Question

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 $30 million per year. Plane B has a life of 10 years, will cost $132 million, and will produce net cash flows of $25 million per year. Shao plans to serve the route for only 10 years. Inflation in operating costs, airplane costs, and fares is expected to be zero, and the company’s cost of capital is 12%. By how much would the value of the company increase if it accepted the better project (plane)? What is the equivalent annual annuity for each plane?

Answer 1

Plane A will have to be bought twice as its life is only 5 years, hence cash flows are calculated & used accordingly

Plane A
Discount rate	12.000%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-100	30	30	30	30	-70	30	30	30	30	30
Discounting factor	1.000	1.120	1.254	1.405	1.574	1.762	1.974	2.211	2.476	2.773	3.106
Discounted cash flows project	-100.000	26.786	23.916	21.353	19.066	-39.720	15.199	13.570	12.116	10.818	9.659
NPV = Sum of discounted cash flows
NPV Plane B =	12.76
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Plane B
Discount rate	12.000%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-132	25	25	25	25	25	25	25	25	25	25
Discounting factor	1.000	1.120	1.254	1.405	1.574	1.762	1.974	2.211	2.476	2.773	3.106
Discounted cash flows project	-132.000	22.321	19.930	17.795	15.888	14.186	12.666	11.309	10.097	9.015	8.049
NPV = Sum of discounted cash flows
NPV Plane B =	9.26
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Plane A is better and firm value will increase by NPV = 12.76 million

Equvalent annuity(EAA) plane A=	1.77
Required rate =	12.000%
Year	0	1	2	3	4	5
Cash flow stream	1.77	1.77	1.77	1.77	1.77	1.77
Discounting factor	1.000	1.120	1.254	1.405	1.574	1.762
Discounted cash flows project	1.768	1.578	1.409	1.258	1.123	1.003
Sum of discounted future cashflows =	8.14
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Equvalent annuity(EAA) plane B=	1.39
Required rate =	12.000%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	1.39	1.39	1.39	1.39	1.39	1.39	1.39	1.39	1.39	1.39	1.39
Discounting factor	1.000	1.120	1.254	1.405	1.574	1.762	1.974	2.211	2.476	2.773	3.106
Discounted cash flows project	1.392	1.243	1.110	0.991	0.885	0.790	0.705	0.630	0.562	0.502	0.448
Sum of discounted future cashflows =	9.26
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor