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Loan Commitments

Loan Commitments. Dan Galai and Zvi Wiener The Hebrew University of Jerusalem. Loan Commitment and Credit Lines. Borrower and Lender (single or a consortium) Specific goal (debt maturity, big project, etc.) General use (liquidity needs, emergency, etc.) Specific date or open-end use

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Loan Commitments

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  1. Loan Commitments Dan Galai and Zvi Wiener The Hebrew University of Jerusalem

  2. Loan Commitment and Credit Lines • Borrower and Lender (single or a consortium) • Specific goal (debt maturity, big project, etc.) • General use (liquidity needs, emergency, etc.) • Specific date or open-end use • Single use or revolving account • Initial fee, undrawn (facility) fee, drawn fee • Embedded options: • Abandon • MAC - Material Adverse Change in the opinion of the bank Galai, Wiener

  3. Example – J. C. Penney Company Galai, Wiener

  4. Motivation • Loan commitments are the source for more than three quarters of all bank loans to corporations. • In this paper we do not deal with the incentives of firms to use credit lines nor with the reasons for banks to offer credit lines. • We propose a new model for the valuation of loan commitments and some of their main features including the MAC (Material Adverse Change) clause. • Important in a low interest rate environment. Galai, Wiener

  5. Galai, Wiener

  6. Literature on Loan Commitment • Papers focusing on why and how to use LC from the corporate perspective? The LC is analyzed as part of the liquidity management of the firm. • Papers investigating the banks perspective in supplying LC. • Models of the economic value of LC and how to price it. Galai, Wiener

  7. Loan Commitments • Help reduce uncertainty. • Provide more flexibility. • Can reduce probability of default (and improve rating), include embedded options. • Are NOT measured or reported in many cases (IFRS). • Proper valuation model must be based on Contingent Claims Analysis and should take into account all embedded options. Galai, Wiener

  8. 8 צבי וינר

  9. Credit loss T Merton’s model assets Non-default path debt time Galai, Wiener

  10. Merton’s model value Debt D D A Assets Galai, Wiener

  11. Merton’s model value Debt D D A Assets Galai, Wiener

  12. Merton’s model value Equity Debt D D A Assets Probability of default Galai, Wiener

  13. Loan Commitment First period loan Second period loan 0 T1 T2 Flexibility versus cost and uncertainty Lower interest rate for shorter maturity Crucial variable V1 = value of assets at T1 decision Two identical firms C and D with equal initial assets - V0 We consider a two-period model: firm D takes a two period loan firm C takes a one period loan and signs at t=0 a LC Galai, Wiener

  14. Loan Commitment First period loan Second period loan 0 T1 T2 decision Firm obligations of both sides – similar to a forward Borrower can decide not to use the LC Lender can deny the loan at his discretion (!) Galai, Wiener

  15. Type 1 – forward Value of LC Bankruptcy LC = 0 Voluntary use LC > 0 Involuntary use LC < 0 V0 V* D V1 Galai, Wiener

  16. Type 2 – irrevocable Value of LC Bankruptcy LC = 0 Voluntary use LC > 0 No Involuntary use LC = 0 V0 V* D V1 Galai, Wiener

  17. Type 3 – MAC (typical) Value of LC MAC is applied LC = 0 Voluntary use LC > 0 Involuntary use LC < 0 V0 V* D V1 MAC Galai, Wiener

  18. Effect of volatility Value of LC V0 V* D V1 Galai, Wiener

  19. The present value of LC for alternative leverage ratios and volatilities • Notice that the value of LC can decline with leverage for very risky projects. Galai, Wiener

  20. Thank you!Merci beaucoup! Galai, Wiener

  21. Zvi Wiener

  22. Galai, Wiener

  23. Contingent Claims Analysis • The major cost to credit line borrowers is the interest charge on the drawn down amount. Interest accrues between payment dates at a fixed contractual spread above the level of a default-free reference rate or as a fixed rate. • Hence, credit line contract includes a valuable embedded option of the borrower. When his cost of debt is high, he may use the credit line as a cheaper source of capital. Galai, Wiener

  24. Assumptions • Firm C at time t=0 has total assets worth V0, and it decides to finance them with debt, B0, and equity S0=V0-B0. • Debt is assumed to mature at T1, with face value F1. • Debt will be refinanced at time T1 for an additional period  (till T2=T1+). • Firm D, is identical to C in all parameters, except that C also purchases LC from Bank B. • The LC is acquired at time t=0 till T1. At T1 firm C must decide whether to exercise the LC or not . • If firm C exercises the line of credit, it borrows the amount guaranteed by LC for a the period of time , at a promised, fixed interest rate R*. Galai, Wiener

  25. Assumptions (cont.) • The LC is a proportion  of other term loans of the firm on a pari passu basis and when LC is exercised the money is used to refinance the firm’s old debt. • We denote by V1, S1 and B1 the value of the assets of the firm, its equity and debt at time T1, before the LC is exercised. Galai, Wiener

  26. The 3 states • We evaluate the LC from the bank perspective, and do this recursively. Hence, at time T1, there are three states: the first state is that firm C is bankrupt at T1. This bankruptcy occurs when V1 < F1 and the firm cannot fully pay its obligations to debtholders, F1. The second state is when the value of assets is so high that the firm decides not to exercise the LC, and the third state is when C exercises the LC. Galai, Wiener

