Question 1171213
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.