Calculate the total initial investment.

The initial investment includes the cost of the capital project and the working capital.

$$\text{Initial Investment} = \text{Cost of Capital Project} + \text{Working Capital}$$ $$\text{Initial Investment} = \text{N}100,000 + \text{N}10,000 = \text{N}110,000$$

We will subtract the annual cash flows from the initial investment until the investment is fully recovered.

Year	Item	Cash Flow (N)	Cumulative Cash Flow (N)
0	Initial Outlay	(110,000)	(110,000)
1	Cash Flow Year 1	40,000	(110,000) + 40,000 = (70,000)
2	Cash Flow Year 2	50,000	(70,000) + 50,000 = (20,000)
3	Cash Flow Year 3	60,000	(20,000) + 60,000 = 40,000
4	Cash Flow Year 4	10,000	40,000 + 10,000 = 50,000

The initial investment of N110,000 is not fully recovered by the end of Year 2, as the cumulative cash flow is still (N20,000). By the end of Year 3, the cumulative cash flow becomes positive (N40,000), meaning the payback period falls within Year 3.

To find the exact payback period, we use the formula:

$$\text{Payback Period} = \text{Last year with negative cumulative cash flow} + \frac{\text{Amount still needed}}{\text{Cash flow in the next year}}$$ $$\text{Payback Period} = 2 \text{ years} + \frac{\text{N}20,000}{\text{N}60,000}$$ $$\text{Payback Period} = 2 \text{ years} + \frac{1}{3} \text{ year}$$ $$\text{Payback Period} = 2 \text{ years} + 0.3333 \text{ years}$$ $$\text{Payback Period} = 2.3333 \text{ years}$$

To express the fractional part in months:

$$0.3333 \text{ years} \times 12 \text{ months/year} \approx 4 \text{ months}$$

Therefore, the Payback Period is 2 years and 4 months.

The Payback Period (PBP) for this project is $\text{2 years, 4 months}$.