13D Filing: Longwood Fund II, L.P. and Kalvista Pharmaceuticals Inc. (KALV)

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D

Under the Securities Exchange Act of 1934

(Amendment No.     )*

KalVista
Pharmaceuticals, Inc.

(Name of Issuer)

Common Stock, $0.001 par value

(Title of Class of Securities)

483497103

(CUSIP Number)

(Name, Address and Telephone Number of Person Authorized to Receive Notices and Communications)

October 12, 2017

(Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this
schedule because of §§240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the following box: ☐

Note: Schedules filed in paper format shall
include a signed original and five copies of the schedule, including all exhibits. See §240.13d-7 for other parties to whom copies are to be sent.

The information required on the remainder of this cover page shall not be
deemed to be filed for the purpose of Section 18 of the Securities Exchange Act of 1934 (Act) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act
(however, see the Notes).

SCHEDULE 13D

Item 1. Security and Issuer.

This statement on
Schedule 13D relates to the Common Stock, $0.001 par value per share (the Common Stock), of KalVista Pharmaceuticals, Inc. (the Issuer). The Issuers principal executive office is located at 55 Cambridge Parkway, 9th
floor, Cambridge, Massachusetts 02142.

Item 2. Identity and Background.

(a) This Schedule 13D is being filed on behalf of each of the following persons pursuant to Rule 13d-1(k) of Regulation D-G under the Securities Exchange Act
of 1934, as amended (the Exchange Act): Longwood Fund II, L.P. (LFII), Longwood Fund II GP, LLC (LFII GP), Christoph Westphal, M.D., Ph.D. (Westphal), and Richard Aldrich (Aldrich)
(collectively, the Reporting Persons). The Reporting Persons are making this single, joint filing because they may be deemed to constitute a group within the meaning of Section 13(d)(3) of the Exchange Act. The agreement
between the Reporting Persons to file as a group (the Joint Filing Agreement) is attached hereto as Exhibit A.

(b)-(c) The principal
business of LFII is that of a private investment partnership. The sole general partner of LFII is LFII GP. The principal business of LFII GP is that of a limited liability company acting as the general partner of LFII. Westphal and Aldrich are the
managers of LFII GP, and both Westphal and Aldrich are members of LF II GP; additionally, Aldrich is a member of the Board of Directors of the Issuer.

The principal business address of each of the entities and individuals named in this Item 2 is Longwood Fund, Prudential Tower, Suite 1555, 800 Boylston
Street, Boston, Massachusetts 02199.

(d)(e) During the last five years, none of the Reporting Persons or individuals named in this Item 2 has
(i) been convicted in any criminal proceeding (excluding traffic violations or similar misdemeanors); or (ii) been a party to a civil proceeding of a judicial or administrative body of competent jurisdiction resulting in his being subject
to a judgment, decree or final order enjoining future violations of, or prohibiting or mandating activities subject to, federal or state securities laws or finding any violation with respect to such laws.

(f) Each of the individuals named in this Item 2 is a citizen of the United States.

Item 3. Source and Amount of Funds or Other Consideration.

On November 21, 2016, LFII acquired an aggregate of 369,419 shares of common stock of the Issuer in exchange for 1,268,971 shares of KalVista
Pharmaceuticals, Ltd. Series B Preferred Stock in connection with the closing of the share purchase transaction (the Transaction) whereby KalVista Pharmaceuticals, Ltd. became a wholly-owned subsidiary of Carbylan Therapeutics, Inc.,
which changed its name to KalVista Pharmaceuticals, Inc. (the Company). On the effective date of the Transaction, the closing price of the Companys common stock was $9.38 per share. All numbers give effect to the 14:1 reverse stock
split effected by the Company on November 21, 2016. Prior to the reverse stock split, the closing price of the Companys common stock was $0.67 per share.

On October 12, 2017, LFII purchased an aggregate of 565,065 shares of common stock of the Issuer for an aggregate purchase price of $4,866,961.35. All
such shares were purchased with working capital.

Item 4. Purpose of Transaction.

Westphal and Aldrich, by virtue of their roles as the managers of LFII GP, may each be deemed to hold certain voting powers with respect to the reportable
securities owned by LFII. Except as otherwise described in this statement, the Reporting Persons do not have any present plans or proposals that relate to or would result in: (i) the acquisition by any person of additional securities of the
Issuer, or the disposition of securities of the Issuer; (ii) an extraordinary corporate transaction, such as a merger, reorganization or liquidation, involving the Issuer or any of its subsidiaries; (iii) a sale or transfer of a material
amount of assets of the Issuer or any of its subsidiaries; (iv) any change in the present board of directors or management of the Issuer, including any plans or proposals to change the number or term of directors or to fill any existing
vacancies on the board; (v) any material change in the present capitalization or dividend policy of the Issuer; (vi) any other material change in the Issuers business or corporate structure; (vii) changes in the Issuers
charter, by-laws or instruments corresponding thereto or other actions which may impede the acquisition of control of the Issuer by any person; (viii) causing a class of securities of the Issuer to be de-listed from a national securities
exchange or to cease to be authorized to be quoted in an inter-dealer quotation system of a registered national securities association; (ix) a class of equity securities of the Issuer becoming eligible for termination of registration pursuant
to Section 12(g)(4) of the Exchange Act; or (x) any action similar to any of those enumerated above.

Item 5. Interest in Securities of
the Issuer.

The information below is based on a total of 10,783,631 shares of Common Stock outstanding as of October 12, 2017, according to
information supplied by the Issuer.

(a) LFII beneficially owns 934,484shares of Common Stock, or approximately 8.7% of the Common Stock outstanding. LFII
GP, as the general partner of LFII, may be deemed to indirectly beneficially own the securities owned by LFII.

(b) The managers of LFII GP may be deemed
to share the power to vote or direct the voting of and to dispose or direct the disposition of the securities of the Issuer that are beneficially owned by LFII. Each such person disclaims beneficial ownership of all securities other than those he or
she owns directly, if any, or by virtue of his or her indirect pro rata interest, as a member of LFII GP, in the securities owned by LFII and such person may be deemed to have sole power to vote or direct the voting of and to dispose or direct the
disposition of the securities of the Issuer that are beneficially owned by LFII.

(c) Except as described in this statement, none of the Reporting Persons
has effected any transactions in the Common Stock in the 60 days prior to the date of this statement.

(d) Except as described in this statement, no person
has the power to direct the receipt of dividends on or the proceeds of sales of, the shares of Common Stock owned by the Reporting Persons.

(e) Not
applicable.

Item 6. Contracts, Arrangements, Understandings or Relationships with Respect to Securities of the Issuer.

The Issuer has entered into an indemnification agreement with each of its directors and executive officers, including Aldrich. The indemnification agreement,
among other things, require the Issuer or will require the Issuer to indemnify Aldrich (and in certain cases LFII) to the fullest extent permitted by Delaware law, including indemnification of expenses such as attorneys fees, judgments, fines
and settlement amounts incurred by Aldrich in any action or proceeding, including any action or proceeding by or in right of the Issuer, arising out of his services as a director. The form of Indemnification Agreement for the Issuers directors
and officers is attached as Exhibit 10.5 to the Issuers Registration Statement on Form S-1 (File No. 333-211818), and is incorporated herein by reference.

Item 7. Material to be Filed as Exhibits.

Exhibit A
– Joint Filing Agreement

Exhibit B – Form of Director and Officer Indemnification Agreement, filed on June 3, 2016 as Exhibit 10.12 to the
Issuers Registration Statement on Form S-1 (File No. 333-211818), and incorporated herein by reference.

SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true,
complete and correct.

Date: October 20, 2017