Question

United Airlines plan to buy 34 airplanes for $120,000,000. Flight operations and ground costs are expected to be $7,000,000 per year and $4,000,000 per year respectively. United expects to sell 300,000 tickets and variable costs are expected to be 20 percent of revenue. With a 14 percent required rate of return, what minimum price per ticket are needed to justify the purchase of the airplanes? (Assume a 20- year life and no salvage value for the airplane at the end of 20 years)(Hint: Income = Rev. - Variable cost-Fixed Cost, find annual revenue).

Answer 1

Step-1:Calculation of annual revenue
	Suppose minimum price per ticket is "x"
			Per Unit	Total
	Sales		x	300000x	$ 121.33
	Less:
	Variable cost		0.20x	60000x	$    24.27
	Contribution Margin		0.80x	240000x	$    97.06
	Less:
	Fixed Cost:
	Flight Operations		$       70,00,000
	Ground Costs		$       40,00,000	$          1,10,00,000
	Net annual revenue			240000x-11000000
Step-2:Calculation of present value of annuity of 1
Present value of annuity of 1		=	(1-(1+i)^-n)/i	Where,
		=	(1-(1+0.14)^-20)/0.14	i	14%
		=	6.623130552	n	20
Step-3:Calculation of minimum price per ticket
As per question,
Present value of annual revenue			=	Initial cost of investment
240000x-11000000	*	6.623131	=	$       12,00,00,000
240000x-11000000			=	$    1,81,18,320.19
240000x			=	$    2,91,18,320.19
x			=	$                   121.33
So,
Minimum price per ticket is			$ 121.33