Q1 Carrefour Is Expecting Its New Center To Generate The Fol

Q1carrefour Is Expecting Its New Center To Generate the Following Cas

Q1: Carrefour is expecting its new center to generate the following cash flows: The initial investment is $35,000,000. The net operating cash flows are projected as follows: Year 1: $6,000,000; Year 2: $8,000,000; Year 3: $16,000,000; Year 4: $20,000,000; Year 5: $30,000,000.

Determine the payback period for this new center.

Calculate the net present value (NPV) of the project using a cost of capital of 15%. Should the project be accepted based on these calculations?

Paper For Above instruction

Introduction

Investing in new projects involves critical financial analysis to assess their viability and future profitability. Key tools in this assessment include calculating the payback period, which indicates how quickly an initial investment can be recovered, and the net present value (NPV), which measures the value added by the project considering the time value of money. This paper conducts detailed calculations for Carrefour’s proposed new center, evaluating whether it should be undertaken based on its payback period and NPV, using a discount rate of 15%.

Payback Period Calculation

The payback period measures the time it takes for cumulative cash flows from a project to equal the initial investment. Given an initial investment of $35,000,000, and annual net cash flows of $6,000,000, $8,000,000, $16,000,000, $20,000,000, and $30,000,000 over five years, the cumulative cash flows are:

  • Year 1: $6,000,000
  • Year 2: $6,000,000 + $8,000,000 = $14,000,000
  • Year 3: $14,000,000 + $16,000,000 = $30,000,000
  • Year 4: $30,000,000 + $20,000,000 = $50,000,000
  • Year 5: $50,000,000 + $30,000,000 = $80,000,000

At the end of Year 3, the cumulative cash flow is $30,000,000, which is still less than the initial investment. During Year 4, the cash flow is $20,000,000, which surpasses the remaining amount of $5,000,000 ($35,000,000 - $30,000,000).

Calculating the precise point within Year 4:

Remaining amount after Year 3: $5,000,000

Cash flow in Year 4: $20,000,000

Fraction of Year 4 needed: $5,000,000 / $20,000,000 = 0.25

Thus, the payback period = 3 years + 0.25 year = 3.25 years.

Net Present Value (NPV) Calculation

The NPV considers the time value of money, discounting each cash flow at a rate of 15%. The formula for NPV is:

\[

NPV = -Initial\ Investment + \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t}

\]

where \( CF_t \) is the cash flow in year \( t \), and \( r \) is the discount rate (15%).

The calculation for each year's discounted cash flows:

- Year 1: \( \frac{6,000,000}{(1 + 0.15)^1} = \frac{6,000,000}{1.15} \approx 5,217,391 \)

- Year 2: \( \frac{8,000,000}{(1.15)^2} = \frac{8,000,000}{1.3225} \approx 6,048,048 \)

- Year 3: \( \frac{16,000,000}{(1.15)^3} = \frac{16,000,000}{1.5209} \approx 10,522,036 \)

- Year 4: \( \frac{20,000,000}{(1.15)^4} = \frac{20,000,000}{1.7490} \approx 11,431,471 \)

- Year 5: \( \frac{30,000,000}{(1.15)^5} = \frac{30,000,000}{2.0114} \approx 14,911,711 \)

Sum of discounted cash flows:

\[

5,217,391 + 6,048,048 + 10,522,036 + 11,431,471 + 14,911,711 = 48,130,657

\]

Subtracting the initial investment:

\[

NPV = 48,130,657 - 35,000,000 = \boxed{13,130,657}

\]

Since the NPV is positive, the project adds value to Carrefour and should be accepted.

Conclusion

The payback period of approximately 3.25 years indicates that Carrefour will recover its initial investment in just over three years, which is generally considered acceptable depending on the company’s investment criteria. The positive NPV of approximately $13.13 million suggests that the project is financially viable and will generate additional value exceeding the required return of 15%. Therefore, based on both the payback period and NPV calculations, Carrefour should proceed with the investment in the new center.

References

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