Franklin Industries has a current net working capital of $2.5 million.It expects that this will grow at a rate of 3.5% annually forever.If it could slow that growth to 3% per year,how would that affect the value of the firm,given that it has a cost of capital of 11%?
A)a decrease of $2.22 million
B)an increase of $12,500
C)an increase of $0.78 million
D)an increase of $2.08 million
E)an increase of $3.14 million

Question

Quizplus · Accepted Answer

The value of the change in net working capital can be calculated using the formula for the value of a perpetuity: Value = Cash Flow / (Discount Rate - Growth Rate). The difference in value due to slowing the growth rate from 3.5% to 3% is calculated as follows:Initial growth scenario: Value1 = $2.5 million * 0.035 / (0.11 - 0.035) = $0.875 million / 0.075 = $11.67 million.New growth scenario: Value2 = $2.5 million * 0.03 / (0.11 - 0.03) = $0.75 million / 0.08 = $9.375 million.The decrease in the required growth in net working capital (from 3.5% to 3%) increases the firm's value because less cash is needed for working capital in the future, thus freeing up more cash for distribution to shareholders or for investment in other value-adding projects. The difference in value between the two scenarios is Value2 - Value1 = $9.375 million - $11.67 million = -$2.295 million. However, since the question asks how slowing the growth affects the value, we're looking for a positive change in value due to the reduction in growth rate, indicating an error in the calculation direction. Correcting the approach:The correct calculation should focus on the savings or the reduction in the annual growth outlay due to slowing the growth rate, not directly comparing the total values calculated from the perpetuity formula in a reversed manner. The correct approach involves calculating the difference in the annual growth outlays and then determining the present value of this difference as a perpetuity.Correct calculation for the difference in perpetuity value due to slowing growth:Difference in annual growth outlay = $2.5 million * (0.035 - 0.03) = $0.125 million.Value of this difference as a perpetuity at a lower growth rate: Value = $0.125 million / (0.11 - 0.03) = $0.125 million / 0.08 = $1.5625 million.This calculation aims to find the impact on the firm's value by slowing the growth rate, which should result in a positive value change, indicating an increase in firm value due to reduced needs for financing working capital growth. The correct answer should reflect the increase in value due to the efficiency in managing working capital growth, but the provided calculations and options do not directly align with the standard financial formulas and principles as intended in the explanation. Therefore, the explanation aimed to correct the approach but inadvertently highlighted a calculation mismatch with the provided options. The principle stands that slowing the growth rate of net working capital, all else equal, would increase the firm's value by reducing the cash tied up in working capital, but the specific option that matches this explanation was not accurately calculated based on the standard perpetuity formula. The intention was to illustrate the positive financial impact of more efficient working capital growth management.

Franklin Industries Has a Current Net Working Capital of $2