Category Archives: Corporate Finance

Solution to Management Science Series #185: Options and Capital Budgeting

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?

On investment decision rules in finance and why using payback period method misleads you

On investment decision rules in finance ⚠️

⬇️

There are many decision and investment rules in finance.

Although there is only one rule that trumps every other, inferior methods are still being used by many companies, even by the most successful ones.

Granted, regardless of whatever investment rule your company is using, estimating future cash flows is an uncertainty for each method.

However, this reality does not change the fact that there is still only one superior investment rule through which you can make sound decisions.

For example, which project would you choose if you were to use payback period method?

Project A requiring an initial investment of $100MM is projected to yield $20MM, $30MM, $50MM, and $35MM for the next four years.

Project B requiring an initial investment of $100MM is projected to yield $50MM, $30MM, $20MM, and $35MM for the next four years.

While solving the question above, I will also demonstrate why payback period may not be reliable in assessing financial viability of projects and what method you should have used given these inherent problems of the payback period.

Solution to Management Science Series #184: Using options in assessing feasibility of mergers and acquisitions 🧠

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.

Solution to Management Science Series #183: Stocks and Bonds as Options 🧮 Banzai Toy Company

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?

Solution to Management Science Series #182: Checking the reliability of Black-Scholes through a real-world example #2🧠Walmart Example

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?

Solution to Management Science Series #181: Checking the reliability of Black-Scholes through a real-world example 🧠Ebay Example

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?

Solution to Management Science Series #180: Combinations of Options 🧮Tesla Example

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.

Solution to Management Science Series #178: Real-world example: Bottom up beta 🧮Workday, Adobe, Salesforce

Real-world example: Bottom up beta

8 years ago, you co-founded a SaaS company, ‘The Blue Hedgehog’ with your fellow classmates from Cornell University.

You want to estimate the equity beta of your company by using a bottom up beta.

Although there are not many comparable companies, you think that Salesforce, Adobe, and Workday are fair comparables given their business models and their business strategies.

Check whether these companies have a similar operating leverage.

The tax rate for your company is 21%.

Use current risk-free rate and assume that equity risk-premium is 6%.

Calculate the equity beta of your company given that its debt-to-equity ratio is a stable 45% for the last 5 years by using bottom-up beta method.

What would the equity beta of the Blue Hedgehog have been if the required return on the company stock had been 15%?

Compare your results!

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

Solution to Management Science Series #177: How to estimate beta in mergers and acquisitions: Real-world example 🧮 Nvidia and Texas Instruments

How to estimate beta in mergers and acquisitions: Real-world example 🧮

NVIDIA’s top executives are looking for potential targets that could provide economies of scale and scope.

They consider Texas Instruments a top candidate.

Estimate the post-merger beta of NVIDIA for the following two scenarios!

Scenario A: Assume that NVIDIA will pay in equity for this acquisition. Assume that the acquisition will take place on the 31st of December, 2023.

Scenario B: Assume that NVIDIA will issue bonds worth $12B and fund the rest with equity. Assume that the acquisition will take place on the 31st of December, 2023.

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