Equity Capital Markets & Corporate Actions
Theoretical Ex-Rights Price (TERP) & Rights Formula
Calculate the Theoretical Ex-Rights Price TERP = (N * P_cum + M * P_sub) / (N + M), Nil-Paid Right Value per new share, Right Value per existing share, and lapsed-rights dilution loss.
Prove why discounted subscription rights are wealth-neutral only if exercised or sold!
In an M-for-N preemptive Rights Issue, shareholders receive transferable nil-paid rights allowing them to subscribe for M new shares at discounted Subscription_Price P_sub < P_cum for every N existing Cum-Rights shares held! Because N shares worth N * P_cum combine with M cash subscriptions M * P_sub across N + M post-issue shares, the Theoretical Ex-Rights Price is TERP = (N * P_cum + M * P_sub) / (N + M)! Each right to buy 1 new share at P_sub is worth Nil-Paid Value V_new = TERP - P_sub, and the right value detached from each old share is V_old = (M / N) * (TERP - P_sub) = P_cum - TERP!
Verify on a 1-for-4 Rights Offering (Existing_Ratio N = 4 in B2, New_Shares_Ratio M = 1 in B3), Cum_Rights_Price P_cum = $50.00 (B4), Subscription_Price P_sub = $35.00 (30.0% discount, B5), and Investor_Holdings S_hold = 1,000 shares ($50,000 initial portfolio, B6): TERP is (4 * 50.00 + 1 * 35.00) / (4 + 1) = 235 / 5 = $47.00/sh; Nil-Paid Value per New-Share Subscription Right is 47.00 - 35.00 = $12.00; Right Value per Existing Share is 50.00 - 47.00 = $3.00; and verify wealth neutrality: (a) Exercising 250 new shares costs $8,750 -> 1,250 shares * $47.00 = $58,750 - $8,750 cash = $50,000; (b) Selling rights yields 1,000 * $47.00 + 250 * $12.00 = $47,000 + $3,000 = $50,000; whereas (c) Letting rights expire unexercised & unsold forfeits $3,000.00!
| ECM Rights Offering Metric (1-for-4 @ $35 vs $50 Cum-Rights) | Formula | Verified Output |
|---|---|---|
| Theoretical Ex-Rights Price (TERP) | (N * P_cum + M * P_sub) / (N + M) | $47.00 / share |
| Nil-Paid Value per New-Share Right | TERP - P_sub | $12.00 / new share |
| Detached Right Value per Old Share | P_cum - TERP = (M / N) * (TERP - P_sub) | $3.00 / old share |
| Unexercised / Unsold Lapse Loss (1,000 sh) | (P_cum - TERP) * S_hold | $3,000.00 Wealth Loss |
General M-for-N Theoretical Ex-Rights Price (TERP) Formula
Validate N > 0, M > 0, and 0 < P_sub < P_cum (if P_sub >= P_cum, rational investors buy cheaper in the open market rather than exercising rights)!
=LET(n_ex, B2, m_nw, B3, p_cm, B4, p_sb, B5, IF(OR(n_ex <= 0, m_nw <= 0, p_sb <= 0, p_cm <= p_sb, B6 < 0), "Invalid Rights Offering", ROUND((n_ex * p_cm + m_nw * p_sb) / (n_ex + m_nw), 4)))Nil-Paid Subscription Right Value & Lapsed-Rights Wealth Loss Formula
Test a deeper 2-for-3 rescue recapitalization (N = 3, M = 2 at P_sub = $25): TERP drops to (150 + 50) / 5 = $40.00 and passive lapse loss jumps to $10,000 on 1,000 shares!
=IF(ISTEXT(E2), E2, ROUND((B4 - E2) * B6, 2))Try the example
Use the original values or change them to test your understanding.