To calculate the net present value (NPV) of Project X for Yellow Circle Paint, we follow these steps:

1. Calculate the net cash flows for each year, including the initial investment, operating cash flows, changes in net working capital, and the terminal value from equipment sale.

2. Discount these cash flows at the project's cost of capital (9.45%).

Step-by-Step NPV Calculation

1. Initial Investment at Time 0:

• Equipment cost: -$318,000
• Initial change in net working capital: -$14,000
• Total cash flow at Time 0: -318,000 - 14,000 = -$332,000

2. Year 1 Cash Flow:

• Operating cash flow: $183,000
• Change in net working capital: -$3,000
• Total cash flow for Year 1: 183,000 - (-3,000) = 183,000 + 3,000 = $186,000

3. Year 2 Cash Flow:

• Operating cash flow: -$31,000
• Change in net working capital: -$7,000
• Total cash flow for Year 2: -31,000 - (-7,000) = -31,000 + 7,000 = -$24,000

4. Year 3 Cash Flow:

• Operating cash flow: $174,000
• Change in net working capital: -$4,000
• After-tax cash flow from sale of equipment: $52,000
• Total cash flow for Year 3: 174,000 - (-4,000) + 52,000 = 174,000 + 4,000 + 52,000 = $230,000

5. Calculate Present Value of Each Cash Flow:

• $NPV = \frac{C_0}{(1 + r)^0} + \frac{C_1}{(1 + r)^1} + \frac{C_2}{(1 + r)^2} + \frac{C_3}{(1 + r)^3}$
• $r = 0.0945$ (cost of capital)

Year 0: $PV_{0} = -332,000$

Year 1: $PV_{1} = \frac{186,000}{(1 + 0.0945)^1} = \frac{186,000}{1.0945} \approx 169,993.15$

Year 2: $PV_{2} = \frac{-24,000}{(1 + 0.0945)^2} = \frac{-24,000}{1.198} \approx -20,034.22$

Year 3: $PV_{3} = \frac{230,000}{(1 + 0.0945)^3} = \frac{230,000}{1.3103} \approx 175,499.24$

6. Sum All Present Values to Find NPV:

$NPV = PV_{0} + PV_{1} + PV_{2} + PV_{3}$ $NPV = -332,000 + 169,993.15 - 20,034.22 + 175,499.24$ $NPV \approx -6,541.83$

Conclusion:

The net present value (NPV) of Project X is approximately -$6,541.83. Since the NPV is negative, it suggests that the project would decrease the value of Yellow Circle Paint, and it may not be a profitable investment under the given assumptions.

Would you like more details or have any questions?

Related Questions:

1. How would the NPV change if the cost of capital increased to 12%?
2. What is the effect of removing the loan and financing the project with internal funds?
3. How does a change in the after-tax cash flow from equipment sale affect the NPV?
4. What is the impact of changes in net working capital if they were delayed by one year?
5. How sensitive is the NPV calculation to changes in the project's operating cash flows?

Tip:

Always consider the sensitivity analysis for critical assumptions like the cost of capital and cash flow estimates to better understand project risks and potential returns.