Category Archives: Finance

Solution to Management Science Series #195: Valuing Options to Expand

Casca is a video games company based in Midland. It has created many of the most well-known IPs in the video game industry.

Financial analysts of Casca estimate that Casca has a total value of $2.3B according to their DCF models. These IPs and franchises are highly valuable and Casca aims to create new video game franchises for the foreseeable future.

Developing these video game franchises also allows Casca to enter toy and merchandising industry, establishing a new adjacent business activity. Casca could initiate and expand this business activity over the next 4 years.

Current cost of this business activity is estimated to be $1B. Expected cash flows are after-tax $120M per year for 18 years. Cost of capital for toy companies is estimated to be 17%. Casca analysts investigated annualized standard deviations in firm value for publicly-traded toy companies.

With appropriate risk and company-specific adjustments, Casca thinks that the appropriate volatility value for this project is around 27%. Should Casca expand into toy business?

Solution to Management Science Series #194: Valuing Oil Reserves

Ace Chemicals has claims on oil reserves amounting to 5 billion barrels in the South Arkham Sea. Ace’s rights to develop these reserves will expire in 30 years.

Currently, developing these reserves will cost Ace $20 per barrel. Use Crude Oil WTI Futures as a proxy for the current market price of oil. Production costs per barrel is estimated to be $40 per barrel.

Use appropriate risk-free rate for this project. Also, how would your model consider the volatility of this project?

Factor in the cost of delay of the project in your model and decide whether Ace should start developing reserves now or rather wait.

Solution to Management Science Series #193: Valuing Patents/Licenses by Using Options

Toy company called Shippuden made a license agreement with the video games company called ‘SUGA’. The license would allow Shippuden to produce the toys including figures and playsets of the IP owned by SUGA for the next 10 years. Shippuden will produce and market the toys.

Financial analysts of Shippuden completed the DCF analysis and it was estimated that future cash flows for this licensing project would amount to $6.7 billion. It is also estimated that current cost of developing the products and starting production would be around $7.2 billion.

This is a new project for Shippuden and it has not been involved in such projects before. So, its analysts adjusted the risk of the project accordingly and the standard deviation of returns on such projects is estimated conservatively at 53%.

Should Shippuden collaborate with SUGA immediately on this licensing project?

How valuable will this project be if Shippuden has the option to delay the development and the production?

What would have been the right action for Shippuden if the development and production of the toy had cost $6 billion instead of $7.2 billion originally? Should Shippuden develop and start production in this case?

Solution to Management Science Series #191: Binomial Model at Its Finest: Okami Games Example 🎮

Okami Games is a prominent video game developer and publisher financed by both debt and equity. Okami is planning to undertake a new AAA-level game.

If this game garners critical acclaim, the value of Okami in a year will be $560M. If the game fails miserably, Okami’s value will be $430M. Current enterprise value of Okami is $495M, which takes the prospect of the new game into consideration.

Okami has outstanding zero coupon bonds due in a year with a face value of $520M. The yield on a 1-year US Treasury Bill is 4% EAR. Okami does not pay any dividends.

-First, use the binomial model to calculate the current value of Okami’s debt and equity.
-If Okami has 400,000 shares of common stock outstanding, what is the price per share of Okami’s equity?

Okami has also another option to develop a brand-new triple-A game of the survival horror genre. This new game is expected to either increase the value of Okami to $600M or decrease Okami’s value to $400M by the end of the year.

Okami believes that the value of the firm today will remain at $495M even if this new project replaces the preceding one.

-First, use the binomial model to calculate the current value of Okami’s debt and equity if Okami chooses this new project over the preceding one. Calculate the price per share of Okami’s equity accordingly.

-Without calculating any values, could you make a definite claim on which project would benefit the shareholders and the bondholders? Subsequently, corroborate your claim with the algebraic solution.

Solution to Management Science Series #190: Real-world application of the binomial model: Milk Example 🧮

Real-world application of the binomial model

You have built a trading company called ‘Gold Milk’. The company buys milk from farmers at the wholesale price and resells it to the diary companies and restaurant chains at a higher retail price.

Gold Milk generates its revenues mostly during the spring period. Today is December 1st and milk sells for $2.40 per gallon. Based on your models, milk prices will be either $3.50 or $1.35 per gallon on March 1.

You do not know the probabilities of each state occurring. The three-month risk-free rate for borrowing and lending is 1.5%. Gold Milk has the ability to pass the price changes onto its customers and adjusts prices accordingly in March.

Diary King is a diary company and wants to buy milk from you. The company plans to buy 2 million gallons of milk from Gold Milk at $2.50 per gallon on March 1st. Diary King says that it can pay you $1,500,000 up front on December 1st for this contract in order to mitigate your risk.

Should Gold Milk sign the contract with Diary King?

Solution to Management Science Series #189: Using Binomial Option Pricing Model to Value a Put 🧮

As an options trader at the CBOE, you are tasked with pricing a European put option on Quake Games, Inc.

The strike price is $75 and there are 6 months until expiration. Quake Games’ common stock does not pay dividends and is currently trading at $57.

Based on your models, the future stock price is predicted to be either $92 or $40 at the end of the next 6-month period. The effective annual risk-free rate is 4%. Estimate the price of the put?

How much of a share of the stock do you need to buy or short and how much do you need borrow or lend at the risk-free rate to replicate the put through a synthetic portfolio?

Check whether your synthetic portfolio replicating the put will have the same payoffs as those of the put at expiration!

Solution to Management Science Series #188: Using Binomial Option Pricing Model to Value a Call 🧮

Using Binomial Option Pricing Model to Value a Call 🧮

As an options trader at the CBOE, you are tasked with pricing a European call option on Quake Games, Inc. The strike price is $75 and there are 6 months until expiration.

Quake Games’ common stock does not pay dividends and is currently trading at $57.

Based on your models, the future stock price is predicted to be either $92 or $40 at the end of the next 6-month period.

The effective annual risk-free rate is 4%. Estimate the price of the call?

How much of a share of the stock do you need to buy and how much do you need borrow at the risk-free rate to replicate the call through a synthetic portfolio?

Check whether your synthetic portfolio replicating the call will have the same payoffs as those of the call at expiration!

Solution to Management Science Series #187: Prologue to Black-Scholes Option Pricing Model: Binomial Option Pricing Model in a Single Period Example 🧮

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?

Solution to Management Science Series #186: Shareholders of a highly leveraged firm choosing a negative-NPV and highly risky project!

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?

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?