A company is financed as follows:   • 400 million $1 shares quoted at $3.

Equity: 400m shares at $3 → $1,200m

Existing debt: $800m

New debt raised: $200m

Project NPV: $100m

Step 1 – Initial firm value:

= 1,200 + 800 = $2,000m

Step 2 – After raising $200m debt and investing in project:

Debt becomes = 800 + 200 = $1,000m

Firm value increases by NPV of 100 → new firm value = 2,000 + 100 = $2,100m

Wait – careful: raising debt also adds cash before investment, then project adds NPV:

After raising debt: 2,000 + 200 = 2,200

After investing in project with NPV 100: +100 → 2,300m total firm value

So final:

Firm value = 2,300m

Debt = 1,000m

Equity (by MV) = 2,300 – 1,000 = 1,300m

Step 3 – Gearing ratio (market value):

Gearing = Debt / (Debt + Equity)

= 1,000 / (1,000 + 1,300)

= 1,000 / 2,300 ≈ 43.48%

To avoid an immediate breach, the bank’s maximum gearing must be at least above 43.48%.

The lowest option that does this is 44%.