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2023 | OriginalPaper | Chapter

Debt/Loan Risk, Bankruptcy Cost and Debt/Loan Pricing

Author : Zhiqiang Zhang

Published in: Fundamental Problems and Solutions in Finance

Publisher: Springer Nature Singapore

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Abstract

This chapter explores the discount rate estimation for debt capital, or debt pricing. Similar to previous chapter, the standard of the solution is a discount rate model structured as “risk free rate + (debt) risk premium”. This is even more tough. A major obstacle is the quantification of bankruptcy cost which has been a tough problem unsolved after decades intensive research. So we model the bankruptcy cost first, and then find the solution to the debt risk premium and then the discount rate for debt capital. Our debt pricing model derived from the bankruptcy cost model coincides exactly with the debt pricing model derived by Robert C. Merton in 1974 via another reasoning path. The two debt pricing models hence can confirm each other and both are undoubtedly correct. However, the model has been idle over decades because it is deemed as serious defected. It turns out finally the deemed serious defects are nothing but the advantages of the model; in addition, the model can help to solve all three problems in bank loan decision. We further discuss some specific application issues for pricing a specific loan. The debt pricing model is further confirmed to be sound in theory and flexible in practice.

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previous chapter Certainty Equivalent, Risk Premium and Asset Pricing

next chapter Capital Asset Pricing: An Easy and Unified Solution

Note that Xe^−rT = 100, rather than X = 100.

Please note that the annual cost is an annuity due or annuity in advance rather than an annuity in arrears or an ordinary annuity; the annual cost in amount is 0.1491 million dollars and 0.1571 million dollars respectively.

The annual cost in amount is 0.4547 million dollars and 0.4793 million dollars respectively.

The annual cost in amount is 0.3056million dollars and 0.3222 million dollars respectively.

2.7786%/0.6776% − 1 = 310.0649%; 3.0561%/0.7453% − 1 = 310.0496%; 3.2218%/0.7857% − 1 = 310.0547%. The slightly differences of the annual cost increases are caused by the normal rounding.

We will discuss it in detail in Chapter “Tax Shield, Bankruptcy Cost and Optimal Capital Structure”.

Until 2009, Zhang Zhiqiang corrected the misunderstanding of the concept, established the bankruptcy cost model by using option pricing method, solved the problem of bankruptcy cost measurement, and further derived the optimal capital structure model.

A similar concept is financial distress cost, which is said to include also agency cost, etc. They are actually all aroused from the debt financing and covered by the bankruptcy cost. To avoid unnecessarily conceptual confusions, we will not use those new concepts.

J. and Warner J. B. (1977), Bankruptcy Costs: Some Evidence, The Journal of Finance, 32: 337–347.

Sergei A. Davydenko, Ilya A. Strebulaev, Xiaofei Zhao, A Market-Based Study of the Cost of Default, The Review of Financial Studies, v 25, n 10, 2012.

The empirical range of σ; for equity is around 20–40%; so the reasonable range of σ; for the whole firm is about 15–35%. See Cumby et al. [1].

This reflects that how correctness and preciseness Merton’s concept and reasoning is.

The markup method in loan pricing can hardly be justified in theory, because the price or interest rate of a loan should be related to its (default) risk rather than its cost.

See Aswath Damodaran, Equity Risk Premiums (ERP): Determinants, Estimation and Implications—The 2008–2015 Edition at Damodaran Online (http://pages.stern.nyu.edu/~adamodar/).

Note that the answer is 32 million dollars, rather than: 80 million dollars/2 = 40 million dollars. The calculation is a little more complicated here. Readers interested in solving the problem can try to work out by yourselves. Such an exercise will help you to understand the following part better.

Zhang Z, Yu M. The value of loan guarantees based on option pricing model. China Valuation. 2013 June;6–10.

Zhang Z. ZZ financial discovery, University of International Business and Economics Press. 2008 November.

Zhang Z. Shufang Xiao, Tax Shield, Bankruptcy Cost and the Optimal Capital Structure, Accounting Research. 2009;4:47–55.

Robert C. Merton, on the pricing of corporate debt: the risk structure of interest rates. J Financ. 1974;29:449–70.

Zhiqiang Z, Basic model of loan pricing. China Asset Appraisal. 2017;(4):26–29.

Zhang Z. Research on the application of loan pricing model. China Appraisal J. 2021;9:14–20.

Zhang Z, Finance—fundamental problems and solutions. Springer; 2013.

Zhang Z. Option Theory and Corporate Finance. Huaxia Publishing House:Beijing. 1999 June.

Title: Debt/Loan Risk, Bankruptcy Cost and Debt/Loan Pricing
Author: Zhiqiang Zhang
Publisher: Springer Nature Singapore
Book: Fundamental Problems and Solutions in Finance
Print ISBN: 978-981-19-8268-2

Electronic ISBN: 978-981-19-8269-9

Copyright Year: 2023
DOI: https://doi.org/10.1007/978-981-19-8269-9_8