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.

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rejkjavik rejkjavik · Answer 1 · 2019-10-05T17:26:30+02:00

Answer:

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

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

[tex]CF_o = -12, 000, 000[/tex]

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:

[tex]NPV = CF_o + \sum_{i =1}^{15} \frac{CF_i}{(1+r)^i}[/tex]

[tex]= -12,000,000 + \sum_{i =1}^{15} \frac{1,500,000}{(1+r)^i}[/tex]

[tex]=-12,000,000 + 1,500,000 \sum_{i =1}^{15} \frac{1}{(1+r)^i}[/tex]

[tex]=-12,000,000 + 1,500,000 \frac{(1-(1+r)^{-15})}{r}[/tex]

[tex] =-12,000,000 + 1,500,000 \frac{(1-(1+0.09)^{-15})}{0.09}[/tex]

= 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.