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.