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 $29 million per year. Plane B has a life of 10 years, will cost $132 million and will produce net cash flows of $24 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 8%.

1. By how much would the value of the company increase if it accepted the better project (plane)? Enter your answer in millions. For example, an answer of $1.23 million should be entered as 1.23, not 1,230,000. Do not round intermediate calculations. Round your answer to two decimal places.

2. What is the equivalent annual annuity for each plane? Enter your answers in millions. For example, an answer of $1.23 million should be entered as 1.23, not 1,230,000. Do not round intermediate calculations. Round your answers to two decimal places.

   Plane A:

   Plane B:

Answer 1

a )For plane A , the cash inflows are shown below,

	Year	Cash Inflow (CF)	PV factor =    (1 + r)^t	PV of cash inflow       =   CF/ (1 + r)^t
	1	29	1.08	26.85185185
	2	29	1.1664	24.86282579
	3	29	1.259712	23.02113499
	4	29	1.36048896	21.31586573
	5	29	1.469328077	19.73691271
Total				115.7885911

NPV for plane A = Cash inflow - cash outflow= 115.78 - 100 =15.78 mil $

	Year	Cash Inflow (CF)	PV factor =    (1 + r)^t	PV of cash inflow       = CF/ (1 + r)^t
	1	24	1.08	22.22222222
	2	24	1.1664	20.57613169
	3	24	1.259712	19.05197378
	4	24	1.36048896	17.64071647
	5	24	1.469328077	16.33399673
	6	24	1.586874323	15.12407105
	7	24	1.713824269	14.00376949
	8	24	1.85093021	12.96645323
	9	24	1.999004627	12.00597521
	10	24	2.158924997	11.11664371
Total				161.0419536

NPV for plane B = Cash inflow - cash outflow= 161.04 - 132 =29.04 mil $

According to NPV ,the better project would be plane B and the value of the company would increase by 29.04 mil $

b) The formula for Equivalent annual annuity,

EAA = [r * NPV] / [ 1- (1+r)-n ] ------- r = rate per period, n= number of periods

Hence for Plane A , EAA = ( 0.08 * 15.78) / ( 1- 1.08-5) = 3.7768 or 3.78 mil $ ( rounding to 2 decimal)

Hence for Plane B , EAA = ( 0.08 * 29.04) / ( 1- 1.08-10​​​​) = 4.3278 or 4.33 mil $ (rounding to 2 decimal)