The Sleepless in L.A. case study discusses a business school student who landed a summer job at an investment bank in Los Angeles, California as an analyst. He was tasked to analyze the junk bonds of MicroComp in the market and discovered that MicroComp was in financial distress. While it has assets with a market value of $115.5 million, its debts amounted to $150 million. Can option pricing be used to value MicroComp’s risky bonds?

Walid Busaba, Zeigham Khokher, Elliott Weinstein

Harvard Business Review (905N11-PDF-ENG)

August 12, 2005

### Case questions answered:

- How can one use the Black-Scholes Model to price options? What inputs does it require? How do these different inputs affect the values of both call and put option prices?
- Referring to case Exhibit 3, can you use the Black-Scholes model to verify the value of these publicly traded options? Does the model give the same value as the market value? Why or why not?
- Can option pricing help justify why MicroComp’s market capitalization is not zero?
- Can option pricing be used to value MicroComp’s risky bonds?

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## Sleepless in L.A. Case Answers

This case solution includes an Excel file with calculations.

#### Introduction – Sleepless in L.A.

The Sleepless in L.A. case study discusses a business school student who landed a summer job at an investment bank in Los Angeles, California as an analyst. He was tasked to analyze the junk bonds of MicroComp in the market and discovered that MicroComp was in financial distress. While it has assets with a market value of $115.5 million, its debts amounted to $150 million.

#### Objectives

• What are the Black-Scholes-Merton Model’s assumptions and limitations, and how can we use the model for pricing options?

• Why did the company’s market capitalization remain $ 26.5 million?

• Can option pricing be used for the company’s risky bond?

#### Black-Scholes-Merton Model (BSM Model)

The Black-Scholes-Merton model, also known as the Black-Scholes-Merton (BSM) model, is a mathematical formula for pricing and options contracts. It is one of those essential concepts in modern financial theory and was developed in 1973. It estimates the variation over time of a financial instrument. It is only used for the pricing of European options or items since it does not account for United States options that can be exercised before their expiry date.

The formula, when utilized, leads to a boom in options trading. It gives a mathematical opinion concerning the Chicago Board Options Exchange activities and other options markets globally. It is often used with provided adjustments that market participants give.

Most people term it as the best way of determining fair price options. That said, the following are other vital components and facts on the use or application of this formula today.

#### Black Scholes Model in Price Options

This model needs five input variables, current stock price, expiration date, the strike price of an option, volatility, and the risk-free rate. The equation is a second-order differential equation.

There are several assumptions made while using the formula. The formula assumes a lognormal distribution of stock price that relies on the fact that asset price cannot have a negative value and is limited to zero. There is also the assumption that the options can only be exercised on the date of expiry or maturity.

This is why it is not accurate for the American option. The model assumes that there are no dividends or returns that the stock pay. Yet the stock market is very volatile. This is because the market’s direction cannot be easily predicted.

#### Microcomp’s financial distress

Microcomp had fallen on hard times since the burst of the tech bubble in 2000 and had seen the market value of its outstanding bonds falling drastically. However, Microcomp’s chief executive officer had hired an investment bank to understand better the pricing of junk bonds of its company in the marketplace.

Looking at the balance sheets ( Exhibit 1), it was clear that Microcomp was in financial distress. It had outstanding debt of $150 million while the market value of its assets was 115.5 million, but why did its market capitalization remain 26.5 million and not fall to zero?

Taking a closer look at the case study presented, it is true to say that option pricing helps justify why the market capitalization of MicroComp’s market is not zero. Their outstanding debts were $150 million, whereas their assets’ market value was $115 million.

The market capitalization should have therefore gone to a zero value. This can be explained by situations such as shareholder’s borrowings, for example, via bonds, selling part of the firm’s assets for cash, or a repurchase option for the firm at the time of maturity of the debt. Those who bought the bonds have a call option to the bonds also a right to sell the bonds but not at the strike price.

The facility, therefore, comes with a…

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MBA student, Boston