# Prob. 1 Zion Aviation Rates: Discount rate6.0% Option Pricing: Risk-free rate2.5% PV of Cap. Ex. (Yrs. 1-2) Scenario: No Real Options Maturity4.0 Start1234567 PV of NCF Cash from Operations...

Prob. 1
Zion Aviation
Rates:
Discount rate    6.0%                                    Option Pricing:
Risk-free rate    2.5%                                    PV of Cap. Ex. (Yrs. 1-2)
Scenario: No Real Options                                     Maturity    4.0
Start    1    2    3    4    5    6    7        PV of NCF
Cash from Operations        1.0    3.0    4.9    6.9    8.8    10.8    12.7        Risk free rate
minus: Capital Expenditures    1.0    6.0    5.5    1.0    1.3    1.5    1.8    2.0        Volatility    35%
= Net Cash Flow (NCF)                                        BS calculations:
Terminal Value                                11.0        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    7        N(d2)    ERROR:#DIV/0!
Cash from Operations    - 0    1.0    3.0    4.9    6.9    8.8    10.8    12.7        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            1.0    1.3    1.5    1.8    2.0        Difference:
= Net Cash Flow (NCF)                                         - Value of Option over PV    ERROR:#DIV/0!
Terminal Value                                11.0         - % of PV    ERROR:#DIV/0!
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.
Prob. 2
Network Expansion with New Aircraft
Start        Phase I        Phase II        Phase III        PV of Revenues    Costs    Net    Probability    Expected Value
Success        115
70%    9
Utah
50%    7
Failure        - 0
30%    1
Success        122
55%    19
22%    8
Failure        - 0
45%    2
Success
72%    9            Success        99
55%    15
Arizona
20%    12
Start                        Failure        - 0
5                    45%    2
Failure                - 0
8%    2
Failure                        - 0
28%    5                            Total
v. MAR 2022
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Answered 1 days AfterApr 06, 2022

## Solution

Prateek answered on Apr 07 2022
Prob. 1
Zion Aviation
Rates:
Discount rate    6.0%                                    Option Pricing:
Risk-free rate    2.5%                                    PV of Cap. Ex. (Yrs. 1-2)    5.9
Scenario: No Real Options                                     Maturity    4.0
Start    1    2    3    4    5    6    7        PV of NCF    36.5
Cash from Operations        1.0    3.0    4.9    6.9    8.8    10.8    12.7        Risk free rate    2.5%
minus: Capital Expenditures    1.0    6.0    5.5    1.0    1.3    1.5    1.8    2.0        Volatility    35%
= Net Cash Flow (NCF)    (1.0)    (5.0)    (2.6)    3.9    5.6    7.3    9.0    10.7        BS calculations:
Terminal Value                                11.0        d1    3.11
PV of NCF    26.0
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.                                    N(d1)    1.00
Scenario: Real Options                                     d2    2.41
Start    1    2    3    4    5    6    7        N(d2)    0.99
Cash from Operations    - 0    1.0    3.0    4.9    6.9    8.8    10.8    12.7        Price of call    31.2
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...
SOLUTION.PDF