Explanation

To solve this problem, we need to find the present value of $50,000 at the end of Year 10, discounted back to the end of Year 5.

Step 1: Understand the timeline

• Cash flow: $50,000 at Year 10
• We need PV at Year 5
• Discount rate: 5%

Step 2: Calculate the number of periods From Year 5 to Year 10 is 5 years (10 - 5 = 5 periods)

Step 3: Apply the present value formula The formula for present value is: $PV = \frac{FV}{(1 + r)^n}$ Where:

• FV = Future Value = $50,000
• r = discount rate = 5% = 0.05
• n = number of periods = 5

Step 4: Calculate $PV = \frac{50,000}{(1 + 0.05)^5}$ $PV = \frac{50,000}{(1.05)^5}$ $PV = \frac{50,000}{1.2762815625}$ $PV = 39,176.31$

Step 5: Compare with options The calculated value of $39,176.31 is closest to option C: $39,176.

Why not the other options?

• Option A ($30,696): This would be the present value if we discounted $50,000 for 10 years (50,000/(1.05)^10 = 30,696), not for 5 years.
• Option B ($37,311): This is incorrect and doesn't match the calculation.
• Option C ($39,176): Correct, matches our calculation.

Key Concept: This question tests understanding of present value calculations and the ability to discount cash flows to different points in time.