DeepSeek V4.1 Flash (Venice) (thinking on) on Discounted cash flow valuation with mid-year option and a sensitivity grid

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   "final_message": "Done. `solve.py` computes the DCF valuation from `input.json` and writes `answer.json`.\n\nKey implementation points:\n- **PV of FCF**: discounts each year by `(1+wacc)**t`, or `(1+wacc)**(t-0.5)` under the mid-year convention.\n- **Terminal value**: Gordon growth `fcf_N*(1+g)/(wacc-g)`, always discounted by `(1+wacc)**N` (even mid-year).\n- **Derived metrics**: EV, equity, per-share, terminal share, implied EV/EBITDA.\n- **Error case**: if `terminal_growth >= wacc`, writes `{\"error\": \"growth_not_below_wacc\"}`.\n- **Sensitivity grid**: one row per `sens_wacc`, one entry per `sens_growth`, per-share rounded to 4 decimals, `null` when growth \u2265 that row's wacc.\n- **Rounding**: money to 2 decimals; `per_share`, `terminal_share`, `implied_ev_ebitda` to 6 decimals.\n\nVerified on the given input (mid-year) and on a growth\u2265wacc case.",
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    "result": "{\n \"units\": \"millions, except per share\",\n \"fcf\": [\n  364.6,\n  338.9,\n  322.3,\n  298.6,\n  334.7,\n  383.7,\n  379.0,\n  440.0,\n  442.1\n ],\n \"wacc\": 0.1083,\n \"terminal_growth\": 0.031,\n \"mid_year\": true,\n \"net_debt\": 1248.7,\n \"shares\": 287.69,\n \"ebitda_last\": 751.2,\n \"sens_wacc\": [\n  0.0883,\n  0.0983,\n  0.1083,\n  0.1183,\n  0.1283\n ],\n \"sens_growth\": [\n  0.0,\n  0.015,\n  0.025,\n  0.035,\n  0.1183\n ]\n}"
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     "content": "import json\nimport sys\n\n\ndef compute(fcf, wacc, g, mid_year, net_debt, shares, ebitda_last):\n    n = len(fcf)\n    pv_fcf = 0.0\n    for t in range(1, n + 1):\n        exp = (t - 0.5) if mid_year else t\n        pv_fcf += fcf[t - 1] / (1.0 + wacc) ** exp\n    terminal_value = fcf[-1] * (1.0 + g) / (wacc - g)\n    pv_terminal = terminal_value / (1.0 + wacc) ** n\n    enterprise_value = pv_fcf + pv_terminal\n    equity_value = enterprise_value - net_debt\n    per_share = equity_value / shares\n    terminal_share = pv_terminal / enterprise_value\n    implied_ev_ebitda = enterprise_value / ebitda_last\n    return {\n        \"pv_fcf\": pv_fcf,\n        \"terminal_value\": terminal_value,\n        \"pv_terminal\": pv_terminal,\n        \"enterprise_value\": enterprise_value,\n        \"equity_value\": equity_value,\n        \"per_share\": per_share,\n        \"terminal_share\": terminal_share,\n        \"implied_ev_ebitda\": implied_ev_ebitda,\n    }\n\n\ndef main():\n    with open(sys.argv[1]) as f:\n        data = json.load(f)\n\n    fcf = data[\"fcf\"]\n    wacc = data[\"wacc\"]\n    g = data[\"terminal_growth\"]\n    mid_year = data[\"mid_year\"]\n    net_debt = data[\"net_debt\"]\n    shares = data[\"shares\"]\n    ebitda_last = data[\"ebitda_last\"]\n    sens_wacc = data[\"sens_wacc\"]\n    sens_growth = data[\"sens_growth\"]\n\n    if g >= wacc:\n        with open(sys.argv[2], \"w\") as f:\n            json.dump({\"error\": \"growth_not_below_wacc\"}, f)\n        return\n\n    res = compute(fcf, wacc, g, mid_year, net_debt, shares, ebitda_last)\n\n    sensitivity = []\n    for sw in sens_wacc:\n        row = []\n        for sg in sens_growth:\n            if sg >= sw:\n                row.append(None)\n            else:\n                r = compute(fcf, sw, sg, mid_year, net_debt, shares, ebitda_last)\n                row.append(round(r[\"per_share\"], 4))\n        sensitivity.append(row)\n\n    answer = {\n        \"pv_fcf\": round(res[\"pv_fcf\"], 2),\n        \"terminal_value\": round(res[\"terminal_value\"], 2),\n        \"pv_terminal\": round(res[\"pv_terminal\"], 2),\n        \"enterprise_value\": round(res[\"enterprise_value\"], 2),\n        \"equity_value\": round(res[\"equity_value\"], 2),\n        \"per_share\": round(res[\"per_share\"], 6),\n        \"terminal_share\": round(res[\"terminal_share\"], 6),\n        \"implied_ev_ebitda\": round(res[\"implied_ev_ebitda\"], 6),\n        \"sensitivity\": sensitivity,\n    }\n\n    with open(sys.argv[2], \"w\") as f:\n        json.dump(answer, f, indent=1)\n\n\nif __name__ == \"__main__\":\n    main()\n"
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    "result": "exit=0\nstdout:\n{\n \"pv_fcf\": 2105.26,\n \"terminal_value\": 5896.57,\n \"pv_terminal\": 2337.13,\n \"enterprise_value\": 4442.39,\n \"equity_value\": 3193.69,\n \"per_share\": 11.101156,\n \"terminal_share\": 0.526098,\n \"implied_ev_ebitda\": 5.913727,\n \"sensitivity\": [\n  [\n   11.6688,\n   13.4786,\n   15.1617,\n   17.4763,\n   null\n  ],\n  [\n   9.974,\n   11.3036,\n   12.4923,\n   14.0566,\n   null\n  ],\n  [\n   8.6014,\n   9.6036,\n   10.4721,\n   11.5777,\n   null\n  ],\n  [\n   7.4686,\n   8.2397,\n   8.8916,\n   9.6999,\n   null\n  ],\n  [\n   6.5187,\n   7.1224,\n   7.6223,\n   8.2293,\n   60.4644\n  ]\n ]\n}\nstderr:\n"
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        "content": "Done. `solve.py` computes the DCF valuation from `input.json` and writes `answer.json`.\n\nKey implementation points:\n- **PV of FCF**: discounts each year by `(1+wacc)**t`, or `(1+wacc)**(t-0.5)` under the mid-year convention.\n- **Terminal value**: Gordon growth `fcf_N*(1+g)/(wacc-g)`, always discounted by `(1+wacc)**N` (even mid-year).\n- **Derived metrics**: EV, equity, per-share, terminal share, implied EV/EBITDA.\n- **Error case**: if `terminal_growth >= wacc`, writes `{\"error\": \"growth_not_below_wacc\"}`.\n- **Sensitivity grid**: one row per `sens_wacc`, one entry per `sens_growth`, per-share rounded to 4 decimals, `null` when growth \u2265 that row's wacc.\n- **Rounding**: money to 2 decimals; `per_share`, `terminal_share`, `implied_ev_ebitda` to 6 decimals.\n\nVerified on the given input (mid-year) and on a growth\u2265wacc case.",
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        "reasoning_content": "Both work. Let me double-check the sensitivity null condition: \"null when growth >= wacc\". Yes. And the last row has growth 0.1183 == wacc 0.1283? No, 0.1183 < 0.1283, so computed. Good.\n\nEverything looks correct."
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