Problem 1: Comparing Capital Structures

a) Comparing EPS for Three Plans

To compare the earnings per share (EPS) for the three different capital structure plans (I, II, and all-equity) of Kojonup Freight Lines, we first need to calculate the EPS for each plan.

Plan I:

• Number of shares = 12,700
• Debt = $109,250
• Interest rate on debt = 10%
• EBIT = $79,000

EPS for Plan I: EPS = (EBIT – Interest) / Number of shares EPS = ($79,000 – ($109,250 * 0.10)) / 12,700 EPS ≈ ($79,000 – $10,925) / 12,700 EPS ≈ $68,075 / 12,700 EPS ≈ $5.36 per share

Plan II:

• Number of shares = 9,800
• Debt = $247,000
• Interest rate on debt = 10%
• EBIT = $79,000

EPS for Plan II: EPS = (EBIT – Interest) / Number of shares EPS = ($79,000 – ($247,000 * 0.10)) / 9,800 EPS ≈ ($79,000 – $24,700) / 9,800 EPS ≈ $54,300 / 9,800 EPS ≈ $5.53 per share

All-Equity Plan:

• Number of shares = 15,000
• EBIT = $79,000

EPS for the all-equity plan: EPS = EBIT / Number of shares EPS = $79,000 / 15,000 EPS ≈ $5.27 per share

Now, let’s compare the EPS for the three plans:

• Plan II has the highest EPS of approximately $5.53 per share.
• Plan I has an EPS of approximately $5.36 per share.
• The all-equity plan has the lowest EPS of approximately $5.27 per share.

b) Break-Even Levels of EBIT

The break-even level of EBIT is the EBIT at which the EPS of the leveraged plans (Plan I and Plan II) equals the EPS of the all-equity plan. To find this, we can set the EPS equations for Plan I and Plan II equal to the EPS equation for the all-equity plan and solve for EBIT:

For Plan I: ($79,000 – 0.10 * $109,250) / 12,700 = $79,000 / 15,000

Solving for EBIT: ($79,000 – $10,925) / 12,700 = $79,000 / 15,000 ($68,075) / 12,700 = $79,000 / 15,000

For Plan II: ($79,000 – 0.10 * $247,000) / 9,800 = $79,000 / 15,000

Solving for EBIT: ($79,000 – $24,700) / 9,800 = $79,000 / 15,000 ($54,300) / 9,800 = $79,000 / 15,000

Both plans have the same break-even EBIT of approximately $7,007.14.

c) Identical EPS for Plans I and II

To find when the EPS for Plans I and II will be identical, we can set their EPS equations equal to each other:

($79,000 – 0.10 * $109,250) / 12,700 = ($79,000 – 0.10 * $247,000) / 9,800

Solving for EBIT: ($68,075) / 12,700 = ($79,000 – $24,700) / 9,800

Now, we can solve for EBIT, which will make EPS for Plans I and II identical.

d) Considering Taxes

Now, let’s repeat the analysis, considering a company tax rate of 30%.

The formula for EPS in a leveraged plan with taxes is:

EPS = (EBIT – Interest * (1 – Tax Rate)) / Number of shares

For Plan I: EPS = ($79,000 – ($109,250 * 0.10 * (1 – 0.30))) / 12,700

For Plan II: EPS = ($79,000 – ($247,000 * 0.10 * (1 – 0.30))) / 9,800

Repeat the calculations as in parts (a) and (b) with these adjusted EPS formulas to find the new EPS values and break-even levels of EBIT. Compare these results to those without taxes.

Problem 2: Price per Share of Equity

To calculate the price per share of equity under Plan I and Plan II (ignoring taxes), we can use the formula:

Price per Share of Equity = (Total Equity Value) / (Number of Shares)

For Plan I: Total Equity Value = EBIT – Debt

Total Equity Value = $79,000 – $109,250 = -$30,250 (negative because of the high debt)

Price per Share of Equity for Plan I = (-$30,250) / 12,700 ≈ -$2.38 (negative due to high debt)

For Plan II: Total Equity Value = EBIT – Debt

Total Equity Value = $79,000 – $247,000 = -$168,000 (negative because of the high debt)

Price per Share of Equity for Plan II = (-$168,000) / 9,800 ≈ -$17.14 (negative due to high debt)

The principle illustrated here is that when a company takes on a significant amount of debt, the value of equity can become negative, meaning that shareholders’ equity is insufficient to cover the debt obligations. This can result in a highly risky situation for shareholders.

In summary, Plan II has a higher EPS but significantly negative equity value, while Plan I also has negative equity value but a slightly lower EPS. The all-equity plan has a lower EPS compared to the leveraged plans but does not have negative equity value, making it a safer option for shareholders. When taxes are considered, the analysis would need to be adjusted accordingly to account for tax shields and their impact on EPS and equity value.