Question

3B A railway track will be used for 15 years. During the construction of the railway track line, 05 either type A or type B ties may be used. Type A ties have an installed cost of $6 and a 10- year life; type B will cost $4.50 with a 6-year life. If at the end of 15 years, the ties used have a remaining useful life of at least 4 years they will be used elsewhere for a different project and can fetch a salvage value of $3 each. Any ties that are taken off after the end of their life or if it is very near to the end of its life to be used elsewhere, then, it can be sold for $0.50 each. Give the most cost-effective plan for the 15 year analysis period using NPW method at 8% interest.

Answer 1

The most cost-effective plan for the 15 year analysis period using the NPW method at 8% interest is to use type A ties for the first 10 years and type B ties for the remaining 5 years.

Step-by-step explanation:

The most cost-effective plan for the 15 year analysis period using the NPW (Net Present Worth) method at 8% interest is to use type A ties for the first 10 years and type B ties for the remaining 5 years.

Here's how to calculate the net present worth:

1. Calculate the present worth of the type A ties for the first 10 years. Discount the installation cost of $6 and the salvage value of $3 at 8% for 10 years.
2. Calculate the present worth of the type B ties for the remaining 5 years. Discount the installation cost of $4.50 and the salvage value of $3 at 8% for 5 years.
3. Add the present worth of the type A and type B ties to get the net present worth.

Comparing this plan to other options will help determine if it is the most cost-effective one. Other options could involve using only type A ties, only type B ties, or a combination of both throughout the 15 years.

Answer 2

The most cost-effective plan for the 15-year analysis period can be determined using the NPW method at an 8% interest rate.

Step-by-step explanation:

The most cost-effective plan for the 15-year analysis period can be determined using the Net Present Worth (NPW) method at an 8% interest rate. To calculate the NPW, we need to compare the costs and salvage values of type A and type B ties over the 15-year period.

Let's assume we use type A ties for the first 10 years and type B ties for the remaining 5 years. The initial cost for type A ties would be 10 * $6 = $60, and the initial cost for type B ties would be 5 * $4.50 = $22.50.

At the end of the 15 years, the salvage value for the type A ties would be 4 * $3 = $12, and the salvage value for the type B ties would be 1 * $3 = $3.

To calculate the NPW, we need to discount the future cash flows to present value using the 8% interest rate. The NPW can be calculated as follows:

1. Calculate the present value of the initial costs: $60 / (1 + 0.08)^0 + $22.50 / (1 + 0.08)^10 = $60 + $10.13 = $70.13
2. Calculate the present value of the salvage values: $12 / (1 + 0.08)^15 + $3 / (1 + 0.08)^15 = $4.28 + $1.07 = $5.35
3. Calculate the NPW: NPW = present value of salvage values - present value of initial costs = $5.35 - $70.13 = -$64.78

The negative NPW indicates that this plan is not cost-effective at an 8% interest rate. Therefore, an alternative plan should be considered.