The City Transit Authority (CTA) is trying to decide between railcars manufactured by French Corp and Japan Rail Car. The French Corp cars cost more to buy initially, but they are expected to last for 10 years. The Japan Rail Car cars are cheaper initially, but they will wear out in 6 years. The cash flows related to each of the choices are presented below. If the CTA’s cost of capital is 8 percent, which type of car should the CTA buy? Support your answer.

The Japan Rail Car should be purchased

Explanation:

To find the answer we can use the Net Present Cost. By calculating the total net present value of the total costs involved in both projects, the cheaper alternative can then be chosen.

The cash-flows for both projects are constant so an annuity can be used to calculate them.

Please refer to the annuity table attached.

The French Corp Car

It will cost $275,000 originally and then $10,000 every year after that. The cost of capital is 8%. The goal is to find the present value of all the cost. That can be done by,

=  (275,000) + PV of Annuity of $10,000 for 10 year and cost of capital 8% p.a. (look at the table for the intersection of 10 years and 8%)

= 275,000 + 10,000 (6.710)

= 275,000 + 67,100

= $342,100

The Japan Rail Car

It will cost $195,000 originally and then $15,000 every year after that. The cost of capital is 8%. Using the same method,

=  (195,000) + PV of Annuity of $15,000 for 6 year and cost of capital 8% p.a. (look at the table for the intersection of 6 years and 8%)

= 195,000 + 15,000(4.623)

=195,000 + 69,345

= $264,345

The Japan Rail Car costs less in terms of total cost over its period of operation and so should be the one purchased by the CTA.