  27. Valuation of identical firm D: • Value of equity and debt of firm D • is the face value of the new debt of the firm (to be paid at T2 if the firm is solvent) Galai, Wiener

  28. Assumptions re firm C • Firm C is identical to firm D but at t=0 it purchased the LC. • We assume it raised additional funds from the initial shareholders to finance this cost, but as far as productive assets, it is identical to D, • We also assume that firm C raised (zero-coupon) debt with face value of F1 at T1. • In addition we assume that firm C purchased at t=0 a line of credit, which allows it to roll over its debt at time T1 at the yield R*. • Since the use of LC is optional, the firm C will make a decision at T1 based on the realized value of its assets V1. Galai, Wiener

  29. The 3 states • In Figure 2 we show the three states at time T1: • In the first state, when , the firm is bankrupt and no new debt is raised. • In the second state where it is worth exercising the LC since . The critical firm value, , is the value of assets at T1 such that In the third case, when , the firm is doing well and there is no incentive to exercise the LC since the market cost of debt is cheaper than the rate R*. Galai, Wiener

  30. The value of LC • In order to find the present value of the LC at time t=0 we calculate the value of LC at time T1 as a function of V1 and then use the option pricing theory to find the present value of LC at t=0. • This can be done either numerically (as a simple integration with the risk-neutral density of V1) or analytically using the compound option model (based on the two-dimensional normal density function). Galai, Wiener

  31. At time T1 the firm needs to refinance its debt by paying the amount F1. In order to do so it can issue a new bond maturing at T2. The present value of the bond must be F1 in order to fully refinance the old debt, thus the equation for F2 is: • By solving this equation with respect to F2 we get F2(V1) and as a result also the required yield on the new debt: Galai, Wiener

  32. This critical value can be found by solving the following equation: • The value of the LC at time T1 is given by Galai, Wiener

  33. LC as a function of Leverage ratio LC1 B0/V0=70%, R*=5.37% B0/V0=90%, R*=11.39% PDF of V1 V1 Galai, Wiener

  34. Simulation Results • In order to illustrate our model, and analyze the results we use the following basic numerical example: • Initial value of productive assets: V0 = $100, • r = 5% risk free interest rate in both period 1 and period 2, • T1 = 1 (one year), • T2 = 2 (two years), and thus  = T2 –T1 = 1, • Volatility of assets’ rates of return  = 20%. • We assume that the required initial leverage is . Galai, Wiener

  35. Figure 3. The face value of the new debt required for refinancing the old one. F2 F1 er V1 F1 Galai, Wiener

  36. Figure 4. The yield to maturity of the new debt required as a function of V1. y2 r V1 F1 Galai, Wiener

  37. LC0 The value of LC0 as a function of the promised yield R* Galai, Wiener

  38. The yield on debt with and without LC as a function of V1 when R*=5.37% YTM no LC with LC R* V1 F1 V* Galai, Wiener

  39. The PD of the firm with and without LC as a function of V1 when R*=5.37% YTM no LC with LC V1 V* F1 Galai, Wiener

  40. The first year yield of the loan Galai, Wiener

  41. Value of LC as a function of MACF Galai, Wiener

  42. Literature Review • Theoretical studies present alternative explanations for the main function of credit lines. Campbell (1978), Thakor (1982), James (1982), and Melnik and Plaut (1986) argue that credit lines improve the completeness of financial markets. • Boot et al. (1987), Berkovitch and Greenbaum (1991) and Holmstrom and Tirole (1998) argue that lines of credit serve as interest rate or liquidity protection while mitigating moral hazard problems. Galai, Wiener

  43. Literature Review • Morgan (1993) provides an asymmetric information model in which a LC dominates an ordinary debt contract when investment projects have random returns that are costly to observe and random costs that are completely unobservable. • Sufi (2007) empirically examines the factors that determine whether firms use LC or cash in liquidity management. His major conclusion is that LC are a viable liquidity substitute only for firms with high cash flow. • Demiroglu and James (2011) review the use of bank LC. They conclude that access to lines of credit is not a perfect substitute to cash, since they are contingent on the credit quality of the borrower as well as on the financial conditions of the bank. Galai, Wiener

  44. Valuation of Loan Commitments • Turnbull (2003) values loans with perfectly foreseen drawdowns using a reduced-form valuation methodology proposed by Jarrow and Turnbull (1995, 1997). • Hughston and Turnbull (2002) consider default as a point process with intensity depending on both the unique characteristics of the borrower and the state of the economy. They incorporate state dependent drawdowns. The break even loan spread is such that it equalizes the present value of the revenues and costs of the loan. • Loukoianova et al. (2006) models non-committed credit lines as an option on the credit spread with a reverse knock-out option. • Jones (2001) models credit quality as a jump-diffusion process. Parameters are estimated with monthly bond data for 105 firms. Galai, Wiener

  45. Merton’s model value Debt D V0 D Assets Galai, Wiener

  46. Value of LC on the decision date LC Exercise LC Borrow at market price Bankruptcy V1 V1* F1 Galai, Wiener

  47. Credit loss T Merton’s model assets Non-default path debt time Galai, Wiener

  48. Merton’s model value Debt D V0 D Assets Galai, Wiener

  49. Merton’s model value Equity Debt D D A Assets Probability of default Galai, Wiener

  50. Merton’s model $ firm equity debt F V Galai, Wiener

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