PharmaCo has a capital structure consisting of $10 billion in market equity and $1 billion in outstanding debt. The firm expects to generate free cash flows of $700 million next year, which are projected to grow at 3% per year in perpetuity. PharmaCo currently holds $2.6 billion in excess cash, which it plans to use entirely to finance an acquisition. Their cost of debt and equity are 3% and 7% respectively. BioEdge has $2.5 billion in market equity and $1.5 billion in debt. The firm is expected to generate $300 million in free cash flows next year, growing at 5% per year in perpetuity. BioEdge has 100 million shares outstanding, currently trading at $25 per share. Their cost of debt and equity are 7% and 10% respectively. PharmaCo is offering to acquire BioEdge using $2.6 billion in internal cash reserves. The merger is expected to generate $50 million in additional free cash flows next year, entirely from operational improvements in BioEdge, which will grow at 4% per year in perpetuity. Both firms are subject to corporate tax rate of 30%. What is the equity value of the merged firm after the transaction (in billions)?

Question

BlackTom AI · Accepted Answer

The problem describes a merger where PharmaCo (with 10B equity, 1B debt, and 2.6B excess cash) plans to acquire BioEdge (2.5B equity value implied by 100M shares at 25, and 1.5B debt). Free cash flow (FCF) growing perpetually, tax rate, and the effect of an acquisition with internal cash are all given. I will evaluate each answer option by breaking down the components and then comparing to the options.

Step 1: Restate the key data for each firm
- PharmaCo before merger:
  - Market equity: 10B
  - Debt: 1B
  - Excess cash: 2.6B (to be used entirely to finance acquisition)
  - FCF next year: 0.7B, growth: 3% per year, perpetuity
  - Cost of debt: 3%; Cost of equity: 7%
- BioEdge before merger:
  - Market equity: 2.5B (100M shares × 25)
  - Debt: 1.5B
  - FCF next year: 0.3B, growth: 5% per year, perpetuity
  - Cost of debt: 7%; Cost of equity: 10%
- Merger effects:
  - Additional FCF next year from operational improvements: 0.05B, growth 4% perpetuity
  - Corporate tax rate: 30%
  - After-tax framework; assume FCFs are after-tax cash flows for valuation purposes

Step 2: Compute standalone enterprise values (EVs) using a weighted average cost of capital (WACC) for each firm, based on given debt/equity mix and tax shield.
- PharmaCo: total capital V = 10B + 1B = 11B. D/V = 1/11, E/V = 10/11. Tax rate T = 30%.
  - After-tax cost of debt = rd × (1 − T) = 0.03 × 0.70 = 0.021.
  - WACCPharma = (D/V) × after-tax rd + (E/V) × re = (1/11) × 0.021 + (10/11) × 0.07 ≈ 0.001909 + 0.063636 ≈ 0.0655 (6.55%).
  - FCF1 = 0.7B, g = 3% → value of perpetuity = FCF1 / (WACC − g) = 0.7 / (0.0655 − 0.03) ≈ 0.7 / 0.0355 ≈ 19.7B.
- BioEdge: total capital V = 2.5B + 1.5B = 4.0B. D/V = 1.5/4 = 0.375, E/V = 2.5/4 = 0.625.
  - After-tax rd = 0.07 × (1 − 0.30) = 0.049.
  - WACCBioEdge = (D/V) × after-tax rd + (E/V) × re = 0.375 × 0.049 + 0.625 × 0.10 ≈ 0.018375 + 0.0625 ≈ 0.0809 (8.09%).
  - FCF1 = 0.3B, g = 5% → value of perpetuity = 0.3 / (0.0809 − 0.05) ≈ 0.3 / 0.0309 ≈ 9.72B.
- Combined standalone EV before synergy = 19.7B + 9.72B ≈ 29.4B.

Step 3: Incorporate the synergistic effect and the financing details of the merger.
- Synergy FCF: +0.05B next year, growing at 4% perpetually. This is an additional cash flow attributable to the merged entity.
- We need the WACC of the merged firm to value the synergy perpetuity. Since the merger is financed with PharmaCo’s 2.6B excess cash (i.e., no new debt is issued in the transaction) and the target’s debt remains, the post-merger capital structure roughly combines the pre-merger debt pools (1B from PharmaCo and 1.5B from BioEdge) and subtracts the 2.6B cash used from PharmaCo. The cash used reduces cash on the asset side but does not create new debt; the net effect on the capital structure is an increased debt load with the cash outlay already accounted as a reduction in cash.
- Post-merger approximate capitalization:
  - Debt: 1B + 1.5B = 2.5B
  - Equity: (PharmaCo equity + BioEdge equity) − cashused ≈ (10B + 2.5B) − 2.6B = 9.9B. This is a rough sketch that leaves us with an equity base in the vicinity of 9.9B before any revaluation from synergy; the exact number will adjust through the valuation of the combined firm’s free cash flow.
- Merged WACC approximation: using D/V = 2.5 / (9.9 + 2.5) ≈ 2.5 / 12.4 ≈ 0.2016; E/V ≈ 0.7984. After-tax rd = 0.03 × 0.70 = 0.021. WACC ≈ 0.2016 × 0.021 + 0.7984 × 0.07 ≈ 0.00423 + 0.05589 ≈ 0.0601 (6.01%). This is a rough, lower-bound-like WACC given the heavy equity base after merger.
- Value of synergy perpetuity at merged WACC: FCF1_synergy = 0.05B, g_synergy = 4%. Value_synergy ≈ 0.05 / (0.0601 − 0.04) ≈ 0.05 / 0.0201 ≈ 2.49B.
- Total merged enterprise value (EV) ≈ Standalone EV (29.4B) + Value_synergy (2.49B) ≈ 31.9B.
- Equity value of merged firm would then be roughly EV minus net debt. Net debt post-merger ≈ 2.5B (debt) − cash remaining. Since PharmaCo’s 2.6B cash was used to finance the acquisition, the remaining cash is small or zero; net debt ≈ 2.5B. Therefore, equity value ≈ 31.9B − 2.5B ≈ 29.4B.

Step 4: Compare to answer choices
- 58B, 48B, 38B, 28B are the four options.
- Our approximate equity value around 29.4B lands closest to 28B among the listed choices. The rough steps above carry simplifications (e.g., exact post-merger WACC, handling of cash, and the precise division of synergies between debt and equity), but the direction and magnitude consistently point toward a value in the upper twenties to around thirty billion, with 28B being the closest discrete option.

Step 5: Quick check of why the other options are unlikely
- 58B and 48B: these would require much larger standalone values or synergy effects than provided by the given FCFs and growth rates; they would imply a far larger WACC discounting or much larger component values than computed.
- 38B: plausible by rough math but farther from our computed vicinity (29–30B) given the stated inputs; would require a slightly higher synergy value or a lower net debt impact than our calculation.
- 28B: sits closest to the derived rough equity value after accounting for standalones, synergy, and the debt/cash structure described.

Conclusion (interpretation, not a stated final verdict): The reasoning above shows how the standalone values, synergy, and the merger financing interact to yield an equity value in the vicinity of the upper twenties to around thirty billion, with 28B being the closest match among the provided choices.

SP25-BL-BUS-F402-4299 Final Exam (optional)

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