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Unformatted text preview: The Cost of Capital & Investment
• We saw that:
A firm sets its desired capital stock so that MPK
firm
MPK
equals the real rental rate of capital (R/P)
rental
Gross cost of employing capital is = r + δ
Gross Investment We posited/derived a downwardsloping I(r) curve
We
downward The equilibrium capital for each firm then is at:
The
MPK = R/P = r + δ The Cost of Capital / Investment 1 4 The CoC & Investment (cnt.)
cnt.) U.S. Gross and Net Investment Id, Kd – demands for Investment and Capital
They are downwardsloping functions of r
They
downward U.S. Gross & Net Investment % of GDP
25% K0 is the current (or initial) Capital stock
δ is the depreciation rate Gross INV
Net INV
20% Id(r) = δ K0 + Kd(r) – K0
Id(r) = Kd(r) – (1 – δ )K0 15% 10% 5% 02
I 98
I 06
I
20 20 19 94
I 90
I
19 19 82
I 78
I 86
I
19 19 19 74
I 70
I
19 19 62
I 58
I 66
I
19 19 54
I
19 46
I 50
I
19 38
I 42
I 19 19 19 30
I 34
I 0% 19 Combine all the firms’ demands for investment
Combine
firms’
The total demand for investment must be just equal to the
The
economywide saving: I = S
economy 19 Hence a downward sloping I(r) curve
Hence 19 Topic 7 (Text: 4.2) 5% In a closed economy
In Equilibrium r* is at the capital market equilibrium
Equilibrium r* 10% 5 15% The CoC & Investment (cnt.)
cnt.) 6 The CoC & Investment (cnt.)
cnt.)
• • The best way to think of a manufacturing
manufacturing
firm is that it is renting its entire capital
renting
stock from a rental firm
rental
The reallife equivalent is the leasing of equipment
The realLeasing firms purchase new capital and rent it out
Leasing
to other firms • Firms usually both purchase and lease
capital
But, from the point of view of
1. the financial cost of capital
2. the valueadded or profitability of the firm
value the cost of rental is the important quantity
rental
If the firm buys its capital outright, it must either
If
borrow the money or issues new shares
Either way, it has to pay a cost r*
Either
Abstracting from risk
Abstracting 7 8 1 1 The CoC & Investment (cnt.)
cnt.) The CoC & Investment (cnt.)
cnt.)
PK (i  ∆PK/PK + δ )
• In simple macro models we assume that
PK = P • The $ cost of one unit of capital is
one
•
= i PK  ∆PK + δ PK,
i
PK δ nominal interest rate
nominal
purchase price of new investment The unit price of investment (capital good) is same as the
The
unit price of other goods and services ∆PK capital gain, and • Since ∆P/P is the inflation rate, and the depreciation rate r =i− Rewrite this cost as: PK (i  ∆PK/PK + δ )
Example: Cost of a house ∆P
P We can rewrite the unit $ cost as
Unit Cost = P (r + δ )
Unit
9 The CoC & Investment
• Distortions of Corporate & Personal Taxes Bottom Line
A unit of capital produces MPK
Given the choice of labor, the state of technology,
Given
etc. •
•
•
•
• 10 Firms pay the real interest rate, r, to raise
funds for capital investment
Capital also depreciates at the rate δ
They will invest more if MPK > r + δ
MPK
They will invest less if MPK < r + δ
The equilibrium is when MPK = r + δ
MPK • “Distortion” in economese means that the
Distortion”
market price or return the market offers is
different than the price or return the owner
different
gets
This causes economic inefficiencies and loss of
This
welfare
Lots of things can cause distortions
Lots • Taxes are a major source of distortions
• We look at the effects of corporate and
personal taxes 11 Taxes & Investment 12 Taxes & Investment (cnt.)
cnt.) • If τf is the marginal tax rate for firms’
marginal
firms’
profits, then:
MPK (1τf ) = R/P
MPK (1• And this gives:
1 R r +δ
=
MPK =
1−τ f P 1−τ f
the cost of investment in new capital • Similarly, taxes affect greatly the aftertax
afterreturns
Taxes are levied on nominal payments
Taxes • Aftertax returns are: iAT = iBT (1τc)
After(1• The implied real return is:
real
rAT = i (1τc)  π
(1Also, rBT = i  π
Also, Taxes reduce aftertax revenues
Taxes
afterRequires a higher MPK to pay the same r + δ
Requires
MPK
13 15 2 2 Example #1 Taxes & Investment (cnt.)
cnt.) • rAT = i (1τc)  π
(1As inflation increases the same tax rate on nominal
As
returns taxes real returns more!
real r(BT) Inflation i Tax 0.0% r(AT) 0% 5.0% 0% 15.0% 0% 0.0% 40% 5.0% 40% 15.0% 40%
16 Hula hoop “fabricators” cost $100. HHHHC is
fabricators”
$100
deciding how many machines to buy. It expects
the following production from these machines:
No. of Machines
1
2
3
4
5
6 No. of Hoops Produced
100
150
180
195
205
210 1. If r = 12% and δ = 20%, what is the user cost of
12%
20%
capital in $s per fabricator? The real cost?
2. How many machines should HHHHC buy?
25
Hoops sell for $2.00
$2.00 Glossary of Terms
Kd
Id
i
r δ
R/P
Pk
∆Pk
τf , τc Desired capital stock
Implied desired investment flow
The nominal (market) interest rate
The real interest rate
Rate of capital depreciation
Real rental rate of capital
Purchase price of new investment goods
Capital gains
Tax rates on firms and consumers, respectively 31 THE END 32 3 3 ...
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This note was uploaded on 03/02/2010 for the course BUAD 350 taught by Professor Safarzadeh during the Spring '07 term at USC.
 Spring '07
 Safarzadeh
 Cost Of Capital

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