Financing Durable Assets

Transcription

1 Duke University, NBER, and CEPR Finance Seminar MIT Sloan School of Management February 10, 2016

2 Effect of Durability on Financing Durability essential feature of capital Fixed assets comprise as much as 72% of aggregate capital stock Includes structures (both residential and non-residential) infrastructure, equipment, and consumer durable goods Focus on tangible durable assets but intangible assets similar Variation in durability Depreciation rates vary from as low as 1% (new residential structures) to as high as 31% (computing equipment) How does durability affect financing? Can durable assets serve as collateral and facilitate financing? Intuitively, as the assets become more durable, they provide the creditor with the security to wait longer before being repaid.... And hence the debtor need not set aside as much of his initial borrowing to finance early debt repayments, leaving more to finance the initial investment Hart/Moore (1994)

3 Effect of Durability on Financing (Cont d) To the contrary: durable assets are harder to finance Durability increases resale/collateral value allowing more borrowing But durability also raises price of asset and hence financing need Net effect: raises down payments Implications Choice between vintages: new, durable vs. used, non-durable assets Trade in used capital goods Technology adoption: dominated technologies may be adopted Rent vs. buy decision Also: effect of legal enforcement Critical distinction between durability and pledgeability Durability impedes financing Pledgeability facilitates financing Hart/Moore (1994) is about pledgeability not durability

4 Model of Durable Asset Financing Discrete time, infinite horizon, deterministic productivity Entrepreneurs ( borrowers or firms ) Measure ρ (0, 1) enter each period; survive with probability 1 ρ; measure 1 alive Preferences: t=0 βt d t with β (0, 1), d t 0, and β ˆβ(1 ρ) Initial net worth w 0 (cash-in-hand) In equilibrium, well capitalized entrepreneurs are financiers Equilibrium (gross) interest rate R = β 1 Limited enforcement Borrowers can default and abscond with all cash flows and fraction 1 θ of assets without exclusion where θ [0, 1) Rampini/Viswanathan (2010, 2013, 2015) Optimal dynamic contract can be implemented with one-period ahead debt subject to collateral constraints

5 Model of Durable Asset Financing (Cont d) Technology New assets last for two periods New, durable assets k d last two periods price 1 Used, non-durable assets k nd one period of useful life left price q Perfect substitutes in production; output Af(k d + k nd ) where A is TFP and f is (strictly) increasing, concave, and lim k 0 f k (k) = +

6 Entrepreneur s Problem Recursive Formulation Given net worth w, entrepreneur solves v(w) max d + βv(w ) (1) d,k d,k nd,b,w R 3 + R2 subject to budget constraints for current and next period w + b d + k d + qk nd (2) Af(k d + k nd ) + qk d Rb + w (3) and the collateral constraint θqk d Rb (4) Endogenous state variable: net worth w

7 Characterization of Entrepreneur s Problem Well-behaved dynamic program Return function concave; constraint set convex Operator defined by (1) to (4) satisfies Blackwell s sufficient conditions Solution:! value function v; strictly increasing; concave First order conditions Denote multipliers on (2) and (3) by µ and βµ and on (4) by βλ µ = 1 + ν µ = βµ [Af k (k d + k nd ) + q] + βλ θq + ν d µq = βµ Af k (k d + k nd ) + ν nd µ = µ + λ µ = v w(w ) Envelope condition: v w (w) = µ Value function continuously differentiable

8 Down Payment When collateral constraint binds, b = R 1 θqk d and so 1 R 1 θq is minimal down payment required per unit of new, durable assets In equilibrium, Down payment on new, durable assets exceeds used capital price > q R θ + R > q Otherwise new, durable assets would dominate (arbitrage) Why do new, durable assets require larger down payment? = 1 R 1 θq = 1 R 1 q }{{} user cost u d + R 1 (1 θ)q }{{} non-pledgeable part of resale value New, durable assets down payment includes 1 θ of resale value

9 Durability and Financing Need Financing need of new, durable and used, non-durable assets Time t t + 1 t + 2 Used, non-durable assets Value q 0 Collateral value 0 Borrowing 0 Internal funds required q

