A project that provides annual cash flows of \$5,000 for 4 years, with a required rate of return of 8\%, has a present value closest to which of the following amounts?

• A. \$16,620
• B. \$18,520
• C. \$13,620
• D. \$20,000

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the problem. The goal is to calculate the present value (PV) of a series of annual cash flows using the formula for the present value of an ordinary annuity. The cash flows are \$5,000 per year for 4 years, and the required rate of return is 8%.
2. Step 2: Recall the formula for the present value of an ordinary annuity: \( PV = C \times \frac{1 - (1 + r)^{-n}}{r} \), where \( C \) is the annual cash flow, \( r \) is the required rate of return (expressed as a decimal), and \( n \) is the number of periods.
3. Step 3: Substitute the given values into the formula: \( C = 5000 \), \( r = 0.08 \), and \( n = 4 \). The formula becomes \( PV = 5000 \times \frac{1 - (1 + 0.08)^{-4}}{0.08} \).
4. Step 4: Calculate the term \( (1 + r)^{-n} \). This involves raising \( (1 + 0.08) \) to the power of \( -4 \). Then subtract this value from 1.
5. Step 5: Divide the result from Step 4 by \( r \) (0.08), and multiply the quotient by \( C \) (5000). This will give the present value of the cash flows. Compare the calculated value to the provided options to determine the closest match.