Debby’s Dance Studios is considering the purchase of new sound equipment that will enhance the popularity of its aerobics dancing. The equipment will cost $24,300. Debby is not sure how many members the new equipment will attract, but she estimates that her increased annual cash flows for each of the next five years will have the following probability distribution. Debby’s cost of capital is 10 percent. Cash Flow	Probability
$ 3,980	0.4
5,280	0.2
8,140	0.2
10,600	0.2 What is the expected net present value?

To calculate the expected net present value (NPV) of Debby’s Dance Studios' new sound equipment investment, we need to:

1. **Calculate the expected cash flow** for each year.
2. **Calculate the present value** of these expected cash flows.
3. **Subtract the initial cost** from the total present value to determine the NPV.

### Step 1: Expected Annual Cash Flow
The expected cash flow is computed as the weighted average of all possible cash flows using their respective probabilities.

\[
\text{Expected Cash Flow} = (3,980 \times 0.4) + (5,280 \times 0.2) + (8,140 \times 0.2) + (10,600 \times 0.2)
\]

Let's calculate this.

\[
\text{Expected Cash Flow} = 3,980 \times 0.4 + 5,280 \times 0.2 + 8,140 \times 0.2 + 10,600 \times 0.2
\]

### Step 2: Present Value of Expected Cash Flows
The present value of each expected cash flow is calculated using the formula:

\[
\text{PV} = \frac{\text{Expected Cash Flow}}{(1 + r)^t}
\]

Where:
- $ r = 10\% = 0.10 $ (cost of capital)
- $ t = \text{year number (1, 2, 3, 4, or 5)} $

We sum the present values for all 5 years.

### Step 3: Net Present Value (NPV)
The net present value is the sum of the present values minus the initial investment of $24,300.

\[
\text{NPV} = \sum \text{PV} - 24,300
\]

Now, let's calculate the NPV.The expected net present value (NPV) of the new sound equipment for Debby's Dance Studios is approximately **-54.13**. This slightly negative NPV suggests that the investment may not generate enough cash flow to cover the initial cost, considering the studio's 10% cost of capital.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How would a change in the cost of capital affect the NPV?
2. What if the probability of attracting more members increases? How does that impact NPV?
3. How would a different number of years for cash flows impact the result?
4. What does a negative NPV indicate for investment decisions?
5. How would an increase in initial cost affect this analysis?

**Tip:** Always compare NPV to other investment alternatives to determine the best use of capital.

Debby’s Dance Studios is considering the purchase of new sound equipment that will enhance the popularity of its aerobics dancing. The equipment will cost $24,300. Debby is not sure how many members the new equipment will attract, but she estimates that her increased annual cash flows for each of the next five years will have the following probability distribution. Debby’s cost of capital is 10 percent. Cash Flow Probability: $3,980 - 0.4, $5,280 - 0.2, $8,140 - 0.2, $10,600 - 0.2. What is the expected net present value?

Explore the step-by-step solution for calculating the expected net present value (NPV) of Debby’s Dance Studios' sound equipment purchase. Learn how to apply probability-weighted cash flows and discounted cash flow analysis with a 10% cost of capital. Suitable for business and finance students.

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