## Investment Example

Real Options Valuation (ROV) offers powerful tools and logic to assess investment decisions. Herein, we show a simple application of ROV, by valuating a firm’s decision to invest in a new factory.

In this example, we show how the Net Present Value (NPV) may lead the firm to take unnecessary risk: in this example, we show that a positive NPV leads the firm to invest in a factory with a large probabiility to have negative profits in the following years. ROV, however, internalizes the possibility of different outcomes and advices the firm to only invest when the probability of reversal of positive cash flows is low enough or the gains of investing this year are high enough.

Assumptions:

The assumptions we present are for exposition purposes, and our only intention is to offer the reader an insightful perspective of ROV for investments. In the projects of our clients, we consider much more complex and realistic contexts to improve efficiency and create value for our clients.

• Investment is completely irreversible. The factory infrastructure can only be used for a single purpose and any machinery cannot be sold in the future.

• The firm can postpone investment. It can invest this year, and next year. Decision:

Value to invest this year =
18M€

Value to wait =
16.98M€

VS

The cost to abdicate the expected value of investing today exceeds the value of waiting for additional information by 1.02M€ (18 - 16.98). Thus, the firm would optimally invest today.

The intuition of this result is simple. The smaller is the irreversibility of investment, that is the smaller is the investment, the smaller is the value of waiting for further information. In this case, the firm is already better of by benefiting of cash flows this year, rather than waiting for next year to invest.

NPV Investment this Year

NPV Investment next Year

= -1.82M€

18M€

66.7%

33.3%

60M€ - 32M€

1.1

= 25.45M€

30M€ - 32M€

1.1

Value to invest this year =
10M€

Value to wait =
12.12M€

VS

NPV Investment this Year

NPV Investment next Year

60M€ - 40M€

1.1

= 18.18M€

33.3%

= -9.09M€

30M€ - 40M€

1.1

10M€

66.7%

NPV Investment this Year

NPV Investment next Year

10M€

33.3%

66.7%

60M€ - 40M€

1.1

= 18.18M€

= -9.09M€

30M€ - 40M€

1.1

This Year

Next Year

60M€

1.1

66.7%

50M€

33.3%

= 54.55M€

= 27.27M€

30M€

1.1

This Year

Next Year

60M€

30M€

33.3%

50M€

66.7%

Invest this year

VS

Wait for next year

What if investment=32M€?

The DCFs are the same as in the case above. But the NPVs are now different:

The value of waiting for additional information exceeds the cost to abdicate the expected value of investing today by 2.12M€. Thus, the firm would optimally wait for further information instead of investing today and take the risk of a bad scenario. This simple example shows how a positive NPV can be misleading. The NPV suggests the firm to invest today making it take unnecessary risk. Next, we recalibrate the investment level and show how the decision may change.

If, however, a good scenario is confirmed next year, the firm can invest 40M€ to obtain a DCF of 60M€. Discounting back to the present (18.18M€) and multiplying by the probability that a good scenario occurs (66.7%) implies an expected NPV of 12.12M€.

Analysis:

The NPV to invest this year is positive: the DCF exceeds the Investment cost by 10M€.  Standard analysis, thus, suggests that the firm should invest in the factory.

But, standard analysis ignores two important factors. It ignores heterogeneity of scenarios: in the next year, the factory has a DCF of 60M€ in a good scenario and 30M€ in a bad scenario. Thus, if the firm invests this year and the bad scenario occurs next year, the firm has invested in an unprofitable factory.

Standard analysis also ignores (or misguides about) optimal investment timing. When the NPV is positive, standard analysis suggests the firm should invest. But the firm can usually delay investment and obtain further information, stopping it from making some unprofitable investments. In this example, if the firm does not invest this year, it will only invest next year if a good scenario occurs.

If a bad scenario is confirmed next year, the firm can invest 40M€ to obtain a DCF of 30M€. Thus the firm would not invest.

• Investment= 40M€. The NPVs, then, are:

• This year, the new factory has a Discounted Cash Flow (DCF) of 50M€.

• Next year, the factory has a DCF of 60M€ with a 66.7% probability. And has a DCF of 30M€ with a 33.3% probability.

• Discount rate= 10%. In present terms, the DCFs are:

Standard analysis again suggests the firm should invest this year: the NPV is 18M€. Should the firm invest this year or should it wait as in the previous example?

If a bad scenario is confirmed next year, the firm can invest 32M€ to obtain a DCF of 30M€. Thus, the firm would still not invest.

If a good scenario is confirmed next year, the firm can invest 32M€ to obtain a DCF of 60M€. Discounting back to the present (28M€) and multiplying by the probability that a good scenario occurs (66.7%) yields an expected NPV of 16.98M€. # WATSON & NOBLE

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