Topic 6 - Capital Structure Part 2

Question 1

Problem 1 - Optimal Capital Structure (Context)

Answer 1

My Company has $200m debt and $800m equity
Maximum debt ratio (debt/assets) is 40%
I need to choose between 20%, 30% or 40% debt ratios for an optimal cap structure
Total Assets amount cannot change.
If I borrow more debt, proceeds are used to buy back stock.
I.Rs for debt are linked to credit ratings, and credit ratings are determined by EBIT coverage ratios.
My company is expected to maintain $80m, with a current rating of AAA (I.R rate of 4.3%)
Current stock beta (levered beta) is 1.5
Risk free rate is 4%
Market Risk Premium (expected return – risk free rate) is 5%
Your company faces a marginal tax rate of 30%

Question 2

Problem 1 - Optimal Capital Structure - Q1 - I Increase my debt ratio to 30%, what’s the EBIT cov. Ratio, credit rating and interest rate?
(compute EBIT cov. ratio using current I.R. Based on this, corresponding credit rating and new I.R.
compute EBIT cov. ratio again with new I.R – Repeat until they’re all lined up in the same row.)

Answer 2

• 30% debt, assuming current interest (4.3%)
  Interest Expense is $300m (new debt) * 4.3% (current interest) which = $12.9m
  EBIT coverage = $80m /$12.9m = 6.2 (A+ Rating) Table 2
• A+ rating, assuming new interest [risk free rate of 4% + A+ default spread from table 0.63%)
  Interest Expensive is $300m * 4.63% (new interest) which = $13.89m
  EBIT coverage = $80m / $13.89m = 5.76 (A+ Rating) Table 2

Therefore, at 30% debt ratio, we have an EBIT Cov. Ratio of 5.76, credit rating of A+, and an interest rate of 4.63%

Question 3

Problem 1 - Optimal Capital Structure - Q1 - I increase my debt ratio to 40%, what’s the EBIT cov. ratio, credit rating and interest rate?
(same as before)

Answer 3

-40% debt, assuming current interest (4.3%)
Interest Expense is $400m (new debt) * 4.3% (current interest) = $17.2m
EBIT Coverage = EBIT (80m) / Interest Expense (17.2m) = 4.65

• A Rating: of 4.71 New Interest Rate is 4.71% (rfr of 4% + table A’s rating of 0.71%))
  4.71% (new interest) * $400m (new debt) = 18.84m
  EBIT Coverage = EBIT (80m) / New Interest Expense (18.84m) = 4.2463
• This is a A- Rating, gives us 4.84% off the combination of the RfR and the table1 A- figure
  4.84% (new new interest) * 400m = 19.36m
  80m / 19.36m = 4.13

Therefore, at a 40% debt ratio, we have an EBIT cov. ratio of 4.13, a interest rate of 4.84% and a credit rating of A-

Question 4

Problem 1 - Optimal Capital Structure - Q1 - What’s unlevered beta of common stock?

Answer 4

My Current Leveraged Beta is 1.5, with a D/E ratio of 0.25 (200m/800m)
We can find the unleveraged beta using this formula.
Lev Beta / [1 + (1 – tax) * D/E]
which is
1.5 / [1 + (1 – 30%) * 0.25) = 1.277

Question 5

Problem 1 - Optimal Capital Structure - Q1 - What’s the levered beta at the different debt ratios (20%, 30%, 40%)? Calculate the corresponding cost of equity using CAPM

Answer 5

@20%, my D/E ratio is 200m/800m, so my formula looks like
1.277 * [1 + (1 – 30%) * (2/8) = 1.5

@30%, my D/E ratio is 300m/700m
1.277 * [1 + (1 - 30%) * (3/7) = 1.66

@40%, my D/E ratio is 400m/600m
1.277 * [1 + (1 – 30%) * (4/6) = 1.87

Using CAPM, we can find the Cost of Equity
4% (risk-free rate) + Beta (Market Risk Premium)
@20, Re = 4% + 1.5 * 5% = 11.5%
@30, Re = 4% + 1.66 * 5% = 12.3%
@40, Re = 4% + 1.87 * 5% = 13.4%

Question 6

Problem 1 - Optimal Capital Structure - Q1 - Calculate WACC at different debt ratios? Which is best to maximise firm value? (We want the lowest WACC)
WACC = weighting of debt – tax * cost of debt + weighting of equity * cost of equity

Answer 6

@20%, WACC = (0.24.3%)(1 – 30%) + (0.811.5%) = 9.8%
@30%, WACC = (0.34.63%)(1 – 30%) + (0.712.3%) = 9.56%
@40%, WACC = (0.44.84%)(1 – 30%) + (0.6*13.4%) = 9.39% (best one)