Question

Titanic 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 $30 million per year. Plane B has a life of 10 years, will cost $132 million, and will produce net cash flows of $25 million per year. Titanic 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 12%. What is the equivalent annual annuity for Plane B?

A. $2.259 million

B. $1.638 million

C. $2.638 million

D. $1.259 million

E. $3.259 million

Answer 1

Solution

First the NPV of the invest in plane B will be calculated

NPV=Total present value of cashflows-Initial investment

Present value of a cashflow=Cashflow/(1+r)^n

where

r-discount rate per period-12%

n-number of discounting periods

Calculation for Total present value of future cashflows is given below

Excel formula

Thus NPV=141.2555757-132=9.255576

Now to find the Equivalent annuity

NPV opf annuity=Present value of the equivalent annuity payments

Present value of annuity=NPV=Annuity payment*((1-(1/(1+i)^m))/i)

where

i-discount or intrest rate per period-12%

m-number of periods =10

Present value of annuity =NPV=9.255576

Annuity payment=?

Putting values in formula

9.255576=Annuity payment*((1-(1/(1+.12)^10))/.12)

Solving we get

Annuity payment=1.638

Thus the correct answer is $1.638 million

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