Question

A proposed project will cost $1,000 two years from today. Beginning at the end of year five, $300 in annual benefits will be received, continuing until the end of year nine. What is the project's present (year 0) worth at MARR = 5%? A. -$50. B. $111. C. -$94. D. $161. E. none of the above o

Answer 1

To calculate the project's present worth at MARR = 5%, use the formula to find the present value of the future benefits and the present value of the future cost. Then subtract the PV of the cost from the PV of the benefits to find the project's present worth. The present worth at MARR = 5% is $255.15.

Step-by-step explanation:

To calculate the project's present worth at MARR = 5%, we need to find the present value of the future benefits and the present value of the future cost.

The present value of the future benefits can be calculated using the formula:

PV = B * ((1 - (1 + r)^-n) / r)

Where PV is the present value, B is the annual benefit, r is the interest rate, and n is the number of years.

Substituting the values, we get:

PV = $300 * ((1 - (1 + 0.05)^-5) / 0.05)

PV = $1,255.15

The present value of the future cost is simply the cost in year 0, which is $1,000.

The project's present worth is the present value of the benefits minus the present value of the cost:

Present Worth = PV of Benefits - PV of Cost

Present Worth = $1,255.15 - $1,000

Present Worth = $255.15

Therefore, the project's present worth at MARR = 5% is $255.15.

Answer 2

To calculate the present worth of the project, we need to find the present value of the costs and benefits using the given interest rate. The present worth of the project is approximately $907.51.

Step-by-step explanation:

To calculate the present worth of the project, we need to find the present value of the costs and benefits using the given interest rate. The project costs $1,000 two years from today, so we need to find its present value. We can use the formula:

Present Value = Future Value / (1 + Interest Rate)^(Number of years)

Present Value = $1,000 / (1 + 0.05)^2 = $1,000 / 1.1025 ≈ $907.51

The present worth of the project is approximately $907.51.