Question

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 $30 million per year. Plane B has a life of 10 years, will cost $132 million and will produce net cash flows of $27 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 11%.By how much would the value of the company increase if it accepted the better project (plane)? What is the equivalent annual annuity for reach plane?

Answer 1

Answer:

1. If this is accepted the value of the company will increase by $27.0084 million.

2. The equivalent annual annuity for each plane:

Plane A = $2.973 million

Plane B = $4.586 million

Explanation:

1. Let's calculate Net Present Value (NPV) for Plane A:

Initial investment = $100 million

Annual cash flows = $30 million per year

Cost of capital = 11%

n = 5 years

NPV = (Annual cash flows × PVIFA (Cost of capital, n) - Initial investment

where PVIFa is Present Value Interest Factor

NPV = (30 million ×PVIFA (11%, 5) - 100 million

NPV = (30 million × 3.659) - 100 million

NPV = $10.877 million

Let's calculate Net Present Value (NPV) for Plane B:

Initial investment = $132 million

Annual cash flows = $27 million per year

Cost of capital = 11%

n = 10 years

NPV = (Annual cash flows × PVIFA (Cost of capital, n) - Initial investment

where PVIFa is Present Value Interest Factor

NPV = ($27 million ×PVIFA (11%, 10) - $132 million

NPV = ($27 million × 5.8892) - $132 million

NPV = $27.0084 million

In conclusion, the better project is Plane B as it has a higher net present value. If this is accepted the value of the company will increase by $27.0084 million.

2. equivalent annual annuity = NPV/ Present Value Annuity Factor

For Plane A:

equivalent annual annuity = NPV/ Present Value Annuity Factor ( 11%, 5)

equivalent annual annuity =  $10.877 million/ 3.659

equivalent annual annuity = $2.973 million

The equivalent annual annuity for plane A is $2.973 million

For Plane B:

equivalent annual annuity = NPV/ Present Value Annuity Factor ( 11%, 10)

equivalent annual annuity =  $27.0084 million/5.8892

equivalent annual annuity = $4.586 million

The equivalent annual annuity for plane B is $4.586 million