Corporate Accounting and Auditing · Underwriting of Securities

Firm Underwriting Problems and Under-subscription Sums

Updated 10 October 2026 · Fact-checked

Firm underwriting means an underwriter agrees to take a fixed number of shares whatever the public does. To solve a sum, find each underwriter's gross liability, deduct marked applications, their share of unmarked applications and firm shares, then fix any negative balance. The result is net liability, which the underwriter must take up.

Understand Underwriting Problems with Firm Underwriting and Under-subscription

An underwriter promises to take up shares that the public does not subscribe. The promise is stated as a share of the issue. That share is the gross liability. Each underwriter earns commission for giving this promise.

In firm underwriting, the underwriter also agrees to take a fixed number of shares, whatever happens to public subscription. It is as if the underwriter has applied for those shares. So the firm shares reduce his own gross liability. The benefit is that he takes these shares in any case, so his remaining risk is smaller. Commission is still paid on the full gross underwritten amount, including firm shares.

Applications from the public are of two kinds. Marked applications carry the stamp of one underwriter, and they are credited only to that underwriter. Unmarked applications carry no stamp. They are spread over all underwriters, usually in the ratio of their gross liabilities.

An issue is under-subscribed when public applications plus firm shares are less than the shares offered. The shortfall is taken up by the underwriters. The shortfall is shared through the net liability calculation. The sum is solved by building one table with a column for each underwriter.

Sometimes an underwriter's calculation turns negative. This means his credit is more than his gross liability. His net liability is nil. The surplus is passed on to the other underwriters, normally in the ratio of their gross liabilities.

Key rules to remember

Gross liability: Gross liability = Total shares offered × Underwriter's share (%); If part of the issue is not underwritten, apply the percentage only to the underwritten shares, as the question states.
Net liability: Net liability = Gross liability − Marked applications − Share of unmarked applications − Firm underwriting shares; Do the deductions in this order. If the result is negative, the net liability is nil and the surplus is re-allocated.
Unmarked applications share: Share of unmarked = Total unmarked applications × (Underwriter's gross liability ÷ Total gross liability); Use the gross liability ratio unless the question gives another ratio.
Total shares taken by an underwriter: Shares taken = Net liability + Firm underwriting shares; Firm shares are shares he takes anyway. Journal entries and amounts due use this total.
Check for the whole issue: Total net liabilities = Shares offered − Public applications (marked + unmarked) − Total firm underwriting; Use this to check your table before moving on.
Underwriting commission: Commission = Gross shares underwritten × Issue price × Commission rate; It is calculated on the full gross liability, including firm shares, unless the question says otherwise.

How to solve Underwriting Problems with Firm Underwriting and Under-subscription questions

Use one table with a column for every underwriter. The same method works whether or not firm underwriting is given.

1Read the question and note the total issue, the underwriting ratio, the total applications, the marked applications of each underwriter and the firm underwriting shares.
2Work out gross liability for each underwriter in shares.
3Separate the unmarked applications: total applications less total marked applications. Spread them in the gross liability ratio.
4For each underwriter, subtract marked applications, then unmarked share, then firm shares, from gross liability. This gives net liability.
5If any net liability is negative, make it nil. Spread the surplus among the other underwriters in the ratio of their gross liabilities, and recompute.
6Add firm shares to net liability to get the total shares each underwriter takes. Check that net liabilities total the shortfall.
7Compute commission or amounts payable if the question asks. Write the answer under clear headings.

Quickest way: One-table method with a total check

When to use it: Use it for any exam sum with three or fewer underwriters when you have only a few minutes.

Draw columns A, B, C and a Total column.
Fill the rows: Gross, Marked, Unmarked, Firm, Net. Write the gross ratio next to the unmarked row.
Check that Total net equals shares offered minus public applications minus total firm shares.
If the check fails, recheck the unmarked total. It is the most common error.
Mark any negative net as nil and re-spread the surplus only after the first table is complete.

Common mistakes in Underwriting Problems with Firm Underwriting and Under-subscription

Counting marked applications again in the unmarked pool.
Students take total applications as unmarked without deducting marked ones.
Fix: Always do unmarked = total applications − total marked applications.
Deducting firm underwriting from the total public applications instead of from the underwriter's own gross liability.
Firm shares are confused with public applications.
Fix: Treat firm shares as the underwriter's own application. Deduct them in his column only.
Leaving a negative net liability in the table.
Students forget that an underwriter cannot take fewer than nil shares.
Fix: Set it to nil. Spread the surplus to the other underwriters in the gross liability ratio and recheck the total.
Spreading unmarked applications in the wrong ratio.
Students use the net liability or underwriting commission ratio.
Fix: Use the gross liability ratio unless the question states a different ratio.
Calculating commission only on net shares taken.
Students link commission to the shares actually allotted to the underwriter.
Fix: Calculate commission on the full gross shares underwritten, including firm shares, unless the question says otherwise.
Forgetting to add firm shares when stating the shares an underwriter takes.
The answer stops at net liability.
Fix: Write the answer as net liability + firm shares, and show both.

