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Case Study: Calculating the Present Value of an Option Using Black-Scholes

## About the Excel Sheet and Case Study Materials

The case study materials (including the excel file) provide all of the parameters you will need.  If you read carefully, there is no need for outside research – all of the required information is in the case study or the associated excel document.

I have provided an excel sheet to correspond to the case study (here).  It includes a template for answering question 1 below as well as a template for calculating the value of an option using Black-Scholes.  I would note that the template provided allows for dividends, but in this case study there are no dividends discussed so set the dividend parameter to 0%.

HINT:  You can use the Goal Seek function in excel to back solve for any one of the Black-Scholes inputs, if you know the value of the option.

Here is the assignment

1.Complete Exhibit 4 of the case study on the template provided in the Excel sheet.

2.Calculate the present value of the option to enter the MRAM market. Identify each of the parameters you are using as an input to the option model.

3.What is the combined NPV of the SDRAM and MRAM opportunities added together? What does that suggest the hedge fund should do?

4.Vary the inputs to the option pricing model one at a time. How far off can you be on each input (assuming the other inputs do not change) without changing your recommendation in question 3?  Are the inputs all independent or is there one that if you changed it, it might change other inputs as well?

5.You present your findings to management at the hedge fund and they ask you the following questions (treat each in isolation not as a cumulative impact):

A) I think the MRAM market will develop quicker than you do. We will need to commit to enter within the next three years.  Should we still do it?
B) I think the investment you projected is too small. Exhibit 2 in the paper work is way too low.  I think it is going to be twice as much to effectively enter the MRAM market.  Should we still do it?
C) I don’t like your estimate of the volatility. There is a company called Memory Maker that is focused in the nascent MRAM market and has publicly traded options.  Today, Memory Maker’s stock price is \$20.00 and a call option expiring in one year at \$25.00 has a price of \$2.25.  Can you benchmark the MRAM market volatility off of that option? Should we still enter the SRAM/MRAM deal?
D) Wait, the whole reason you told me to do the crazy option thing is that the MRAM market is pretty risky and difficult to project. Yet, on Exhibit 3 in the paperwork you did a projection of the MRAM market and you have the same Beta and Cost of Equity as the SRAM market which we understand and is more developed.  You are telling me it is riskier, but you are using the same cost of equity?  How can that be right?
E) Ok, you convinced me. I know need to do some liquidity planning to make sure we have cash on hand to make the investments when needed.  Based on the model you used, how much am I going to be investing now?  How much might I be investing later and when would that be?