Spartan Airlines has not debt, and its current assets are worth $50 per share. Management knows

the value of the company's assets, but the current stock price of Spartan Airlines is only $40 per

share. If Spartan issues equity, Spartan's management anticipates that the market will react

negatively and that Spartan will only be able to sell the new shares for $35 per share. Currently,

Spartan has 100,000 shares outstanding. Spartan is considering investing in a new airplane that

will cost $350,000. Management anticipates that the present discounted value of increased

earnings from purchasing the new plane is $450,000.

a) If Spartan had the cash available to purchase the new plane, should it make the purchase?

b) If Spartan needs to finance the purchase of the new plane with equity, will it make sense for it

to purchase the plane?

Answer:

a) Yes, Spartan must purchase the new plane as NPV is positive that is $100,000

b) Yes, Spartan should purchase the new plane by financing with equity as NPV in that case is coming positive.

Step-by-step explanation

a)

Net present value (NPV) is the difference between the sum of the present value of the expected future earnings from the project and the initial cost of that project. The Present value of the future earnings from the new plane is greater than the cost of the new plane that implies positive NPV. A positive NPV means that the company will generate future profits by investing in this new project. Hence the company should purchase the new plane.

The NPV of the project is given by - 

NPV = $450,000 - $350,000

         = $100,000

b)

Spartan should take the project by financing with equity as NPV in that case is coming positive.

The number of new shares the company will issue is 350,000 / 35 = 10,000 shares.

As the current market environment of Spartan shares is not promising so if the company issues new shares it will bear additional cost i.e. ( 40 - 35 ) * 10,000 i.e. $50,000.

Hence the total cost of the investment will become $400,000 ( 350,000 + 50,000 ).

Total PV of the Increased earnings is $ 450,000.

The resultant NPV is $50,000 ( 450,000 - 400,000 ) i.e. positive.

Note - 

Cost of issuing a new share for Spartan is $35 and the value is compared with its market price of before issuing the new shares that is $40.

Reference - 

https://www.investopedia.com/terms/n/npv.asp