To compute the Net Present Value (NPV) for Project "A," I will walk through the process step-by-step.

Formula for NPV:

$NPV = \sum_{t=0}^n \frac{CF_t}{(1 + r)^t}$ Where:

• $CF_t$ = Cash flow at time $t$
• $r$ = Discount rate (9% or 0.09 here)
• $t$ = Time period (in years)

Step-by-step Calculation:

Cash Flows for Project "A"

$\text{At } t = 0: CF_0 = -20,000$ $\text{At } t = 1: CF_1 = 4,200$ $\text{At } t = 2: CF_2 = 6,000$ $\text{At } t = 3: CF_3 = 8,000$ $\text{At } t = 4: CF_4 = 11,000$

Discount Rate:

$r = 0.09$

Step 1: Calculate Present Value for Each Cash Flow

1. At $t = 0$: $\frac{CF_0}{(1 + r)^0} = \frac{-20,000}{1} = -20,000$

2. At $t = 1$: $\frac{CF_1}{(1 + r)^1} = \frac{4,200}{(1.09)^1} = \frac{4,200}{1.09} \approx 3,853.21$

3. At $t = 2$: $\frac{CF_2}{(1 + r)^2} = \frac{6,000}{(1.09)^2} = \frac{6,000}{1.1881} \approx 5,051.30$

4. At $t = 3$: $\frac{CF_3}{(1 + r)^3} = \frac{8,000}{(1.09)^3} = \frac{8,000}{1.29503} \approx 6,175.51$

5. At $t = 4$: $\frac{CF_4}{(1 + r)^4} = \frac{11,000}{(1.09)^4} = \frac{11,000}{1.41158} \approx 7,791.51$

Step 2: Sum All Present Values

$NPV = -20,000 + 3,853.21 + 5,051.30 + 6,175.51 + 7,791.51$

$NPV \approx 2,871.53$

Final Answer:

The Net Present Value (NPV) for Project "A" is approximately $2,871.53.

Let me know if you'd like to see the NPV calculated for Project "B" or need further details!

Questions:

1. What is the purpose of NPV in project evaluation?
2. Why is discounting cash flows necessary when calculating NPV?
3. How does the discount rate impact the NPV value?
4. Can an NPV be negative, and what does it indicate?
5. How is the decision rule for NPV applied in capital budgeting?

Tip:

Always compare NPVs of projects to choose the one with the highest value, provided the NPV is positive.