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## Real Options Exercises Case Solution

### Introduction:

In this situation, the feasibility of Project Sable is going to be evaluated at the yearly discount rate of 10 percent. This project has two phases in which the investors can invest (phase one and phase two) or in one of the both phases or in neither of them. To be acknowledged, the investor cannot invest in second phase without investing in first phase of the Project Sable(Luehrman, 2009).

In phase one of the Project Sable, investor will invest the 100 dollars, which will provide the return of either 160 dollar or 60 dollar after passing one year of the project with equal probability. At the time when the investor will received the payout form its first investment, it can be reinvested in phase two of the project which will give the payout of either 20 percent more than the original outflow from phase one or 20 percent less than the outflow received from phase one of Project Sable with equal probability.

### Worth of the Project while Grabbing Phase One Opportunity:

If the investor will grab only the phase one opportunity than the expected cash flow form this project after the completion of one year will be 110 dollars. At the discount rate of 10 percent, the present value of the cash flow will be 100 dollars, which will give the zero Net Present Value (NPV) from this project.

In short, if the investor will only invest in phase one of Project Sable than it will be on the break even position where it earns no profits, and will not suffer from any type of losses. Table 1.1 shows the calculation for returns received from investing in phase one of Project Sable.

### Table 1.1:

Discount Rate 10%  Outflow
Year 0  Year 1
0.5

\$   160.00
\$      80.00
Option 1 \$ (100.00)
0.5
\$      60.00
\$      30.00
Weighted Average Outflow  \$   110.00
Inflow  \$ (100.00)
PV of Outflow  \$   100.00
Net Present Value  \$             –

### Worth of Phase 2:

If the investor will invest in phase two of the Project Sable than it’s worth will be Zero because the present value form this phase is 100 dollars, which gives the Net Present Value of zero dollars. Table 1.2 shows the NPV from phase 2.

If the investor will have to find the other opportunities such as the other options for investing its 100 dollar amount, and it can seek the good potential opportunities for future by investing in phase two of the Project Sable then it should invest in phase two of the project because this phase offers the safely return of the invested amount to the investor.

### Table 1.2:

Discount Rate 10% Cash Flows Option 2 Cash Flows Probability Combined Probability Weighted average

Cash Flows

Year 0  Year 1 Year 2

\$   192.00 0.5 0.25  \$      48.00
0.5

\$   160.00 -100.00
\$      80.00
\$   128.00 0.5 0.25  \$      32.00
Option 1  \$ (100.00)

\$      72.00 0.5 0.25  \$      18.00
0.5
\$      60.00 -100.00
\$      30.00
\$      48.00 0.5 0.25  \$      12.00
Weighted Average Outflow  \$   110.00  \$   110.00
Inflow  \$ (100.00)  \$ (100.00)
PV of Outflow  \$   100.00  \$   100.00
Net Present Value  \$             –  \$             –

### Worth of Project Sable:

The net worth of Project Sable is zero because the Net Present Value (NPV) of this project is zero dollars from both phases, which means that the investor will not earn any profits from this project, but also it will not suffer from any losses by investing in this project. Table 1.3 shows the calculations for project NPV.

### Table 1.3:

 Period 0 Period 1 Period 2 Project 1 \$ (100.00) \$   110.00 \$             – Project 2 \$             – \$ (100.00) \$   110.00 Total Cash Flow \$ (100.00) \$      10.00 \$   110.00 PV of Cash Flows \$ (100.00) \$        9.09 \$      90.91 NPV \$                                                          –

### Value of Project Sable:

In real options, a person can easily measure and estimate the cost for continuing and dismiss the project at any time during the project life. In real options, an investor can easily measure the opportunity cost for a project in which a corporation can take advantage of it and may recognize the costs and benefits form it.

While in the projects assets in place, an investor cannot recognize the costs and actual value to purchase and sell the assets until and unless the actual transaction happens. Assets might be the securities, real estate and other types of property that helps to project the costs and benefits from the investments but it does not provide the amount of opportunity costs for the investors.

### Value of Project Sable:

As it has known that the Net Present Value (NPV) of the project is zero regardless of it that investor are going to invest in both of the phases (phase one and phase two) or in only one phase or in neither of them. So, in that case, if investor invest in any of the phase through debt than form where it will pay the risk free interest rate as it has known that the NPV form this project is zero. By analyzing this fact, it has been recommend to the investor to do not invest through debt, as it will gives the negative return to it. In short, all of the investment should be made through equity financing otherwise the loss of value might be encountered.

### Evaluation of Proposed Launch:

By using the standard discounted cash flow approach, it has been found the company received the negative Net Present Value from all phases of the project by using all the applicable options for 3 percent and 30 percent growth rate and 10 percent and 15 percentdiscount rate. After exercising all applicable options, the lowest negative NPV has been received from the usage of 30 percent growth rate at 10 percent discount level.

For the purpose to conclude the results, the lowest NPV found at the discount level of 10 percent and growth level of 30 percent where the negative NPV is – 245 million dollars. So, it has been concluded that this project is very riskier as compared to other and does not provide the positive
NPV against the out flow have been made during the project life time.

Appendix 1 to 4 shows the calculations of all available options in which growth rate of 30 percent and 3 percent, and discount rate of 10 percent and 15 percent have been used.

### Black Scholes Merton Model:

After ignoring the third phase of the project which is the opportunity to invest 450 million dollars in year six for three constant year’s cash flows and afterward the growth of 30 percent in investment cash flows, it has been applied the Black Scholes Merton model to calculate the NPV for the project, the negative 1.34 million dollars NPV has been found.

After searching the results in corresponding table provided in case exhibit, we have 57.4 percent confident that the standard deviation of this project will lie between the 40 percent and 60 percent. Table 2.1 shows the results calculated by using the Black Scholes Merton model(Rogier van Aarle, 2013).

### Table 2.1:

 Hurdle Rate 10%
 0 1 2 3 4 5 6 7 8 9 Cash Outflow \$       (145) \$      (250) Cash Inflow \$          10 \$          12 \$          15 \$          40 \$          49 \$          63 \$          82 \$        106 \$        138 Net Cash Flow \$       (145) \$          10 \$          12 \$      (235) \$          40 \$          49 \$          63 \$          82 \$        106 \$        138 Present Value of all Cash Flows \$       (145) \$             9 \$          10 \$      (177) \$          27 \$          31 \$          36 \$          42 \$          50 \$          59 NPV \$                                                                                                                                                                                                         (59)

 Cash Out Flow for Phase 1 \$       (145) Cash Out Flow for Phase 2 \$       (188) Present Value of Out Flows \$       (333) Present value of all cash flows \$         273 NPV \$      (1.34) Standard Deviation 57.4%

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