Question 1171213: Cricket World Cup (CWC) is considering a project proposal which requires an initial investment of $72,625 and it is expected to have net cash flows of $15,000 per year for 8 years. The firm cash flows are discounted at a rate of 12 percent.
a. What is the project’s Net Present Value (NPV)? (Rounded to 2 decimal places)
b. What is the project’s discounted payback period? (Rounded to 2 decimal places)
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Absolutely! Let's calculate the NPV and discounted payback period for the CWC project proposal.
**a) Net Present Value (NPV)**
To find the NPV, we need to discount each year's cash flow back to its present value and then sum them up, subtracting the initial investment.
* **Year 0 (Initial Investment):** -$72,625
* **Years 1-8 (Annual Cash Flows):** $15,000 per year
We use the present value formula: PV = CF / (1 + r)^n
Where:
* PV = Present Value
* CF = Cash Flow
* r = Discount Rate (12% or 0.12)
* n = Year
Let's do the calculations:
* **Year 1:** $15,000 / (1.12)^1 = $13,392.86
* **Year 2:** $15,000 / (1.12)^2 = $11,957.91
* **Year 3:** $15,000 / (1.12)^3 = $10,676.71
* **Year 4:** $15,000 / (1.12)^4 = $9,532.78
* **Year 5:** $15,000 / (1.12)^5 = $8,511.41
* **Year 6:** $15,000 / (1.12)^6 = $7,599.47
* **Year 7:** $15,000 / (1.12)^7 = $6,785.24
* **Year 8:** $15,000 / (1.12)^8 = $6,058.25
Now, sum these present values and subtract the initial investment:
NPV = -$72,625 + $13,392.86 + $11,957.91 + $10,676.71 + $9,532.78 + $8,511.41 + $7,599.47 + $6,785.24 + $6,058.25 = $1,889.63
Therefore, the NPV is approximately $1,889.63.
**b) Discounted Payback Period**
The discounted payback period is the time it takes for the discounted cash flows to recover the initial investment.
1. **Year 0:** -$72,625
2. **Year 1:** -$72,625 + $13,392.86 = -$59,232.14
3. **Year 2:** -$59,232.14 + $11,957.91 = -$47,274.23
4. **Year 3:** -$47,274.23 + $10,676.71 = -$36,597.52
5. **Year 4:** -$36,597.52 + $9,532.78 = -$27,064.74
6. **Year 5:** -$27,064.74 + $8,511.41 = -$18,553.33
7. **Year 6:** -$18,553.33 + $7,599.47 = -$10,953.86
8. **Year 7:** -$10,953.86 + $6,785.24 = -$4,168.62
9. **Year 8:** -$4,168.62 + $6,058.25 = $1,889.63
From the above calculations, we see that the discounted payback occurs in year 8.
Therefore:
* **a) NPV:** $1,889.63
* **b) Discounted Payback Period:** 8 years.
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