JTM Airlines, where you work, is looking at potentially buying more gates at their home airport. If it pays the airport $1M, JTM will hold exclusive rights to buy those gates for $17M (at the start) and $17.5M (one year later) at any time in the next 4 years. The option expires at the end of year 4. JTM's discount rate is 10%. What is the NPV of the gate purchases if it bought them today? Use the data in the Excel template provided. b. After you run the numbers for part A, you remember back to your ERAU corporate finance class's coverage of real options. You know that the 4-year option has value, so you decide to calculate it by:

1. Present valuing the purchase price of the gates separately using the riskfree rate. Once JTM decides to go ahead with the purchase, there is no risk to that expenditure.

2. Present valuing the Net Cash Flow excluding those purchase prices. This calculation will include Cap. Ex. for years 3-15 as they are part of the normal operation of the gates and are unrelated to the purchase price.

3. Using the Black-Scholes Option Pricing formula to come up with option's price assuming a 4-year maturity and a 10% price volatility for gate prices.

4. Compare the price of the call option as calculated using the BSO formula with the NPV in the No Real Options scenario. With this, you can decide whether or not the $1M option is worth it or not. Is it?

Please show formulas used.

For the corner section in excel here are the formulas:

d1: =+(LN(S15/S13)+(S16+S17^2/2)*S14)/((S17*S14^0.5))

N(d1): =NORMSDIST(S19)

d2: =+S19-(S17)*S14^0.5

N(d2): =NORMSDIST(S21)

Price of Call: =+S15*S20-(S13*S22*(2.71828^((-S16)*S14)))

Formatting as Table Styles Format Filter N23 C D E F I J J K L M N 0 P Q R s G H JTM Airlines 2 11.9 17.5 3 12.9 5.3 4 9.4 4.1 Scenario: No Real Options 6 7 7 2 8.0 9.8 12.8 15.9 1.3 0.1 0.3 10 15.2 0.1 11 14.9 8.1 8.1 3.5 12 14.6 (0.1) 13 15.5 0.2 14 16.6 15 15.2 0.1 67.8 2 11.9 3 12.9 4 9.4 4.1 A B 41 2 Rates: 3 Discount rule 10.0% 4 Risk-free rate 6.0% 5 6 1 7 Cash from Operations 4.2 8 minus: Capital Expenditure 17.0 9 = Net Cash Flow 10 Terminal Value 11 PV of NCF 12 13 1 14 Cash from Operations 4.2 15 minus: Capital Expenditures 16 = Net Cash Flow 17 Terminal Value 18 PV of NCF 19 PV of Cap. Ex. (Yrs. 1-2) 20 21 22 23 24 25 26 27 28 29 30 5 8.1 3.5 6 8.0 1.3 Scenario: Real Options Z 8 9 9.8 12.8 15.9 0.1 0.3 10 15.2 0.1 11 14.9 8.1 12 14.6 (0.1) 13 15.5 0.2 14 16.6 0.1 15 15.2 4.0 5.3 6.0% 10% 67.8 Option Pricing PV of Cap. Ex. (Yrs. 1-2) Maturity PV of NCF Risk free rate Volatility BS calculations: d1 N(dl) d2 Nd2) Price of call Difference: - Value of Option over PV -% of PV #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 31 Formatting as Table Styles Format Filter N23 C D E F I J J K L M N 0 P Q R s G H JTM Airlines 2 11.9 17.5 3 12.9 5.3 4 9.4 4.1 Scenario: No Real Options 6 7 7 2 8.0 9.8 12.8 15.9 1.3 0.1 0.3 10 15.2 0.1 11 14.9 8.1 8.1 3.5 12 14.6 (0.1) 13 15.5 0.2 14 16.6 15 15.2 0.1 67.8 2 11.9 3 12.9 4 9.4 4.1 A B 41 2 Rates: 3 Discount rule 10.0% 4 Risk-free rate 6.0% 5 6 1 7 Cash from Operations 4.2 8 minus: Capital Expenditure 17.0 9 = Net Cash Flow 10 Terminal Value 11 PV of NCF 12 13 1 14 Cash from Operations 4.2 15 minus: Capital Expenditures 16 = Net Cash Flow 17 Terminal Value 18 PV of NCF 19 PV of Cap. Ex. (Yrs. 1-2) 20 21 22 23 24 25 26 27 28 29 30 5 8.1 3.5 6 8.0 1.3 Scenario: Real Options Z 8 9 9.8 12.8 15.9 0.1 0.3 10 15.2 0.1 11 14.9 8.1 12 14.6 (0.1) 13 15.5 0.2 14 16.6 0.1 15 15.2 4.0 5.3 6.0% 10% 67.8 Option Pricing PV of Cap. Ex. (Yrs. 1-2) Maturity PV of NCF Risk free rate Volatility BS calculations: d1 N(dl) d2 Nd2) Price of call Difference: - Value of Option over PV -% of PV #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 31