The board of education for the Central Catskill School District is considering the acquisition of several minibuses for use in transporting students to school. Five of the school district's bus routes are underpopulated, with the result that the full$-$size buses on those routes are not fully utilized. After a careful study, the board has decided that it is not feasible to consolidate these routes into fewer routes served by full$-$size buses. The area in which the students live is too large for that approach, since some students' bus ride to school would exceed the state maximum of $60$ minutes.

The plan under consideration by the board is to replace five full$-$size buses with eight minibuses, each of which would cover a much shorter route than a full$-$size bus. The bus drivers in this rural school district are part$-$time employees whose compensation costs the school district $$23,000$ per year for each driver. In addition to the drivers' compensation, the annual costs of operating and maintaining a full$-$size bus amount to $$70,000.$ In contrast, the board projects that a minibus will cost only $$30,000$ annually to operate and maintain. A minibus driver earns the same wages as a full$-$size bus driver. The school district controller has estimated that it will cost the district $$22,987,$ initially, to redesign its bus routes, inform the public, install caution signs in certain hazardous locations, and retrain its drivers.

A minibus costs $$37,000,$ whereas a full$-$size bus costs $$130,000.$ The school district uses straight$-$line depreciation for all of its long$-$lived assets. The board has two options regarding the five full$-$size buses. First, the buses could be sold now for $$19,000$ each.

Second, the buses could be kept in reserve to use for field trips and out$-$of$-$town athletic events and to use as backup vehicles when buses break down. Currently, the board charters buses from a private company for these purposes. The annual cost of chartering buse kept ins see. The ive hesite dises have six Years of smited themising ee be gula scheduler year or ave uses

buses. The useful life of a new minibus is projected to be six years also.

Central Catskill School District uses a hurdle rate of $14$ percent on all capital projects.

Use Appendix A for your reference. $($Use appropriate factors$)$ from the tables provided.$)$

$3-$a$.$ Suppose the board of education chooses to buy the minibuses. Calculate the net present value of the following options:

$3-$b$.$ Should the full$-$size buses be sold now or kept in reserve?

$4-$a$.$ From your answer to requirement $(3),$ you know the best option for the board to choose regarding the full$-$size buses if the minibuses are purchased. Now you can ignore the other option. Compute the net$-$present$-$value of purchasing the minibuses.

$4-$b$.$ Should the minibuses be purchased?

$5.$ Compute the internal rate of return on the proposed minibus acquisition.