10 Durability and Financing Need Financing need of new, durable and used, non-durable assets Time t t + 1 t + 2 Used, non-durable assets Value q 0 Collateral value 0 Borrowing 0 Internal funds required q New, durable assets Value 1 q 0 Collateral value q Borrowing R 1 θq Internal funds required 1 R 1 θq New, durable assets require more internal funds > q... despite ability to borrow R 1 θq > 0... because they cost more 1 > q larger financing need

11 User Cost of Capital for Unconstrained Firm Frictionless user cost (rental rate) of capital u would be 1 = u + R 1 u u = R 1 + R Equilibrium user costs with collateral constraints User cost of used, non-durable assets: u nd q In equilibrium q u = R 1 + R User cost of new, durable assets (for unconstrained borrowers): u d 1 R 1 q 1 R 1 R 1 + R = u q = u nd User cost of new, durable assets less than that of used ones

12 Durability and Depreciation Rate In first period, new assets depreciate at depreciation rate δ d 1 q 1 1 R 1 + R = R < 50%... and in second period (when used) at rate δ nd q 0 q = 100%

13 Dividend Paying Firm Once firm starts to pay dividends, it always pays dividends and is unconstrained Marginal value of net worth v w(w) = µ = 1 Firm is unconstrained going forward v w(w ) = µ = 1 and λ = 0 If q > R 1+R, unconstrained firm purchases only new assets u d = βaf k (k d + k nd ) + ν d u nd = βaf k (k d + k nd ) + ν nd Unconstrained firms simply compare user costs Unconstrained firms sell assets once they are old/used Capital stock of unconstrained firm k d solves 1 = β[af k (k d ) + q]

14 Investment Euler Equation and Constrained Investment Severely constrained firm purchases only used capital As w 0 so does k d + k nd and hence f k + Using Investment Euler equations 1 = β µ Af k (k d + k nd ) + (1 θ)q + ν d µ µ 1 = β µ Af k (k d + k nd ) + ν nd µ q µq and combining Euler equations ν d > 0 q }{{} Incr. cost of new capital = β µ (1 θ)q µ }{{} Valuation of resale value + ν d µ ν nd µ Severely constrained firms simply compare down payments More

15 Equilibrium Marginal investor in used capital Indifferent between investing in new and used capital: ν d = ν nd = 0 Investment Euler equations imply Down payment {}}{ 1 R 1 θq q = β µ (1 θ)q µ }{{}}{{} Incr. cost of new capital Valuation of resale value If constrained firm prices used assets, then q > β µ µ < R 1 implies q > R 1+R (or u d < u nd ) Moreover, β µ > 0 so R > q (or > q) µ θ+r R 1+R Market clearing condition in used capital market p(w)(1 ρ)kd (w) = p(w)k nd (w) }{{}}{{} supply of used assets demand for used assets where p(w) is stationary net worth distribution

16 Trade World market for used capital (at price q > R 1+R ) Weak legal enforcement economies net used capital importers Strong vs. weak legal enforcement economies: θ H > θ L Unconstrained firms investment identical: 1 = β[af( k d ) + q] Constrained firms indifferent between new and used assets when Af k (k) + (1 θ)q = Af k(k) q With weak legal enforcement, firms indifferent when their capital stock is larger k L > k H at higher level of net worth More firms use used assets in weak legal enforcement economies

17 Durability and Down Payments: Neoclassical Investment Suppose neoclassical capital depreciates at rate δ per period k = k(1 δ) + q 1 i where q is price of capital and i investment Firm s problem with neoclassical investment: Given w, solve v(w) max d + βv(w ) (5) d,k,b,w R 2 + R2 subject to budget constraints and collateral constraint w + b d + qk (6) Af(k) + qk(1 δ) Rb + w (7) θqk(1 δ) Rb (8)

18 Characterization of Entrepreneur s Problem Well-behaved dynamic program First order conditions Denote multipliers on (6) and (7) by µ and βµ and on (8) by βλ µ = 1 + ν µq = βµ [Af k (k) + q(1 δ)] + βλ θq(1 δ) µ = µ + λ µ = v w(w ) Envelope condition: v w (w) = µ Value function continuously differentiable

19 Effect of Durability on Down Payment and User Cost Effect of durability on down payment Minimal down payment per unit of capital δ = q R 1 θq(1 δ) = R 1 qθ > 0; more durable capital has lower down payment? But keeping q fixed, lower δ reduces frictionless user cost of capital! u R 1 q(r + δ) More durable capital requires larger down payment Fixing frictionless user cost u instead, price is q(δ) = Ru r+δ Down payment keeping user cost fixed (δ) δ = q(δ) 1 θ r+δ < 0 (δ) = q(δ) R 1 θq(δ)(1 δ)

