Valuation and Capital Budgeting Questions

Step 1 — NPV if you invest now (t=0)

• Cash flows: $10M/year for 10 years. Present value factor for a 10-year annuity at 10%: (1 − 1/1.1^10)/0.1 ≈ 6.14457.
• PV of revenues = 10 × 6.14457 = $61.4457M.
• NPV_now = PV − cost = 61.4457 − 50 = $11.4457M.

Step 2 — Expected NPV if you wait one year (decide at t=1)

• If you wait, at t=1 there are two outcomes:
  • 60%: revenues = $20M/year → PV_at1 = 20 × 6.14457 = $122.8914 → NPV_at1 = 122.8914 − 50 = $72.8914
  • 40%: revenues = $5M/year → PV_at1 = 5 × 6.14457 = $30.72285 → NPV_at1 = 30.72285 − 50 = −$19.27715
• Expected NPV at t=1 = 0.6×72.8914 + 0.4×(−19.27715) = $36.02398M.
• Discount back one year to t=0: Expected NPV_wait = 36.02398 / 1.1 = $32.74816M.

Decision

• Compare NPVs at t=0: invest now = $11.45M vs. wait = $32.75M (expected, discounted).
• Recommendation: wait one year — the option to wait and learn has higher expected value.

Intuition about option value

• Waiting gives you a real option: you pay the same cost later but you gain information that lets you invest only when payoff is high or avoid investing when payoff is poor. That asymmetric upside (large gain when $20M outcome occurs) increases expected value enough to overcome the delay/discounting. The calculation above is a simple expected-value real-options view; more sophisticated approaches (e.g., modeling volatility or the ability to abandon mid-stream) typically increase the value of waiting further.