = 4%
- as 37 days is around 1/10
- 1/10 * 4% = 0.4%
they retain 0.4% of spending
Expected value
Each of possible outcomes * probability of outcome occurring
Variance of random variable
- tells us about the spread of possible values of the variable
- an indicator of risk!
𝑉𝑎𝑟(𝑋) = 𝐸[(𝑋−𝐸(𝑋))^2]
- calculate expected value to use equation
- take that away from return and square
- multiple it by the probability for each outcome
What is the expected return of a portfolio?
xr(a) + (1-x) r(b)
What is the variance of the return of the portfolio?
Calculate all possible outcomes and their probabilities and then find the expectations
Capital (flow or stock)?
Capital is measured as a stock
durable and can be used several periods in a row!
Budget Constraint for investors
Always upward sloping.
Cannot be downward sloping as it would mean one of the assets have lower return and higher risk, this wouldn’t happen given assumption of risk averse investors
Budget Constraint if p = -1
- direction of asset movement
- change in original graph
Assets would move in different directions, as p = -1.
E.g. with p = 1, linear combination of assets and would move together, both fall during recession and both increase during boom
decreased return in one asset will be offset by an increased return on the other.
- now graph = 2 straight lines from point B, joined at y axis where risk is equal to 0
when 0 < p < 1, BC will be within the triangle
Closer P is to = 1, closer BC will be to p = 1
and same for p = -1
Rf?
Rm?
rf?
b?
Rf = Return on risk free assets
Rm = expected return on stock markets
rf = realise return on stock market
b = proportion invested in stock market
Risk averse investors therefore Rm > Rf
Budget Constraint
𝑐1+𝑐2/(1+r) ≤𝑤1+𝑤2(1+r)
total consumption cannot exceed present value of total income
- increase in IR makes BC steeper
