Inventory Investment.
Investment Decision and
Expected Profit
Lecture 5
Inventory Accumulation
1. Inventory stocks
1) Changes in inventory holdings represent an
important and highly volatile type of investment
spending.
2) Three basic kinds of inventory stocks:
a. Primary inputs to production
b. Semi-finished goods in the course of
production.
c. Finished goods ready for sale to final users.
Inventory Stocks as a % of Total inventory in
U.S Manufacturing, 1990
31%
32%
37%
Primary
mterial
work-inprocess
Finished
goods
Inventory Stocks As a % of Annual Shipments in U.S
Manufacturing, 1990
60
40
20
0
As a % of
annual
shipments
Primary
materials
Primary
materials
Work-inprocess
Finished
goods
2. Firms need inventories of primary materials to
economize on the costs of producing final output.
3. Most formal theories of inventory management
focus on final goods inventories.
1) Production smoothing
2) Avoidance of stockouts
The firm must balance the costs of inventory
holdings against the costs of involuntary stockouts.
So, it is important to derive a mathematics rule for
optimal inventory management.
Firms hpld finished goods
inventories

1.They can maintain smooth rate of production
despite a variaable rate of demand for their output;
– Rising MC of production(each extra unit is more
expensive to produce than the previous unit)

2. Stock out avoidance: The firm must balance the
cost of inventory holdings against the cost of
involuntary stockouts. For optimal inventory
management use some rules: i.e. Ss Rule
Ss Rule





S and s denotes the levels of inventories.
Profit maximizing firm sets production each period
according to expected demand, plus a constant.
Over time, fluctuating inventories; If demand is higher
than expected, inventories will fall; if demand is lower
than expected inventories will rise.
The firm replenishes its inventories whenever these fall
below a certain low level, s.
The firm targets production so that it will meet expected
demand and also increase inventory holdings back up to a
level, S. where S greater than s.
Empirical Investigations on
Investment Expenditure
1. Even armed with these theories of investment,
however, it is quite difficult to explain—much less
to predict—patterns of investment spending.
2. Several econometric models have been developed
to explain actual investment behavior.
1) The accelerator Model of investment
2) The adjustment-cost approach
3) The q theory
4) Theories based on credit rationing
Investment Decision
Investment
decisions depend on current
sales, the current real interest rate, and
on expectations of the future.
The decision to buy a machine depends
on the present value of the profits the firm
can expect from having this machine
versus the cost of buying it.
Investment and Expectations
of Profit
Depreciation:
rate of depreciation, , measures
how much usefulness the machine loses
from one year to the next.
Reasonable values for  are between 4
and 15% for machines, and between 2
and 4% for buildings and factories.
The
The Present value of
Expected Profits
V(et):
The present value, in year t, of expected profit in
year t+1 equals:
1
 e t 1
1  rt
In year t+2,
1
e
(
1


)

t 2
e
(1  rt )(1  r t 1 )
In year t,
1
1
e
e
V ( t ) 
 t 1
(
1


)

t 2    
e
1  rt
(1  rt )(1  r t 1 )
e
The Present value of
Expected Profits
Computing
the
Present Value of
Expected Profits
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The Investment Decision
as aggregate investment, t as profit
per machine (or per unit of capital) for the
economy as a whole, and V(et) as the expected
present value of profit per unit of capital. This
yields the investment function:
Denote It
I t  I (V ( e t ))
( )
In words: Investment depends positively on the expected present
value of future profits (per unit of capital).
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A Convenient Special Case
Suppose
firms expect both future profits and
future interest rates to remain at the same level
e
as today, so that  e


t 1
and
e
t 1
r
t2
r
e
t2
t
 rt
Economists call such expectations –
expectations that the future will be like the
present –static expectations. Under these two
assumptions, we get
t
e
V ( t ) 
rt  
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A Convenient Special Case
t
Putting V ( t ) 
and
rt  
e
I t  I (V ( e t ))
together give us an equation for investment:
 t 

It  I 
 rt   
The sum of the real interest rate and the
depreciation rate is called the user cost or the
rental cost of capital.
Therefore,
Rental Cost  (rt   )
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Current Versus Expected
Profit
Investment
depends on expected future profit,
but also moves strongly with fluctuations in
current profit.
I t  I (V ( e t ),  t )
(  , +)
 Firms may be reluctant to borrow if current profit
is low. But if current profit is high, the firm may
not need to borrow to finance its investments.
 Even if the firm wants to invest, it might have
difficulty borrowing. Potential lenders may not be
convinced the project is as good as the firms
says.
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Current Versus Expected
Profit
Changes
in
Investment and
Changes in Profit in
the United States
since 1960
Investment and profit
move very much
together.
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Profitability Versus Cash Flow
Profitability
refers to the expected present discounted value
of profits.
Cash flow refers to current profit, or the net flow of cash the
firm is receiving.
Both profitability and cash flow are important for investment
decisions, and are likely to move together.
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Profits and Sales
Changes
in Profit
per Unit of Capital
Versus Changes in
the Ratio of Output
to Capital in the
United States since
1960
Profit and the ratio of
output to capital
move largely
together.
 Yt 

 t  
 Kt 
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The Volatility of
Consumption and Investment
Let’s
look at the similarities between our treatment of
consumption and of investment behavior:
 Whether consumers perceive current movements in
income to be transitory or permanent affects their
consumption decisions.
 In the same way, whether firms perceive current
movements in sales to be transitory or permanent affects
their investment decisions.
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The Volatility of
Consumption and Investment
But
there are also important differences between
consumption decisions and investment decisions:
 When faced with an increase in income that consumers
perceive as permanent, they respond with at most an
equal increase in consumption.
 When firms are faced with an increase in sales they
believe to be permanent, their present value of expected
profits increases, leading to an increase in investment.
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The Volatility of
Consumption and Investment
Rates
of Change of
Consumption and Investment
since 1960
Relative movements in investment
are much larger than relative
movements in consumption.
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The Volatility of
Consumption and Investment
The
figure yields
three conclusions:
 Consumption and investment
usually move together.
 Investment is much more volatile
than consumption.
 Because, however, the level of
investment is much smaller than
the level of consumption, changes
in investment from one year to
the next end up being of the same
overall magnitude as changes in
consumption.
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The end

Questions
 Discussion