Question

A city is considering building a crafts center. After expressing outcomes in monetary terms, the city determines that the initial cost of the crafts center will be $800,000. Annual operating costs (incurred at the end of years 1, 2, 3) will be $300,000 each year. Annual benefits will be $600,000 at the end of years 1, 2 and 3. All costs and benefits will end after year 3.

​At a discount rate of 8% what is the value of this center? In one sentence: Should it be built, and why?

Answer 1

The net present value of the crafts center is calculated using the NPV formula and the given values. The calculated NPV is negative, indicating that it is not financially viable to build the crafts center.

Step-by-step explanation:

To determine the value of the crafts center, we need to calculate the net present value (NPV) of the project. The NPV formula is:

NPV = -Initial Cost + (Annual Benefits - Annual Costs) / (1 + Discount Rate)^t

Plugging the given values into the formula, we get:

NPV = -800,000 + (600,000 - 300,000) / (1 + 0.08)^1 + (600,000 - 300,000) / (1 + 0.08)^2 + (600,000 - 300,000) / (1 + 0.08)^3

Simplifying the equation, we get:

NPV = -800,000 + 300,000 / 1.08 + 300,000 / 1.08^2 + 300,000 / 1.08^3

Calculating the values, we find:

NPV = -800,000 + 277,777.78 + 256,172.84 + 236,850.05

NPV = -29,199.33

Since the NPV is negative, it indicates that the present value of the costs exceeds the present value of the benefits. Therefore, based on the given information, it is not financially viable to build the crafts center.