Your firm currently has net working capital of

​$133 comma 000133,000

that it expects to grow at a rate of

66​%

per year forever. You are considering some suggestions that could slow that growth to

33​%

per year. If your discount rate is

1010​%,

how would these changes impact the value of your​ firm?

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Part 1

The value of the firm would

▼

decrease

increase

by

​$enter your response here.

**** ** ​(Select from the​ drop-down menu; round to the nearest​ dollar.)

To determine how the value of the firm would change based on the growth rate of net working capital (NWC), we can use a perpetuity model formula to calculate the present value of the working capital under the two different growth rates.

### Formula for the present value of NWC growth:

\[
PV = \frac{NWC}{r - g}
\]

Where:
- $ PV $ = present value of the firm’s net working capital
- $ NWC $ = current net working capital (initial value)
- $ r $ = discount rate (10%)
- $ g $ = growth rate of net working capital

#### Current Scenario:
- Initial NWC = \$133,000
- Growth rate $ g $ = 6% (0.06)
- Discount rate $ r $ = 10% (0.10)

\[
PV_{\text{current}} = \frac{133,000}{0.10 - 0.06} = \frac{133,000}{0.04} = 3,325,000
\]

#### Proposed Scenario:
- Growth rate $ g $ = 3% (0.03)

\[
PV_{\text{proposed}} = \frac{133,000}{0.10 - 0.03} = \frac{133,000}{0.07} = 1,900,000
\]

### Change in Value:

\[
\text{Change in Value} = PV_{\text{proposed}} - PV_{\text{current}} = 1,900,000 - 3,325,000 = -1,425,000
\]

So, the value of the firm would **decrease** by **\$1,425,000** if the growth rate of net working capital slows to 3%.

### Summary:

- The value of the firm would **decrease** by **\$1,425,000**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does the perpetuity formula apply in other financial valuation scenarios?
2. What factors affect the discount rate in firm valuations?
3. How does the choice of growth rate influence a firm’s future projections?
4. What are alternative methods for valuing a firm's working capital?
5. How can changes in working capital impact overall firm value?

**Tip**: Always ensure your discount rate accurately reflects market conditions to avoid over- or under-estimating value.

Your firm currently has net working capital of $133,000 that it expects to grow at a rate of 6% per year forever. You are considering some suggestions that could slow that growth to 3% per year. If your discount rate is 10%, how would these changes impact the value of your firm?

Analyze how slowing net working capital growth from 6% to 3% affects firm value using the perpetuity model. This example uses a $133,000 initial NWC and a 10% discount rate to show a $1,425,000 decrease in value. Ideal for finance students and professionals.

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