Practice Problem – NPV

Practice Question

Intro to Finance
Capital Budgeting
NPV
Short Answer

Suppose a company has an investment that requires an after-tax incremental cash outlay of \$12,000 today. It estimates that the expected future after-tax cash flows associated with this investment are \$5,000 in years 1 and 2, and \$8,000 in year 3. Using a 15% discount rate, determine the project’s NPV.

Answer +
Correct Answer: \$1,388.59
Explanation +

To determine the Net Present Value (NPV) of the project, we follow these steps:

Step 1: Define Variables

  • Initial investment (\(C_0\)): \$12,000
  • Cash flows:
    • Year 1: \$5,000
    • Year 2: \$5,000
    • Year 3: \$8,000
  • Discount rate (\(r\)): 15%

Step 2: NPV Formula

\[ NPV = \sum \frac{CF_t}{(1 + r)^t} - C_0 \]

Step 3: Calculate Present Value of Each Cash Flow

  • Year 1: \( \frac{5,000}{(1 + 0.15)^1} = \frac{5,000}{1.15} = 4347.83 \)
  • Year 2: \( \frac{5,000}{(1 + 0.15)^2} = \frac{5,000}{1.3225} = 3780.49 \)
  • Year 3: \( \frac{8,000}{(1 + 0.15)^3} = \frac{8,000}{1.520875} = 5260.27 \)

Step 4: Sum of Present Values

\[ PV = 4347.83 + 3780.49 + 5260.27 = 13,388.59 \]

Step 5: Subtract Initial Investment

\[ NPV = 13,388.59 - 12,000 = 1,388.59 \]

Final Answer

The project's Net Present Value is \$1,388.59.