Answer: The Japan Rail Car should be purchased
Step-by-step 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.