Worked examples

Example 1

Mehta Ltd offered 1,00,000 equity shares of ₹10 each. The issue was underwritten by A 60%, B 30% and C 10%. Applications received for 80,000 shares, including marked applications: A 20,000, B 15,000, C 5,000. A and B had given firm underwriting of 5,000 and 2,000 shares respectively. Commission is 5% of the issue price. Find the shares each underwriter takes up and the commission.

Show the solution

Gross liability: A 60,000; B 30,000; C 10,000.
Marked applications total 40,000. Unmarked = 80,000 − 40,000 = 40,000.
Spread unmarked 6 : 3 : 1: A 24,000; B 12,000; C 4,000.
Net liability of A = 60,000 − 20,000 − 24,000 − 5,000 = 11,000.
Net liability of B = 30,000 − 15,000 − 12,000 − 2,000 = 1,000.
Net liability of C = 10,000 − 5,000 − 4,000 − 0 = 1,000.
Check: net total 13,000 = 1,00,000 − 80,000 − 7,000 firm shares. This agrees.
Total shares taken: A = 11,000 + 5,000 = 16,000; B = 1,000 + 2,000 = 3,000; C = 1,000.
Commission on gross: total 1,00,000 × ₹10 × 5% = ₹50,000. A ₹30,000; B ₹15,000; C ₹5,000.

Answer: A takes 16,000 shares, B takes 3,000 and C takes 1,000. Commission payable is ₹30,000 to A, ₹15,000 to B and ₹5,000 to C, a total of ₹50,000.

Example 2

Sharma Ltd issued 50,000 shares of ₹10 each, underwritten by P 50%, Q 30% and R 20%. Public applications were 39,700 shares, of which marked were P 6,000, Q 11,700 and R 4,000. P gave firm underwriting of 2,000 shares. Find the shares each underwriter takes up. Surplus, if any, is shared in gross liability ratio.

Show the solution

Gross liability: P 25,000; Q 15,000; R 10,000.
Marked total = 6,000 + 11,700 + 4,000 = 21,700. Unmarked = 39,700 − 21,700 = 18,000.
Spread unmarked 5 : 3 : 2: P 9,000; Q 5,400; R 3,600.
P: 25,000 − 6,000 − 9,000 − 2,000 = 8,000.
Q: 15,000 − 11,700 − 5,400 = −2,100, so Q's net liability is nil and the surplus is 2,100.
R: 10,000 − 4,000 − 3,600 = 2,400.
Check before adjusting: 8,000 − 2,100 + 2,400 = 8,300, equal to 50,000 − 39,700 − 2,000.
Spread the surplus 2,100 between P and R in the ratio 5 : 2: P 1,500; R 600.
Adjusted net liability: P = 8,000 − 1,500 = 6,500; R = 2,400 − 600 = 1,800; Q = nil. Total 8,300.
Total shares taken: P = 6,500 + 2,000 = 8,500; Q nil; R 1,800.

Answer: P takes 8,500 shares (6,500 net plus 2,000 firm), Q takes nil and R takes 1,800 shares. The shortfall of 8,300 shares is fully absorbed.

Exam tips

Start every answer with the full table. Step marks are given for gross liability, unmarked shares, net liability and the surplus adjustment.
Always run the total check. If net liabilities do not equal the shortfall, the unmarked figure is usually wrong.
Read the wording on firm underwriting and unmarked applications. Some questions give an order or ratio that overrides the usual method.
In MCQs, work only the column the question asks for. Do not build the full table unless needed, but still deduct marked and firm shares.
If the question asks for commission or journal entries, finish the shares first. Show commission on gross shares and name the rate and base.

Practice questions from Underwriting of Securities

Underwriting Problems with Firm Underwriting and Under-subscription: frequently asked questions

What is the benefit of firm underwriting?

The underwriter takes the firm shares in any case, so these shares reduce his gross liability in the calculation. For the company, the firm shares are certain to be taken up. It also reduces the liability of the underwriter for the rest of the issue.

How are firm underwriting shares treated in the calculation?

They are treated as if the underwriter applied for them himself. Deduct them from that underwriter's gross liability after marked and unmarked applications. Add them back when you state the total shares he takes.

What if an underwriter's net liability comes out negative?

Show it as nil. The surplus is passed to the other underwriters in the ratio of their gross liabilities, unless the question states another ratio. Recompute their net liabilities and check the total.

Is underwriting commission paid on firm shares too?

Yes, in the usual exam treatment commission is calculated on the gross shares underwritten, which includes firm shares. Follow any different instruction given in the question.