20 Adopting Dominated Technologies Suppose two types of neoclassical capital of different durability depreciation rates δ d < δ nd prices q d > q nd such that frictionless user costs u d < u nd, i.e., (r + δ d )q d < (r + δ nd )q nd down payments d > nd, i.e., q d (1 R 1 θ(1 δ d )) > q nd (1 R 1 θ(1 δ nd )) Firm s problem with two types of capital: Given w, solve v(w) max d + βv(w ) d,k j,b,w R 3 + R2 subject to budget constraints and collateral constraint ( ) Af k j + j j θ j w + b d + q j k j j q j k j (1 δ j ) Rb + w q j k j (1 δ j ) Rb

21 Effect of Durability on Down Payment and User Cost Down payment decomposition (δ) = }{{} u + R 1 q(δ)(1 θ)(1 δ) }{{} Jorgensonian user cost non-pledgeable part of resale value User cost depends on firm s discount factor u(w)(δ) = (δ) β µ µ (1 θ)q(δ)(1 δ) = u +β λ Ru µ r + δ (1 θ)(1 δ) More

22 Constrained Firms Adopt Dominated Technologies User cost of type j capital (for possibly constrained borrower) u j (w) = u j + β λ µ q j(1 θ)(1 δ j ) Unconstrained never use less durable low quality capital Since λ = 0, so u j(w) = u j Unconstrained firms simply compare user costs Severely constrained adopt dominated technology As w 0, λ µ 1, so u j(w) = u j + R 1 q j(1 θ)(1 δ j) = j Severely constrained firms simply compare down payments

23 Adopting Dominated Technologies and Legal Enforcement Two countries with strong and weak legal enforcement (θ H > θ L ) As before two types of capital with δ d < δ nd and q d > q nd such that u d < u nd but d > nd More dominated technology use with weak legal enforcement Firm indifferent between two types of capital Af k ( j kj) + (1 θ)q d(1 δ d ) = Af k( j kj) + (1 θ)q nd(1 δ nd ), d nd Lower θ implies indifferent at higher investment k = j kj and hence higher net worth

24 Durability and Composition of Investment Suppose two types of capital are imperfect substitutes Aggregator for capital with constant elasticity of substitution (CES) ( ) 1/γ k σ jk γ j Type-j capital k j, j {d, nd} j Substitution coeff. γ; < γ < 1; elasticity of subst. 1/(1 γ) Factor shares σ j > 0, j; j σj = 1 Firm s problem with two types of capital: Given w, solve v(w) max d + βv(w ) d,k j,b,w R 3 + R2 subject to budget constraints and collateral constraint (( Af σ j k γ j j ) 1/γ ) + j θ j w + b d + q j k j j q j k j (1 δ j ) Rb + w q j k j (1 δ j ) Rb

25 Composition Determined by User Cost or Down Payments First order condition for type j capital u j (w) = β µ µ Af k(k) k k j and dividing condition for nd by condition for d yields ( ) 1 γ u nd (w) u d (w) = kd σ nd k nd σ d Composition of investment determined by... (frictionless) user costs u j(w) = u j for unconstrained firms... down payments u j(w) = j for severely constrained firms Legal enforcement affects investment composition Ratio of down payments nd / d and hence k d /k nd increasing in θ No effect on unconstrained firms

26 Hart/Moore (1994): Pledgeability not Durability We say that the assets become longer lived, or more durable, if [the liquidation value] L(t) rises for all 0 t T. Durability liquidation value (price and use value fixed) Interpretation of their liquidation value L in our model Lk θq(δ)k(1 δ) Effect of L is effect of pledgeability θ in our model not durability

27 Renting Durable Assets Renting/leasing Benefit: higher leverage due to repossession advantage Cost: monitoring cost Two types of capital k j (different δ j ) required (fixed proportions) Severely constrained firms rent both types of assets Moderately constrained rent only more durable assets More

