Using a 10% discount rate, should the city proceed with the building addition now or wait four years?

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Multiple Choice

Using a 10% discount rate, should the city proceed with the building addition now or wait four years?

Think about the time value of money in capital budgeting. A 10% discount rate means future cash flows are worth less in today’s terms, and the farther in the future they occur, the smaller their present value becomes. If the city waits four years, any benefits (or avoided costs) from the building addition that occur then would be worth only about 1/1.1^4 of their nominal amount today. That’s roughly 0.68, meaning future gains are discounted to about 68 cents for every dollar earned four years from now. By contrast, proceeding now starts capturing benefits sooner and avoids the additional costs and uncertainty of waiting. Without a specific set of numbers, the discounting principle alone shows that waiting four years reduces the present value of the project, so acting now yields a higher present value. Therefore, proceed with the addition now.

Think about the time value of money in capital budgeting. A 10% discount rate means future cash flows are worth less in today’s terms, and the farther in the future they occur, the smaller their present value becomes.

If the city waits four years, any benefits (or avoided costs) from the building addition that occur then would be worth only about 1/1.1^4 of their nominal amount today. That’s roughly 0.68, meaning future gains are discounted to about 68 cents for every dollar earned four years from now. By contrast, proceeding now starts capturing benefits sooner and avoids the additional costs and uncertainty of waiting.

Without a specific set of numbers, the discounting principle alone shows that waiting four years reduces the present value of the project, so acting now yields a higher present value. Therefore, proceed with the addition now.

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