Risk Analysis, Real Options, and Capital Budgeting
1. Real Options
A. JTM is looking to buy gates at their home airport. Its discount rate is 7%; the risk free rate is 2.5%. What is the NPV of the purchase if bought today? Use the data in the template and note that the terminal value is as of the end of year 6.
B. After you do part A, you remember back to the concept of real options, which means that JTM can make dynamic changes as time passes:
1. Present valuing the purchase price of the gates (that is, the years 1 and 2 Capital Expenditures) separately using the risk-free rate because once JTM decides to go with the purchase there is no risk.
2. Present valuing the Net Cash Flow excluding those Cap Ex. This calculation will include Cap. Ex. For years 3-6 as they are part of the normal operation of the gates and are unrelated to the purchase price. 3. Use the Black-Scholes Option Pricing formula to come up with option’s priceassuming a 1-year maturity and a 20% price volatility for gate prices.
4. Compare the price of the call option with the NPV in the No Real Options scenario. Is the option worth it?
2. Decision Tree
JTM really liked your work on the option pricing of the gates, so they ask you to look at their 3-phase expansion at their home airport. The three phases are:
a. Upon purchase of the new gates, start a marketing program to promote JTM’s routes to the East Coast, West Coast, and the Caribbean. If all goes well and the market is receptive, they will go on to phase 2.
b. Phase 2 has JTM invest in new routes to the destinations listed. If at any time, JTM finds that this is not going to work, they will pull the plug on everything.
c. Phase 3 has JTM start the new routes to the destinations listed. If things don’t go well on any of the three destinations, they will pull the plug on everything.
d. After much work with other departments, you generate enough data to calculate the NPV of the 3-phase expansion. Before you have a chance to save all your work, there is a power spike and you lose part of your work. You have to complete it for a presentation. Please use the Excel template provided to complete this
Finish the question with the excel file provide bellow
Prob. 1
| JTM | |||||||||||||||||||||
| Rates: | |||||||||||||||||||||
| Discount rate | 7.0% | Option Pricing: | |||||||||||||||||||
| Risk-free rate | 2.5% | PV of Cap. Ex. (Yrs. 1-2) | |||||||||||||||||||
| Scenario: No Real Options | Maturity | ||||||||||||||||||||
| Start | 1 | 2 | 3 | 4 | 5 | 6 | PV of NCF | ||||||||||||||
| Cash from Operations | 2.3 | 3.1 | 3.8 | 4.6 | 5.3 | 6.1 | Risk free rate | ||||||||||||||
| minus: Capital Expenditures | 1.0 | 2.2 | 3.0 | 3.7 | 4.5 | 5.2 | 6.0 | Volatility | |||||||||||||
| = Net Cash Flow | BS calculations: | ||||||||||||||||||||
| Terminal Value | 5.0 | d1 | ERROR:#DIV/0! | ||||||||||||||||||
| PV of NCF | N(d1) | ERROR:#DIV/0! | |||||||||||||||||||
| Scenario: Real Options | d2 | ERROR:#DIV/0! | |||||||||||||||||||
| Start | 1 | 2 | 3 | 4 | 5 | 6 | N(d2) | ERROR:#DIV/0! | |||||||||||||
| Cash from Operations | – 0 | 2.3 | 3.1 | 3.8 | 4.6 | 5.3 | 6.1 | Price of call | ERROR:#DIV/0! alfonso canella: alfonso canella: This is the option pricing formula. It is called the Black-Scholes formula as it was devised by Fisher Black and Myron Scholes. It has five inputs: time to maturity (in years), risk free rate (the alternative investment), the volatility of prices for the specific project (so if this were an oil industry project, the volatility would be the price volatility of crude oil), the strike price (that is, the PV of the Cap Ex necessary to do the project), and the present value of the cash flows that accrue from doing the project. |
||||||||||||
| minus: Capital Expenditures | 1.0 | 3.7 | 4.5 | 5.2 | 6.0 | Difference: | |||||||||||||||
| = Net Cash Flow | – Value of Call over No Real Option | ||||||||||||||||||||
| Terminal Value | 5.0 | – % of PV of No Real Option | |||||||||||||||||||
| PV of NCF | |||||||||||||||||||||
|
alfonso canella: alfonso canella: The NPV function of Excel makes quick work of the yearly cash flows by present valuing them according to when they happen. The terminal value must also be included. It can be put in as a year 16 and included in the NPV function or as a year 15 cash flow, as done here. |
PV of Cap. Ex. (Yrs. 1-2) |
alfonso canella: alfonso canella: The largest cash outflows in the project are considered to be the cost of doing the project. The smaller cash outflows are seen to be operating costs. So, the two large Cap Ex are discounted using the risk free rate as these investments will be made no matter what. Because they will be made no matter what, they are not risky, so the risk free rate is used. |
alfonso canella: alfonso canella: This is the option pricing formula. It is called the Black-Scholes formula as it was devised by Fisher Black and Myron Scholes. It has five inputs: time to maturity (in years), risk free rate (the alternative investment), the volatility of prices for the specific project (so if this were an oil industry project, the volatility would be the price volatility of crude oil), the strike price (that is, the PV of the Cap Ex necessary to do the project), and the present value of the cash flows that accrue from doing the project. |
alfonso canella: alfonso canella: The NPV function of Excel makes quick work of the yearly cash flows by present valuing them according to when they happen. The terminal value must also be included. It can be put in as a year 16 and included in the NPV function or as a year 15 cash flow, as done here. |
Answer part B, 4 in the box below: | ||||||||||||||||
Prob. 2
| JTM | |||||||||||||
| Airport Expansion | |||||||||||||
| Start | Phase I | Phase II | Phase III | PV of Revenues | Costs | Net | Probability | Expected Value | |||||
| Success | 225 | ||||||||||||
| 60% | 22 | ||||||||||||
| East Coast | |||||||||||||
| 30% | 6 | ||||||||||||
| Failure | – 0 | ||||||||||||
| 40% | 10 | ||||||||||||
| Success | 175 | ||||||||||||
| 55% | 10 | ||||||||||||
| West Coast | |||||||||||||
| 30% | 7 | ||||||||||||
| Failure | – 0 | ||||||||||||
| 45% | 7 | ||||||||||||
| Success | |||||||||||||
| 70% | 12 | Success | 221 | ||||||||||
| 75% | 15 | ||||||||||||
| Caribbean | |||||||||||||
| 30% | 12 | ||||||||||||
| Start | Failure | – 0 | |||||||||||
| 8 | 25% | 7 | |||||||||||
| Failure | – 0 | ||||||||||||
| 10% | 5 | ||||||||||||
| Failure | – 0 | ||||||||||||
| 30% | 4 | ||||||||||||
v. JAN ’22
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