Paul D. Childs

Capital budgeting for interrelated projects: A real options approach

This paper explores the effect of project interrelationships on investment decisions and project values in a real options framework. We examine in detail the mutually exclusive case where a firm may invest in the development stage of two projects and then may select only a single project to implement. The firm can develop the projects in parallel or in sequence. The choice of development policy depends on the relative values of the embedded options for each strategy. Sequential development is shown to be superior to parallel development when projects have highly correlated values, and when they require a large commitment of capital for development, are short term in nature, and have relatively low volatility. We also show that the optimal ordering of sequential projects does not always begin with the most profitable project.

Mixed Uses and the Redevelopment Option

This paper considers how the potential for mixing uses and redevelopment impact property value. Operating flexibility of this type is found to significantly increase property value when the correlation between payouts from different property types is low or when redevelopment costs are low. The ability to mix uses and redevelop over time is also shown to affect the timing of initial land development. The shape of the development boundary is shown to differ considerably depending on whether marginal revenue is constant or decreasing to scale. Both policy and empirical implications concerning the effects of multiple-use zoning are discussed.

The Pricing of Multiclass Commercial Mortgage-Backed Securities

This paper considers the pricing of multiclass commercial mortgage-backed securities. A contingent-claims pricing methodology that overcomes state variable dimensionality problems is developed to examine mortgage pools with many distinct underlying assets and whose loan cash flow values are subject to interest rate uncertainty. Security structure and the correlation structure of collateralizing assets within a pool are found to be important determinants of tranche price and required yield spread. By disentangling default loss risk from default-related call risk, we show it is possible that mezzanine investment classes may require lower yield spreads than higher priority investment classes. Of particular interest is the finding that reduced cash flow volatility obtained through pool diversification may actually decrease the value of the first-loss (junior) tranche. When examining the relationship of pool size and tranche value, we find that five to 10 distinct mortgages are required to realize most of the effects of asset diversification.

Optimal Valuation of Claims on Noisy Real Assets: Theory and an Application

A theory for valuing claims on noisy real assets is developed and applied. Central to the theory is determination of the dynamics for the best estimate of real asset value. The dynamics of the value estimate are shown to differ from the dynamics of the true asset value only in the arrival rate of information. The rate of information arrival in the value estimate can be faster or slower than information arrival in the true asset value, which can lead to unexpected outcomes in the valuation and exercise of options on noisy real assets. The theory we develop is illustrated through an application. An imperfectly competitive market for real estate development is examined, in which agents compete over the timing of lead investment. Information spillover and free-rider incentives are shown to cause significant delay in lead investment. Delay together with a competitive response once lead investment has occurred explain observed patterns of development in gentrified urban land markets and multistage development projects. Copyright 2002 by the American Real Estate and Urban Economics Association..

The value of recourse and cross-default clauses in commercial mortgage contracting

Abstract The traditional commercial mortgage contract is written without recourse to any other borrower assets except the subject property. For credit enhancement purposes, many lenders/ investors are today seeking access to additional collateral through recourse or cross-default clauses. This paper considers the contracting value of such clauses. To measure these values and assess other related risk statistics, we apply a contingent-claims approach in which borrowers rationally default when the value of the mortgage meets or exceeds the value of the collateral, where collateral value includes additional assets provided through the mortgage contract. In the case of recourse to an unencumbered asset, default risk is reduced in part simply because additional collateral is available. In addition, when the subject property and additional collateral are less than perfectly correlated, diversification benefits are apparent. In the case of the cross-default clause — which means that default on one loan constitutes default on all loans covered by the clause — risk management benefits are also found to be substantial. For example, default risk resulting from a two-asset cross-default clause arrangement can be reduced by over 50 percent of non-recourse default risk when asset values are uncorrelated.

Valuation and Information Acquisition Policy for Claims Written on Noisy Real Assets

We study contingent claims written on real assets whose values are observed with noise and the acquisition of information to improve irreversible exercise decisions. We determine the conditional expected asset value and show that it can depend on historical observed values. In a noisy setting, claim values are calculated by simply adjusting the asset value and variance inputs and applying standard valuation procedures for pricing European and American options. Noise tends to slow the rate of information arrival, reduce contingent claim value, and provide incentives to purposefully acquire additional information. These incentives are illustrated for the case of secured risky debt. The value of acquired information increases when the option holder is indifferent between exercise alternatives, and decreases as one choice increasingly dominates the other. Opportunities to repeatedly acquire information reduce over- or underinvestment in information.

Managerial Discretion, Agency Costs, and Capital Structure

In a dynamic continuous-time model, we examine the impact of a manager-shareholder conflict over the choice of investment risk on firm value and optimal capital structure. The managers optimal investment risk policy is substantially different from the policy that maximizes equity or total firm value. The resulting agency costs of equity are many times larger than the agency costs of debt. Among a number of important implications, we find that managerial risk-aversion decreases the agency costs of equity. We also find that when equityholders have control rights over financing decisions, optimal leverage may increase relative to optimal leverage when investment risk is chosen to maximize total firm value. Additionally, greater managerial equity compensation may exacerbate the manager-stockholder conflict over investment policy, and in spite of higher agency costs of equity, may increase optimal leverage. Finally, we find that an increase in risk encourages the manager to pursue a more conservative investment strategy, which increases the agency costs of equity. Managerial risk-aversion, however, acts to mitigate this effect of risk on the agency costs of equity.

Bias in an Empirical Approach to Determining Bond and Mortgage Risk Premiums

Empirical studies of bond and commercial mortgage performance often quantify a required risk premium by examining the difference between the promised yield and the realized yield as adjusted for default occurrence. These studies omit the effects of various other sources of risk, however, including collateral asset market risk, interest rate risk, and possibly call risk. These omissions downwardly bias the empirical risk premium estimate on the debt. In this paper, we disentangle and quantify the sources of this bias by modeling secured coupon debt (the commercial mortgage) as used in the calculation of a realized investment return. We consider deterministic and stochastic interest rate economies with mortgage contracts that are either noncallable or subject to a temporary prepayment lockout period. Given realistic parameter values associated with the term structure, underlying asset dynamics, and debt contracting, we show that the magnitude of the bias can be significant.

Effects of Noise on Optimal Exercise Decisions: The Case of Risky Debt Secured by Renewable Lease Income

This paper considers the valuation and default exercise policy of risky coupon debt that is secured by a lease-encumbered noisy real asset. For parameter values used in our analysis, asset value noise is shown to reduce the value of waiting to default. Moreover, the borrower is shown to delay default exercise until the noisy signal of asset value is far into-the-money. This latter finding provides an information-based explanation for the apparent under-exercise of the mortgage default option that has been observed in the literature. An implication of this finding is that, if the claimholder recognizes that noise exists, but the empiricist—who is trying to compare observed exercise policy with that predicted by a noiseless model of asset prices—does not, a “sub-optimal” exercise policy may be inferred when in fact the policy is rational given the information available. This explanation is consistent with evidence from mortgage default studies as to why the observed default exercise boundary is lower than that predicted by standard theoretical option-based models.