# To Wait or Not to Wait? Use of the Flexibility to Postpone Investment Decisions in Theory and in Practice

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## Abstract

**:**

## 1. Introduction

## 2. Background and the Benchmark

_{0}).

#### 2.1. NPV-Strategy, the Two Cases

_{0}. The outcome of the project is revealed only at time T, during which the pay-off from the project is also clarified. In the first case, the time to maturity is one year (T = 1), and in the second case, two years (T = 2). Moreover, assuming that the risk-free rate (r) is set at 10%, the yearly volatility is assumed to be ~0.46, and the present value of expected revenues (S) is assumed to be 103, two equally probably outcomes may arise: A positive outcome (where the investment is profitable), and a negative outcome (where the investment creates a loss).

_{u}) and the negative (S

_{d}) outcomes in terms of ECU for both cases, and the expected value of the NPV-strategy (S) at the start of the experiment t

_{0.}

_{0}(i.e., the passive NPV which disregards flexibility) is in both cases 103, which makes, in both cases, the net payoff from the project equal to 3 (S − I = 103 − 100 = 3). This means that in both cases, the NPV-strategy has a positive expected NPV, before the uncertainty is resolved, but the decision maker takes a risk and can end up with a loss in the case the project will generate the lower value (S

_{d}).

#### 2.2. RO-Strategy, the Two Cases

_{0}is C = (0.5 × 62 + 0.5 × 0) × e

^{-0.1}= 28. Therefore, the expected payoff from the project, i.e., the expanded NPV including the value of the option to postpone the opportunity to invest in 1 year-time, net of the cost of the option, is 8. This is higher than the expected payoff from the NPV-strategy ceteris paribus (8 > 3). In the second RO-strategy case, respectively, the expected value of the project at t

_{0}is C = (0.5 × 98 + 0.5 × 0) × e

^{-0.1×2}= 40. Therefore, the expected payoff from the project, i.e., the expanded NPV including the value of the option to postpone the opportunity to invest in 2 years-time, net of the cost of the option, is 20. We note that the expected payoff from the RO-strategy in the second case is (considerably) higher than that from the NPV-Strategy in the second case (20 > 3).

## 3. The Experiment

#### 3.1. Experimental Design and Tasks

- (a)
- Participants are considered as perfect rational decision makers, which means that they make decisions focalizing exclusively on the consequences generated by the value of the option computed given the theoretical time. Therefore, the participants make decisions based on an evaluation of the investment outcomes, independently from the fact that they are requested to wait 20 min or 60 min in the laboratory.
- (b)
- Participants are considered as decision makers who are psychologically influenced by the length of the real-time they have to spend in the laboratory. Therefore, the participants evaluate differently the utility that they gain from equal investment-outcomes as a consequence of the amount of real time that they spend in the laboratory.

#### 3.2. Participants and Procedures

## 4. Predictions Development

**H1T (Theoretical)**:

“Hyperbolic discount functions are characterized by a relatively high discount rate over short horizons and a relatively low discount rate over long horizons. This discount structure sets up a conflict between today’s preferences, and the preferences that will be held in the future. For example, from today’s perspective, the discount rate between two far-off periods, t and t + 1, is the long-term low discount rate. However, from the time t perspective, the discount rate between t and t + 1 is the short-term high discount rate. This type of preference change is reflected in many common experiences.”

**H1B (Behavioral):**

“We will use the terms savoring to refer to the positive utility derived from anticipating future pleasant outcomes and dread to refer to the negative contemplation of unpleasant outcomes.”

…the ’most you would pay now’ to obtain (avoid) each of five outcomes, immediately, and following five different time delays. The outcomes were: (1) obtain four dollars; (2) avoid losing four dollars; (3) avoid losing one thousand dollars; (4) avoid receiving a (non-lethal) one hundred and ten volt (5) obtain a kiss from the movie star of your choice. Time delays were: (1) immediately (no delay); (2) in twenty-four hours; (3) in three days; year; (4) in one year; (5) in ten years. Subjects were asked to specify the most they would pay for every combination of outcome and time delay.

