Airline X is a newly established company which has intentions to acquire a new fleet of aircrafts for their company. The carrier expects to earn roughly half of its revenue from the domestic market, and majority of its existing fleet servicing the domestic market by the competitors are using the single-aisle jet planes. To kick-start the company's operations, X plans to launch a purchasing program where the airline has determined 737-700 as the main model in its upgrading program. It has signed the purchase contract and confirmed the aircraft introduction plan after some hard negotiations with Boeing. The first batch of ten 737-700 aircraft have a single economy-class layout with 137 available seats, and will be delivered and immediately put into service one year later (in June 2019).The trade price is $34.68 million per aircraft. In view of the large amount in carrier X's purchase, Boeing has provided X a "defer" option, that is, X (the buyer) has the right to delay the aircraft-receiving date for two years, with the price rising to $35.71 million per aircraft if exercised. In addition, Boeing provides X with a guarantee of aircraft residual values at the end of 20 years after purchase ($9.26 million and $9.49 million at the end June of 2039 and 2041, respectively). In the course of reaching this pact, Ascend, a leading provider of expert advisory and valuation services to global aviation industry, has played an important role. These 737-700s are proposed to be put into service on U.S. domestic routes, with average traffic capacity of 700 miles per route, 6 flights per day and 360 available days per year. With these figures, the proposed one-jet traffic capacity can be calculated as 207.144 million seat-miles per year (ASM). It is carrier X's practice that the firm's operating and financial data are analyzed continuously.  Further, the carrier uses the fuel surcharge and fuel derivative tools to hedge the volatility of fuel price. In particular, it is able to lock the aviation kerosene cost at the level when the light sweet crude oil price stays at $100 a barrel. Under these conditions of traffic capacity and fuel price, X has the variable "cash operating cost" (COC) at about $0.060 per ASM and the fixed COC at about $0.015 per ASM leading to a total COC (TCOC) of $0.075 per ASM. These costs are subject to a 1%annual increase, owing to inflation. The carrier exhibits an annualized volatility of 5%for its Yield in the domestic market. Based on X's accounting policy, the airframe and engine have a depreciation period of 25 years, with the residual value at 5% of the initial purchase (book) value. X usually takes 20 years as its aircraft's (economically) useful years in its acquisition decision, and uses the higher figure between the book-value and appraisal-market methods as the residual value. Carrier X uses the current rate of 10-year U.S. Treasury Note, 2%, as the risk-free rate, and its current margin income tax rate is 38.5%. Under the premise that the airline is able to continually hold its flight time for the fleet, if its Yield cannot cover the variable COC and sealing cost, then the manager will probably seal part of the fleet up for safekeeping for a period of a year or more until the Yield can cover the variable COC and unsealing cost. According to the contracts with airports holding idle planes, X needs to pay $0.10 million as the expense of sealing a plane up for a year, and then pay $0.25 million to unseal a plane (this unsealing expense includes the cost to repair the plane so as to restore to airworthiness). Similar to the case of operating costs, there is a 1% annual growth rate for the sealing and unsealing expenses (owing to inflation)

Each year end's Cash Flow can be calculated using the following formula 

CF(t) = [(yield(t)-TCOC(t))*ASM-DA]*(1-Tax) +DA

Where DA (depreciation and amortization amount)=(1-5%)/25*initial book value In the final 20th year of operation, the residual value needs to be added to the cash flow.

Questions to answer

(1) Provide the binomial tree (lattice) for the yield of the acquisition

(2) Calculate the NPV of the project using the tree in Q (1)

(3) Calculate the NPV which include the seal-unsealing option using the tree in Q (1)

The yield, denoted yield(t), is a time varying variable. 

It is the revenue per ASM.

Therefore, one can use the yield as the variable that evolves over time.

Thus one should draw the binomial tree of the yield(t) variable.