28 Literature Hart/Moore (1994) See above Eisfeldt/Rampini (2007) Used capital is cheaper but requires ex-post maintenance cost Durability plays no role Empirical evidence on used capital International trade: Sen (1962), Navaretti/Soloaga/Takacs (2000) Legal enforcement: Benmelech/Bergman (2011)

29 Literature: Durable Goods Theory Optimal durability and planned obsolescence Conventional wisdom: monopolists produce less durable goods Fallacy: Swan (1970, 1972), Sieper/Swan (1973): cost minimization Resuscitated: Barro (1972): impatience; Rust (1986): scrappage Bulow (1982, 1986): escape Coase (1972) time-inconsistency Role of rental markets Coase (1972), Bulow (1982), Stokey (1981): Coasian dynamics Hendel/Lizzeri (2002): leasing ameliorates adverse selection Key driving force: market power Our theory: optimal competitive response to financial constraints More

30 Conclusion Durable assets are harder to finance Durability raises financing need and required down payments Financial constraints especially salient for durable assets Structures (residential and non-residential) and infrastructure Equipment, especially aircraft and ships Consumer durables, especially motor vehicles and household durables Similarly, durable intangible capital (θ = 0), e.g., organization capital Constrained firms (and households) buy used assets, adopt dominated technologies, and rent durable assets Weak legal enforcement economies invest in dominated technologies and import used assets Distinguish durability 1 δ from pledgeability θ

31 User Cost of New Capital for Financially Constrained Firm User cost of durable assets depends on firm s discount factor u d (w) = β µ (1 θ)q µ = u d + β λ (1 θ)q µ User cost of new, durable assets for severely constrained firm As w 0, λ µ 1 so u d (w) Severely constrained firms simply compare down payments Back

32 Effect of Durability on Down Payment and User Cost Down payment decomposition (δ) = }{{} u + R 1 q(δ)(1 θ)(1 δ) }{{} Jorgensonian user cost non-pledgeable part of resale value User cost depends on firm s discount factor u(w)(δ) = (δ) β µ µ (1 θ)q(δ)(1 δ) = u + λ u µ r + δ (1 θ)(1 δ) Durable capital user cost sensitive to financial constraints u(w)(δ) = q(δ) λ 1 θ < 0 δ µ r+δ u(w)(1) = u independent of w (also if θ = 1 but we assume θ < 1) Back

33 Renting Durable Assets Capital goods with different durability Capital k j, j = {d, nd}, with depreciation rate δ d < δ nd and price q j Leontief aggregator k = min{ k d+kd l σ d, k nd+knd l σ nd } Implies k j + kj l = σ jk where k is aggregate capital Rental price u l j R 1 q j(r + δ j + m) where m is monitoring cost Firm cannot abscond with rented capital (repossession advantage) Entrepreneur s problem with rentals: Given w, solve v(w) max d + βv(w ) (9) d,k j,kj l,b,w R 5 + R2 subject to budget, collateral, and technological constraints w + b d + j q j k j + j u l jk l j (10) Af(k) + j θ j q j k j (1 δ j ) Rb + w (11) q j k j (1 δ j ) Rb (12) k j + k l j σ j k (13)

34 Renting Durable Assets (Cont d) First order conditions with multipliers as before and βµ η j on (13) σ j η j = Af k (k) j µq j = βµ η j + βµ q j (1 δ j ) + βλ θq j (1 δ j ) + ν j µu l j = βµ η j + νj l Investment Euler equation (IEE) 1 = β µ η j + (1 θ)q j (1 δ j ) + ν j µ j µ j More constrained firms rent less durable assets Suppose rent and own some type j capital, so ν j = ν l j = 0 and IEE λ (1 θ)(1 δj) = m µ If δ j higher, so multiplier on collateral constraint λ µ higher Back

35 Literature: Durable Goods Theory Optimal durability and planned obsolescence Conventional wisdom: monopolists produce less durable goods Fallacy: Swan (1970, 1972), Sieper/Swan (1973): cost minimization Resuscitated: Barro (1972): impatience; Rust (1986): scrappage Bulow (1982, 1986): escape Coase (1972) time-inconsistency Role of rental markets Coase (1972), Bulow (1982), Stokey (1981): Coasian dynamics Hendel/Lizzeri (2002): leasing ameliorates adverse selection Key driving force: market power Our theory: optimal competitive response to financial constraints Other features Adverse selection Illiquidity Back