**H2B (Behavioral):**

## 5. Results

**Type 1**—are those who did not want to benefit from flexibility and always chose Scenario 1;**Type 2**—are those who wanted to buy the right to exercise the real option, but were not willing to pay enough to buy it;**Type 3**—are those who successfully obtained the right to exercise the option.

**Result 1:**

**Result 2:**

**Result 3:**

**Result 4:**

**Result 5:**

**Result 6:**

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A.

Experimental instructions of the two 20-minute treatments (parameters of the “high option value 20” treatment are in brackets) are translated from Italian. Instructions of the 60-minute treatments only differ in the waiting time.

- 1. Task 1

- 2. Task 2

Investment | Wait 20 min | Lottery Outcome | Final Payoffs |
---|---|---|---|

100 tokens | YES | 162 [198] tokens with 50% | 162 [198] tokens |

100 tokens | YES | 65 [54] tokens with 50% | 65 [54] tokens |

Wait 20 min | Lottery Outcome | Investment | Final Payoffs |
---|---|---|---|

YES | 162 [198] tokens | 100 UMS | (162 − X) [(198 − X)] tokens |

YES | 65 [54] tokens | No investment | (100 − X) tokens |

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Treatment | Waiting Time (min) | Project Outcomes | Net Expected Payoff | |
---|---|---|---|---|

NPV-Strategy Passive NPV (Scenario 1) | RO-Strategy Expanded NPV (Net of the Cost of the Option) (Scenario 2) | |||

Low option value 20 | 20 | 162 / 65 (p = 50%) | 3 | 8 |

High option value 20 | 20 | 198 / 54 (p = 50%) | 3 | 20 |

Low option value 60 | 60 | 162 / 65 (p = 50%) | 3 | 8 |

High option value 60 | 60 | 198 / 54 (p = 50%) | 3 | 20 |

Treatment | Type 1 | Type 2 | Type 3 | Total |
---|---|---|---|---|

Low option value 20 | 12 (27.3%) | 15 (34.1%) | 17 (38.7%) | 44 (100%) |

High option value 20 | 6 (12.5%) | 16 (33.3%) | 26 (54.2%) | 48 (100%) |

High option value 60 | 10 (20.8%) | 17 (35.4%) | 21 (43.8%) | 48 (100%) |

Low option value 60 | 11 (24.4%) | 25 (55.6%) | 9 (20%) | 45 (100%) |

All | 39 (21.1%) | 73 (39.5%) | 73 (39.5%) | 185 (100%) |

Comparison | Mann–Whitney Test (p-Values) |
---|---|

Type 1 vs. Type 2 | 0.16 |

Type 2 vs. Type 3 | 0.49 |

Type 1 vs. Type 3 | 0.26 |

Dependent Variable: WTP | Coef | SE |
---|---|---|

low option value 20 | Reference | |

high option value 20 | −0.83 | 1.98 |

high option value 60 | 0.56 | 2.10 |

low option value 60 | −3.60 * | 2.09 |

BRET | 0.01 | 0.06 |

Male | −0.15 | 1.41 |

Age | 0.04 | 0.32 |

Economics | 1.84 | 1.63 |

delta_ind | −0.00 | 0.00 |

sigma | 8.05 *** | 0.55 |

Constant | 18.98 ** | 7.79 |

Observations | 146 |

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## Share and Cite

**MDPI and ACS Style**

Morreale, A.; Mittone, L.; Vu, T.-T.-T.; Collan, M.
To Wait or Not to Wait? Use of the Flexibility to Postpone Investment Decisions in Theory and in Practice. *Sustainability* **2020**, *12*, 3451.
https://doi.org/10.3390/su12083451

**AMA Style**

Morreale A, Mittone L, Vu T-T-T, Collan M.
To Wait or Not to Wait? Use of the Flexibility to Postpone Investment Decisions in Theory and in Practice. *Sustainability*. 2020; 12(8):3451.
https://doi.org/10.3390/su12083451

**Chicago/Turabian Style**

Morreale, Azzurra, Luigi Mittone, Thi-Thanh-Tam Vu, and Mikael Collan.
2020. "To Wait or Not to Wait? Use of the Flexibility to Postpone Investment Decisions in Theory and in Practice" *Sustainability* 12, no. 8: 3451.
https://doi.org/10.3390/su12083451