Table of contents

1. Introduction to Accounting1h 21m
2. Transaction Analysis1h 13m
3. Accrual Accounting Concepts2h 38m
4. Merchandising Operations2h 30m
5. Inventory1h 55m
6. Internal Controls and Reporting Cash1h 16m
7. Receivables and Investments3h 8m
8. Long Lived Assets5h 1m
9. Current Liabilities2h 19m
10. Time Value of Money1h 23m
- Time Value of Money Equations
  35m
- Using Time Value of Money Tables
  47m
11. Long Term Liabilities2h 45m
12. Stockholders' Equity2h 15m
13. Statement of Cash Flows2h 24m
14. Financial Statement Analysis5h 25m
15. GAAP vs IFRS56m

10. Time Value of Money

Time Value of Money Equations

Financial Accounting

10. Time Value of Money

Time Value of Money Equations

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Multiple Choice

What is the present value (PV) of the following set of cash flows, discounted at an annual rate of 8\%? \[\begin{align}\text{Year 1:} & \quad \$1,000 \\\text{Year 2:} & \quad \$1,500 \\\text{Year 3:} & \quad \$2,000 \end{align}\]Choose the closest answer.

$4,000

$4,200

$3,870

$4,011

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Verified step by step guidance

Step 1: Understand the concept of Present Value (PV). PV is the current worth of a future sum of money or stream of cash flows given a specified rate of return (discount rate). The formula for PV of a single cash flow is: $ PV = \frac{FV}{(1 + r)^n} $, where $ FV $ is the future value, $ r $ is the discount rate, and $ n $ is the number of periods.

Step 2: Break down the problem into individual cash flows for each year. For Year 1, the cash flow is $ \$1,000 $, for Year 2, it is $ \$1,500 $, and for Year 3, it is $ \$2,000 $. Each cash flow will be discounted separately using the formula for PV.

Step 3: Apply the PV formula to each cash flow. For Year 1, calculate $ PV_1 = \frac{1000}{(1 + 0.08)^1} $. For Year 2, calculate $ PV_2 = \frac{1500}{(1 + 0.08)^2} $. For Year 3, calculate $ PV_3 = \frac{2000}{(1 + 0.08)^3} $.

Step 4: Sum up the present values of all individual cash flows to find the total present value. The formula is: $ PV_{total} = PV_1 + PV_2 + PV_3 $.

Step 5: Compare the calculated total present value to the given answer choices and select the closest value. The correct answer is $ \$4,011 $, which is closest to the calculated total PV.