Topic 2 - Investment Flashcards
How do we calculate Future Value (F.V)?
PV(1+I)n
Where:
P.V present value
I: Interest Rate
N: No of years which compounding takes place
E.G:
£100 deposit 6% annum after 4 years
100(1+0.05)4 = 126.25
How do we calculate Present Value (P.V)?
P.V= FV/(1+I)N
OR
P.V= FV x 1/(1+I)N (To the power of N)
E.g:
6% annum. How much do i need to deposit to get 126.25 after 4 years?
126.25/(1+0.06)4 = 100
What is NPV used for?
To see if an investment will be profitable
How do we calculate NPV?
NPV= CF0 + CF1/(1+K)N (to the power of N)
Where;
CF0= Cash flow at time 0 (t0)
CF1= Cash flow at time 1 (t1)
K= Generally means interest
E.G. CF0= -3000 CF1= 900
Over 4 years 10% Interest
NPV= -3000 + 900/(1+0.1)4
When do we accept and reject an investment based on NPV?
If NPV is equal to or greater than 0: ACCEPT
If NPV is less then 0: REJECT
What does the Neoclassical Model believe investment depends on?
1) MPK= F(L,(K+1)) - F(L,K) for Y=F(L,K)
2) Interest rate
3) Tax rule affecting firms
What does the denotations of MPK represent?
MPK= F(L,(K+1)) - F(L,K) for Y=(L,K)
(CURRENT) (PREVIOUS)
Where:
L= Labour Capital
(K+1) = Extra unit of capital
K= CapitalWhat does the formula of MPK represent?
Represent the change in output from getting an extra unit of capital
Why is there diminishing marginal product with capital?
(Yk> 0, Ykk<0)
As capital increases it gets to a point where capital becomes idle so productivity decreases
For the sake of simplicity behind the Neoclassical model what do we assume?
Assume only 2 types of firms:
1) Production Firms:
Don’t own the capital but rent from a rental firm to produce goods and services
2) Rental Firms:
Own capital and rent it to production firms
What does the capital rental market look like?
SEE GRAPH IN NOTES
How do we calculate the change in profit from 1 more unit of capital?
Δ PROFITS= Δ REVENUE - ΔCOST= P x MPK - R
Where R is the rental rate (cost)
How does a production firm maximise profits?
Firm must increase capital to the point where MPK= R/P
R/P is the real cost of capital
How can we accurately see the factors that affect rental price?
We can see this via the Cobb-Douglas production function
How do we calculate the Cobb-Douglas Production function?
Y= AKα L (1-α)
Where:
α and (1-α) is to the power of
A= Technology K = Capital α = Amount of income devoted to capital L = Labour (1-α) = Amount of income devoted to labour
SEE NOTES FOR BETTER VIEW
How can we rewrite the Cobb-Douglas function to work for the MPK?
R/P = MPK = αA(L/K) (1-α)
Where 1-α is to the power of
SEE NOTES FOR CLEARER VIEW
When will equilibrium R/P increase?
K goes down (e.g. Earthquake or War)
L goes up (e.g. Pop. growth or immigration)
A goes up (e.g. Tech improvement or deregulation)
How will rental firms make investment decisions?
Rental firms invest in new capital when benefit of doing so outweighs the cost
The benefit of purchasing (per unit capital): R/P (Income that rental firms earn from renting the unit of capital to production firms)
What are the three costs of capital to rental firms?
Interest rate= 1 x Pk (denoted usually as iPk)
Where Pk is nominal price of capital
Depreciation Cost = δ x Pk
Where δ is rate of depreciation
Capital Loss = -ΔPk
How do we get the nominal cost of capital (Total cost)?
iPk + δPk - ΔPk = Pk(i + δPk - ΔPk/Pk)
Either way works
e.g. Cost of Cars
Pk = 10,000 ΔPk/Pk = 0.06
i = 0.10 δ = 0.20
interest rate cost: 1,000
depreciation cost: 2,000
Capital Loss: -600 (Minus cus ΔPk/Pk = 0.06 repping capital gain) = 2,400
How do we calculate the real cost of capital for a rental firm?
We assume that: ΔPk/Pk = Π
Therefore nominal cost of capital= Pk (i+δ - Π) = Pk (r+δ)
R is there to represent real values: Taking nominal interest and minusing inflation giving real inflation
What does the real cost of capital depend positively on?
- Relative price of capital
- Real Interest Rate
- Depreciation Rate
What does a firm’s net investment depend on?
Profit Rate
How do you calculate profit rate?
R/P - Pk/P (r + δ) = MPK - Pk/P (r + δ )
PROFIT) (COST
What happens when the profit rate is greater than and less than 0?
If profit rate > 0, then increasing K is profitable
If profit rate < 0, then firm increases profits by reducing its capital stock (i.e. not replacing capital as it depreciates)
How do we calculate Net Investment?
ΔK = iN [MPK - (Pk/P) (r + δ )]
(Benefits) (costs)
Where:
iN [ ] = Function that shows how net investment responds to the incentive to invest
How do we calculate Gross Investment?
ΔK + δK = iN [ MPK - (Pk/P) (r+ δ )] + δK
What is the Investment Function denoted as?
