Suppose your company needs $514 million to build a new assembly line. Your target debt-equity ratio is 0.84. The flotation cost of new equity is 9.5 percent, but the flotation cost... Suppose your company needs $514 million to build a new assembly line. Your target debt-equity ratio is 0.84. The flotation cost of new equity is 9.5 percent, but the flotation cost for debt is only 2.5 percent. What is the true cost of building the new assembly line after taking flotation costs into account? Read more

Steps to Solve

1. Identify Given Values

We have the following values:

• Total cost to build = $514 \text{ million}$
• Debt-equity ratio ($D/E$) = $0.84$
• Flotation cost for new equity = $9.5%$ (or $0.095$)
• Flotation cost for debt = $2.5%$ (or $0.025$)

2. Calculate Proportions of Debt and Equity

Using the debt-equity ratio to find the proportions of debt ($D$) and equity ($E$):

Let $E = 1$

• Then, $D = 0.84 \times E = 0.84 \times 1 = 0.84$
• Total value ($V$) = $D + E = 0.84 + 1 = 1.84$

3. Calculate Weights of Debt and Equity

Next, we calculate the weights:

• Weight of equity, $w_e = \frac{E}{V} = \frac{1}{1.84}$
• Weight of debt, $w_d = \frac{D}{V} = \frac{0.84}{1.84}$

4. Calculate Effective Flotation Costs

The effective flotation costs are then calculated as follows:

• Effective flotation cost for equity = $w_e \cdot \text{flotation cost for new equity} = \frac{1}{1.84} \cdot 0.095$
• Effective flotation cost for debt = $w_d \cdot \text{flotation cost for debt} = \frac{0.84}{1.84} \cdot 0.025$

5. Calculate Total Flotation Costs

Now, sum up effective flotation costs to find total flotation cost $F_t$:

$$ F_t = \text{Effective flotation cost for equity} + \text{Effective flotation cost for debt} $$

6. Find True Cost After Flotation Costs

Finally, the true cost of building the assembly line after accounting for flotation costs is given by:

$$ \text{True cost} = \text{Total cost} + F_t $$

7. Final Calculation

Now, substituting the values and calculating each step to get the final true cost.