Question

Gainesville Bus Lines (GBL) is considering two alternative buses to transport people from the commuter lot to the main campus at Midwest State University. This bus service will be provided to students at no cost to them, so this investment will have no incoming revenue stream. Bus S has an initial cost of $50,000 and will have annual operating costs of $25,000 per year for three years. Bus L has an initial cost $75,000 and will have annual operating costs of $23,000 per year for six years. The choice of whether to invest in Bus S or Bus L is a mutually exclusive investment decision – only one bus will be purchased. Inflation is not expected to affect costs. Assume that GBL’s cost of capital is 15 percent.Now, assume that at the end of the useful life of each bus that Gainesville Bus Lines (GBL) will invest in a new bus with identical characteristics. I.e., GBL could purchase Bus S today and it would then buy a new, identical version of Bus S every three years. GBL could purchase Bus L today and it would then buy a new, identical version of Bus L every six years.

4) Calculate the “equivalent annual cost” of operating Bus S. In your calculation, include the annual payment (PMT) value, treating the initial cost of Bus S as an annual annuity, plus Bus S’s annual operating cost.

5) Calculate the “equivalent annual cost” of operating Bus L. In your calculation, include the annual payment (PMT) value, treating the initial cost of Bus L as an annual annuity, plus Bus L’s annual operating cost.

Answer 1

4) Equivalent Annual Cost of Operating Bus S:

Annuity factor=[1-1/(1+r)^t] /r where r=Cost of Capital and t= no.of years

So, Annuity factor for Bus S=[1-1/(1+0.15)³]/0.15

= 2.2833

Equivalent Annual Cost = (Initial cost/ Annuity factor)+ Annual Operating Expenses

= (50000/2.2833)+25000 = 21898.13+25000= $ 46898.13.

So EAC of Bus S is $ 46,898.13.

5)

Equivalent Annual Cost of Operating Bus L:

Annuity factor=[1-1/(1+r)^t] /r where r=Cost of Capital and t= no.of years

So, Annuity factor for Bus L =[1-1/(1+0.15)⁶]/0.15

= 3.7845

Equivalent Annual Cost = (Initial cost/ Annuity factor)+ Annual Operating Expenses

= (75000/3.7845)+23000 = 19817.68+25000= $ 42,817.68

So EAC of Bus L is $ 42,817.68.

Decision:- Since the decision is mutually exclusive, investment should be made in Bus L as the EAC is lower than Bus S.

Bus L has an EAC of $ 42,817.68 as compared to EAC of Bus S of $ 46,898.13. Investing in Bus L will save cost by $ 4080.45.