4. Investment timing option Decision tree and the Black-Scholes valuation Aa Aa

Question

4. Investment timing option Decision tree and the Black-Scholes valuation Aa Aa Suppose a technical glitch in the trading systems in the stock markets led to several erroneous trades. Soon after, Lesnor Co., a professional training company, came up with the idea of developing a new division that would teach securities traders to communicate by using an old style of hand language on the trading floor, which would help revive that dyinglanguage. A young product development employee, Amit, proposed this idea and also submitted the following details about the project: . The division would need an initial investment of $5.5 mion. .Amit expects that this division will bring in an additional $4.8 million at the end of each of the next five years. The project's oost of capital is 10%, and the risk-free rate is 4%. The WACC is used to discount all cash flows. . Based on the given information, what is the project's expected net present value (NPV)? O $12.70million O $10.16 million O $19.05 million O $13.97 million After further research, Amit added a few more details about the project to the proposal. When Amit submitted the proposal, he again included the probability of the project's success based on whether a financial services tax would be impased on the revenues from the project for stock broker training. Based on discussions with lawyers, there is a 60% chance that the tax would not be imposed, in which case the project would generate a cash flow of $7.3 million. If a financial services tax is imposed, the projedt would generate a cash flow of$1.1lion. Lesnor Co. now has the option of knowing about the tax situation before it commits to the project. Lesnors management decides to wait for a year before they make a dedsion on launching the project. However, Amit mentions that the cash flow estimations for the project will remain valid only for the next five years. (For valuation purposes, the project has the same end date even with the option of waiting.) In the meantime, the managers decide to invest$5.5 million in securities for one year, which is expected to generate a rate of retum equal to the projects cost of capital. Based on the information that Amit submitted in his report, calculate the values in the following table. Use the WACC to discount all cash flows Value NPV of the project after one year Option value of waiting Using the Black-Scholes option pricing model (OPM), Amit takes his research a step further and calculates more ariables to find the value of the option of waiting for one year to accept or reject the project. He uses N(di)- 0.8745, N(dz) = 0.8413, and 2.7183 as the approximate value of e. If Amit uses the Black-Scholes OPM, what will be the value of the aption of waiting for one year? O $5.39 million O $9.24 million O $10.01 million O $7.70 million

Explanation / Answer

NPV = -$5.5 Mn + $4.8 Mn/(1+10%) + $4.8 Mn/(1+10%)2 + $4.8 Mn/(1+10%)3 + $4.8 Mn/(1+10%)4 + $4.8 Mn/(1+10%)5

= $12.70 Mn

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Now project cashflow can be calculated as sum of product of cashflows with their probabilities.

Probability of taxation = 0.4

Cashflow with taxation = $1.1 Mn

Probability of no taxation = 0.6

Cashflow without taxation = $7.3 Mn

Cashflow considering both probabilities = (Probability of taxation * Cashflow with taxation) + (Probability of no taxation * Cashflow without taxation)

= (0.4 * $1.1 Mn ) + (0.6 * $7.3 Mn) = $4.82 Mn

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In year 0, money ($5.5 Mn) is invested at cost of capital and Initial Investment only happens in year 1 which becomes our base year (year 0) for NPV analyis after wait period. End date of project remains the same so this project is now a 4 year project instead of 5 year.

In year 1( now year 0 for this analyis), the value of invested money becomes $5.5 Mn * ( 1 + 10%) = $6.05 Mn

CAshflows in the next 4 years are $4.82 Mn

Therefore NPV = -$6.05 Mn + $4.82 Mn/(1+10%) + $4.82 Mn/(1+10%)2 + $4.82 Mn/(1+10%)3 + $4.82 Mn/(1+10%)4

= $9.2287 Mn ~= $9.23 Mn

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Option Value of waiting will be the opportunity cost of mulling the project over for 1 year instead of investing in year 0

Option value of waiting = Loss in value = Opportunity Cost = NPV when not waiting - NPV when waiting

= $12.70 Mn - $9.23 Mn = $3.47 Mn

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Now In order to calculate the option price, we use the formula

Option Price = S* N(d1) - K * e-rfT* N(d2)

Where S = Present value of cashflows if money invested in year 1 after waiting =$15.2787 Mn

(S = $4.82 Mn/(1+10%) + $4.82 Mn/(1+10%)2 + $4.82 Mn/(1+10%)3 + $4.82 Mn/(1+10%)4 )

K = Investment made in year 1 = $6.05 Mn

T = term of project = 4 years

rf = 4%

N(d1) = 0.8745

N(d2) = 0.8413

e = 2.7183

Option Price = ($15.28 Mn * 0.8745) - ($6.05 Mn * 2.7183-0.04*4 * 0.8413) = $9.02 Mn (option B)

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