Category Archives: Finance

Prologue to Black-Scholes Option Pricing Model: Binomial Option Pricing Model in a Single Period Example 🧮

As an equity analyst working at Silverman Fox, you are tasked with pricing a European call option maturing in one year from now.

Strike price of the call is $145 and the underlying stock’s current price is $129.93.

The representative risk-free annual interest rate is 3.95%, which also represents the risk-free borrowing rate.

In your binomial model, the stock price can take only one of two possible values at the end of the year: $163.26 or $110.87.

What should be the current price of the call? How many shares of the stock do you need to buy? How much do you need borrow/invest in the risk-free asset?

Shareholders of a highly leveraged firm choosing a negative-NPV and highly risky project ❗

Mazingo is a globally prominent toy company producing and marketing high-quality robot toys. Details concerning the company’s current situation is shared.

Calculate the market value of equity and debt for this company.

Additionally investigate the following scenario in which Mazingo considers a project that must be taken now or never and also affects both the market value of the firm’s assets and the firm’s asset return standard deviation.

It is a negative-NPV project that would reduce the market value of firm’s assets by $1.75M while changing firm’s cumulative asset return standard deviation to 77%.

Calculate the market value of equity and debt for Mazingo if it were to take on this project. Whom will the project benefit the most; shareholders or the debtholders?

Options and Capital Budgeting

Arkham Games is a game studio creating video games for console manufacturers. The following information is shared for the firm.

Calculate the market value of equity and debt for Arkham Games.

Additionally, the firm has two mutually exclusive investments under consideration. The projects will impact both the market value of the firm’s assets and standard deviation of the return on firm’s assets as was shared.

Calculate the market value of equity and debt if Arkham Games chooses Project A? What if it were to choose Project B? Which project would benefit the stockholders the most?

Using options in assessing feasibility of mergers and acquisitions 🧠

There are two toy companies whose products fundamentally differ and cater to very different segments and targets. One is called Robotformers producing and marketing robots to boys within the 12-15 age group. And the other is called Cindy producing and marketing figures to girls within the 9-11 age group.

Toy industry is known to have risky cash flows exposed to very different factors. If the two companies were to merge, the combined company would have a much more stable cash flow and diversify away some of the risk, making the bankruptcy of both companies less likely.

So, the operations of both firms are very different and the proposed merger is a purely financial merger in which there are no synergies and other value-creating possibilities. Only gain from this merger would be the reduction of the default risk. The premerger information is being shared.

Using Black-Scholes option pricing model and the appropriate risk-free rate, calculate the market value of equity and debt for both companies before the merger.

Assuming that the merger will lead to diversification effect and the post-merger asset return standard deviation is estimated to be 48% and utilizing Black-Scholes again, calculate the market value of equity and debt for the combined firm.

Between stockholders and bondholders, who would benefit the most from this merger? Quantify the benefit/loss to each party.

You found a new toy company called Banzai that would produce and market state-of-the-art action figures with high articulation. Luckily, you won a contract through which Banzai was trusted the license to produce and market toys for the video game ‘The Legend of Sarah’.

Banzai could sell these toys for a single year, i.e. the next year, after which Banzai will cease operations and be disbanded. Banzai has issued debt to help finance this venture. Interest and principal due on the debt next year will be $450M, at which time the debt will be paid off in full.

Banzai’s cash flows next year are being shared.

Each scenario is equally likely to occur. Plot the payoff table for both the bondholders and stockholders!

Assess the position of both parties in terms of options; who are the option holders and writers and what kind of an option do they possess or have they written/sold?

Value the call option ‘WMT250620C00046670’, by using Black-Scholes as of the 10th of January 2025.

Will a rational investor buy this option?

In order to duplicate the call, how much of a share of stock do you need to purchase and how much do you need to borrow?

Checking the reliability of Black-Scholes through a real-world example 🧠

Value the call option ‘EBAY250919C00045000’, by using Black-Scholes as of the 10th of January 2025.

Will a rational investor buy this option?

In order to duplicate the call, how much of a share of stock do you need to purchase and how much do you need to borrow?

Combinations of Options 🧮

You wanted to invest in Tesla stock and also follow a protective put strategy.

Your advisors recommend that you buy the contract ‘TSLA241129P00285000’.

Plot the payoff to the combination of buying the put contract and buying the underlying stock.

Note: Solution of this question, as well as those of all the questions asked so far, is shared on my website.

Find the contract ‘COST241108C00780000’.

Decipher the contract name and define the characteristics of this option.

Plot the payoff diagram of both the option holder and the option seller!

Also create a single plot demonstrating both positions!