Question

An airline is evaluating whether or not to upgrade the engines on their old 757's. There would be an immediate savings of $5,000,000 from selling the old engines to another airline. Because of the better fuel economy of the new engines, future savings are estimated to be $1,500,000 per year for the next 15 years. To pay for the new engines, the airline will withdraw money from an investment paying 9% interest per year compounded annually If the new engines cost $17,000,000, would you recommend they purchase the new engines? Calculate numerical justification AND give a verbal explanation.

Answer 1

the net present value at a rate r = 9% is $91,0.2.61478

Step-by-step explanation:

From data given the initial investment calculated as

The initial investment is

17,000,000-5,000,000 = 12,000,000

Hence at year 0, the company has a cash flow of

`CF_o = -12, 000, 000`

And for the next 15 years the cash flows are:

CF_i= 1,500, 000 for i 1, 2, .., 15

Hence the net present value at a rate r = 9% is:

`NPV = CF_o + \sum_(i =1)^(15) (CF_i)/((1+r)^i)`

`= -12,000,000 + \sum_(i =1)^(15) (1,500,000)/((1+r)^i)`

`=-12,000,000 + 1,500,000 \sum_(i =1)^(15) (1)/((1+r)^i)`

`=-12,000,000 + 1,500,000 ((1-(1+r)^(-15)))/(r)`

`=-12,000,000 + 1,500,000 ((1-(1+0.09)^(-15)))/(0.09)`

= 91,0.2.61478

Since NPV >0 then they should purchase the new engines.

They should purchase the new engines because it would result in a rate of return

greater than the rate of 9% of the other investment.