Topic7-CoC_AAP - Investment The Cost of Capital /...

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Unformatted text preview: Investment The Cost of Capital / Investment Topic 7 (Text: 4.2) 1 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 We posited/derived a downward-sloping I(r) curve We downward- The equilibrium capital for each firm then is at: The MPK = R/P = r + δ 4 The CoC & Investment (cnt.) cnt.) Id , Kd – demands for Investment and Capital They are downward-sloping functions of r They downward- K0 is the current (or initial) Capital stock δ is the depreciation rate Id(r) = δ K0 + Kd(r) – K0 Id(r) = Kd(r) – (1 – δ )K0 Hence a downward sloping I(r) curve Hence Combine all the firms’ demands for investment Combine firms’ The total demand for investment must be just equal to the The economy-wide saving: I = S economyIn a closed economy In Equilibrium r* is at the capital market equilibrium Equilibrium r* 5 1 1 U.S. Gross and Net Investment U.S. Gross & Net Investment % of GDP 25% Gross INV Net INV 20% 15% 10% 5% 02 -I 06 -I 20 20 94 -I 90 -I 86 -I 98 -I 19 19 19 19 82 -I 78 -I 19 19 70 -I 66 -I 74 -I 19 19 19 62 -I 58 -I 19 19 54 -I 50 -I 19 19 42 -I 46 -I 19 38 -I 19 19 30 -I 19 19 34 -I 0% -5% -10% -15% 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 real-life equivalent is the leasing of equipment The realLeasing firms purchase new capital and rent it out Leasing to other firms 7 The CoC & Investment (cnt.) cnt.) • • Firms usually both purchase and lease capital But, from the point of view of 1. the financial cost of capital 2. the value-added 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 8 2 2 The CoC & Investment (cnt.) cnt.) • The $ cost of one unit of capital is one • = i PK - ΔPK + δ PK, i PK δ nominal interest rate nominal purchase price of new investment ΔPK capital gain, and the depreciation rate Rewrite this cost as: PK (i - ΔPK/PK + δ ) Example: Cost of a house 9 The CoC & Investment (cnt.) cnt.) PK (i - ΔPK/PK + δ ) • In simple macro models we assume that PK = P The unit price of investment (capital good) is same as the The unit price of other goods and services • Since ΔP/P is the inflation rate, and r =i− ΔP P We can rewrite the unit $ cost as Unit Cost = P (r + δ ) Unit 10 The CoC & Investment • Bottom Line A unit of capital produces MPK Given the choice of labor, the state of technology, Given etc. • • • • • 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 11 3 3 Distortions of Corporate & Personal Taxes • “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 12 Taxes & Investment • If τf is the marginal tax rate for firms’ marginal firms’ profits, then: MPK (1-τf ) = 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 Taxes reduce after-tax revenues Taxes afterRequires a higher MPK to pay the same r + δ Requires MPK 13 Taxes & Investment (cnt.) cnt.) • Similarly, taxes affect greatly the after-tax afterreturns Taxes are levied on nominal payments Taxes • After-tax returns are: iAT = iBT (1-τc) After(1• The implied real return is: real rAT = i (1-τc) - π (1Also, rBT = i - π Also, 15 4 4 Taxes & Investment (cnt.) cnt.) rAT = i (1-τc) - 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 Example #1 • 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 ΔPk 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 5 5 THE END 32 6 6 ...
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