I = iN [MPK- (PK/P)(r+ δ)] + δK
What happens investment if we were to increase the interest rate (r)? (Following Investment Function)
- raises the cost of capital,
- reduces the profit rate
- reduces investment
(SEE GRAPH)
What happens to investment if we were to increase MPK or decrease Pk/P? (Following Investment Function)
- Increase in profit rate
- Increases investment at any given interest rate
- Shifts Investment curve to the right
(SEE GRAPH)
What is two of the most important tax policies affecting investment?
- Corporate income tax
2. Investment Tax Credit
Why does the impact on investment depend on our definition of profits?
- In our definition (rental price minus cost of capital), depreciation cost is measured using current price of capital, and the corporate income tax would not affect investment
- But, the legal definition uses the historical price of capital
If Pk rises over time then legal definition understates the true cost and overstates profit
So firms could be taxed even if their true econ profit is zero
Thus, corporate income tax discourages investment
What is the Investment Tax Credit (ITC)?
- The ITC reduces a firm’s taxes by a certain amount for each dollar it spends on capital
- Hence ITC effectively reduces Pk, which increases the profit rate and incentive to invest
What is the critique of the Neoclassical investment model?
- Talking about investment in current period instead of future shows the model is too static
- Does not account for changing costs
What is the calculation for Tobin’s Q?
Q = Market Value of installed captial/ Replacement cost of installed capital
Where:
-The numerator: The stock market value of the economy’s capital stock (Money from investors if purchase one unit of capital)
- Denominator: The actual cost to replace the capital goods that were purchased when stock was issued
(Price of Capital) - If Q>1, firms buy more capital to raise the market value of their firms
- If Q<1, firms do not replace capital as it wears out
What is the more formal treatment of Tobin’s Q?
-The cash flow generated each period by firm is:
F(Pt, Kt)
V0 = F(P1,K1)/(1+r) + F(P2,K2)/(1+r)2 + F(P3, K3)/(1+R)3 …
Cost of initally installed capital is:
Pk K0
Therefore, can write Tobin’s q as:
q = V0/Pk K0
What do we assume with the Tobin’s q?
K is durable from year to year.
Capital stock doesn’t change.
If volume same, therefore price is the same….
K= K0 = K1 = Kn P = P0 = P1 = P2= Pn
Using the geometric series formula how can we rewrite the Tobin’s q?
α + αx + αx2 + αx3 =
α/1-x means V0 = F(P,K)/1+r x 1/1- 1/1+r
gives us F(P,K)/r
Therefore, we can write: q= F(P,K)/rPk,K
(CHECK LECTURE 23RD OCTOBER)
What are some elements added on by the q model?
The same factors that - —-Cause a change in investment in the optimal capital stock model are likely to cause a change in investment in the q model.
- Investment is likely to rise if productivity or output prices rise, or the interest rate falls. These factors will lead to an increase in the market value of the firm. A fall in the cost of capital goods would also encourage investment.
- The main feature added by the q model is that current investment will also be infuenced by the future values of these variables.
What does adding adjustment costs enable us to do for the q theory?
Adding this insight to the q-theory enables us to write down a rule that determines investment:
𝐼=1/𝜃(𝑞−1)
Where:
theta (the weird 0)
- Investment will increase when q > 1 and fall when q < 1.
- The θ parameter reflects installation costs: as these rise, investment will respond more gradually.
What’s the relation between q theory and neoclassical model?
- The stock market value of capital depends on the current & expected future profits of capital.
- If MPK > cost of capital, then profit rate is high, which drives up the stock market value of the firms, which implies a high value of q.
- If MPK < cost of capital, then firms are incurring losses, so their stock market values fall, so q is low.
How can we see the relation between the stock market and GDP (wave of pessimism about future profitability of capital)?
Wave of pessimism about future profitability of capital would:
- Cause stock prices to fall
- Cause Tobin’s q to fall
- Shift investment function down
- Cause a negative aggregate demand shock
How can we see the relation between the stock market and GDP (fall in stock prices)?
Fall in stock prices:
- Reduce household wealth
- Shift the consumption function down cause a negative aggregate demand shock
-Might reflect bad news about technological progress and long-run economic growth
What are financing constraints?
- Limits on the amounts they can borrow (or otherwise raise in financial markets)
- If firms faces financing constraints and current profits are low, firm might be unable to obtain funds
What is the denotations behind residential investment?
The flow of new residential investment (Ih)
depends on relative price of housing (Ph/P)
Ph/P determined by supply and demand in the market for existing houses
How is residential investment determined? (Market for housing)
SEE GRAPH IN NOTES
What is the Accelerator Model?
Theory that explains the behaviour of inventory investment without endorsing any particular motive
What are the notations of the Accelerator Model?
N = Stock of Inventories ΔN = Inventory Investment
What are the assumptions behind the accelerator model?
Firms hold a stock of inventories proportional to their output N = βY,
where β is an exogenous parameter reflecting firms’ desired stock of inventory as a proportion of output
What result can we see come out of the assumptions of the accelerator model and the denotations?
Result: ΔN = β ΔY
- Inventory investment is proportion to the change in output.
- When output is rising, firms increase their inventories.
- When output is falling, firms allow their inventories to run down.
