Question

Unequal Lives

Shao Airlines is considering the purchase of 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 are 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)? Do not round intermediate calculations. Enter your answer in millions. For example, an answer of $1.234 million should be entered as 1.234, not 1,234,000. Round your answer to three decimal places.

$   million

What is the equivalent annual annuity for each plane? Do not round intermediate calculations. Enter your answers in millions. For example, an answer of $1.234 million should be entered as 1.234, not 1,234,000. Round your answers to three decimal places.

Plane A: $   million

Plane B: $   million

Answer 1

Requirement (a)-Increase in the Value of the Company

Net Present Value for Plane-A

Year	Annual cash flows ($ in million)	Present Value Factor (PVF) at 11.00%	Present Value of annual cash flows ($ in million) [Annual cash flow x PVF]
1	30.00	0.90090	27.027
2	30.00	0.81162	24.349
3	30.00	0.73119	21.936
4	30.00	0.65873	19.762
5	30.00	0.59345	17.804
TOTAL		3.69590	110.877

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $110.877 Million - $100 Million

= $10.877 Million

Net Present Value for Plane-B

Year	Annual cash flows ($ in million)	Present Value Factor (PVF) at 11.00%	Present Value of annual cash flows ($ in million) [Annual cash flow x PVF]
1	27.00	0.90090	24.324
2	27.00	0.81162	21.914
3	27.00	0.73119	19.742
4	27.00	0.65873	17.786
5	27.00	0.59345	16.023
6	27.00	0.53464	14.435
7	27.00	0.48166	13.005
8	27.00	0.43393	11.716
9	27.00	0.39092	10.555
10	27.00	0.35218	9.509
TOTAL		5.88923	159.009

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $159.009 Million - $132 Million

= $27.009 Million

Therefore, the Increase in the Value of the Company = NPV for Plane-B

= $27.009 Million

Requirement (b)-Equivalent annual annuity for each plane

Equivalent annual annuity for Plane-A = NPV / (PVIFA 11.00%, 5 Years)

= $10.877 Million / 3.69590

= $2.943 Million

Equivalent annual annuity for Plane-B = NPV / (PVIFA 11.00%, 10 Years)

= $27.009 Million / 5.88923

= $4.586 Million

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.