Unequal Lives Shao Airlines is considering two alternative planes. Plane A has a
ID: 2716466 • Letter: U
Question
Unequal Lives
Shao Airlines is considering two alternative planes. Plane A has an expected life of 5 years, will cost $100 million and will produce net cash flows of $29 million per year. Plane B has a life of 10 years, will cost $132 million and will produce net cash flows of $24 million per year. Shao plans to serve the route for only 10 years. Inflation in operating costs, airplane costs, and fares is expected to be zero, and the company's cost of capital is 8%.
By how much would the value of the company increase if it accepted the better project (plane)? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$ million
What is the equivalent annual annuity for each plane? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answers to two decimal places.
Plane A $ million Plane B $ millionExplanation / Answer
Plane A:- (Plan A has life of 5 Years)
Calculation of Net present value:- Present value of cash inflow - Present value of cash outflow
Present value of cash inflow
Years
Cash inflow
Present value factors
Present value of cash inflow
1-5
29
3.993 (NOTE 1)
115.797
Total
115.797
(NOTE 1):- 3.993 are the cumulative present value factors @ 8% for 5 years.
Present value of cash outflow = 100 (Plan A has life of 5 Years)
Plane B:- (Plan B has life of 10 Years)
Calculation of Net present value:- Present value of cash inflow - Present value of cash outflow
Present value of cash inflow
Years
Cash inflow
Present value factors
Present value of cash inflow
1-10
24
6.71 (NOTE 2)
161.04
Total
161.04
(NOTE 2):- 6.71 are the cumulative present value factors @ 8% for 10 years.
Present value of cash outflow = 100 (Plan B has life of 10 Years)
Conclusion:- The value of the company increase by 61.04 (in millions of dollars) if it accepted the better project (Plane B).
Equivalent annual annuity = NPV / Cumulative Present value factors of annuity
Plane A = 15.797 / 3.993* = 3.96 (approx) (in millions of dollars)
Plane B = 61.04 /6.71** = 9.10 (approx) (in millions of dollars)
* Plane A having estimated life of 5 years given in the question. (cumulative present value factors @ 8% for 5 years).
** Plane B having estimated life of 10 years given in the question. (cumulative present value factors @ 8% for 10 years).
Years
Cash inflow
Present value factors
Present value of cash inflow
1-5
29
3.993 (NOTE 1)
115.797
Total
115.797
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