25-11: Western Airlines is considering a new route that will re- quire adding an additional Boeing 777 to its fleet. Western can purchase the airplane for $221.7 million or lease it for $25 million per year. If it purchases the airplane, its seating can be optimized, and the new route is expected to generate profits of $49.5 million per year. If leased, the route will only generate profits of $34.8 million per year. Suppose the appropriate cost of capital is 12.9% and that, if purchased, the plane can be sold at any time for an expected resale price of $221.7 million. Ignore taxes.

Intermediate Financial Management (MindTap Course List)
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Chapter12: Capital Budgeting: Decision Criteria
Section: Chapter Questions
Problem 16P: Shao Airlines is considering the purchase of two alternative planes. Plane A has an expected life of...
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can you show how this was done, i cant figure out the isolation of P was done. the first is the task and the second has the solution also, but i cant figure out how it was done 

P = 6.06%

25-11: Western Airlines is considering a new route that will re-
quire adding an additional Boeing 777 to its fleet. Western can
purchase the airplane for $221.7 million or lease it for $25 million
per year. If it purchases the airplane, its seating can be optimized,
and the new route is expected to generate profits of $49.5 million
per year. If leased, the route will only generate profits of $34.8
million per year. Suppose the appropriate cost of capital is 12.9%
and that, if purchased, the plane can be sold at any time for an
expected resale price of $221.7 million. Ignore taxes.
Transcribed Image Text:25-11: Western Airlines is considering a new route that will re- quire adding an additional Boeing 777 to its fleet. Western can purchase the airplane for $221.7 million or lease it for $25 million per year. If it purchases the airplane, its seating can be optimized, and the new route is expected to generate profits of $49.5 million per year. If leased, the route will only generate profits of $34.8 million per year. Suppose the appropriate cost of capital is 12.9% and that, if purchased, the plane can be sold at any time for an expected resale price of $221.7 million. Ignore taxes.
c. At what (risk-neutral) probability of default would equity
holders' preference for leasing versus purchasing the plane change?
Equity holders' would prefer to lease the plane over purchasing the plane at
any probability of default greater than 6.06%:
(1 - p)(221.7 + 49.5)
(1 – p)(34.8)
-221.7 +
= -25 +
(25)
1.129
1.129
1.129(221.7 – 25)
(1 – p) =
(26)
221.7 + 49.5 – 34.8
Thus p = 6.06%
Transcribed Image Text:c. At what (risk-neutral) probability of default would equity holders' preference for leasing versus purchasing the plane change? Equity holders' would prefer to lease the plane over purchasing the plane at any probability of default greater than 6.06%: (1 - p)(221.7 + 49.5) (1 – p)(34.8) -221.7 + = -25 + (25) 1.129 1.129 1.129(221.7 – 25) (1 – p) = (26) 221.7 + 49.5 – 34.8 Thus p = 6.06%
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