ANTI-COMPETITIVE FINANCIAL CONTRACTING: THE DESIGN OF FINANCIAL CLAIMS.

first order conditions for the entrepreneurial effort choice after a bad and a
good signal. The investor’s incentive compatibility constraint just states that,
after receiving a good signal on Firm 2, the venture capitalist must prefer not
to fund Firm 2. Since if a bad signal is observed, the venture capitalist will
never want to fund firm 2, the contract does not need to prevent any over-
funding behavior in this case. The last constraint ensures limited liability for
the entrepreneur.

The solution to this program is stated in the following:

Lemma 4 The optimal financial contract for the venture capitalist will be con-
tingent on the signal received at date 2.

If a bad signal is observed at date 2, then the entrepreneur is paid RL = 0
in case of failure and RH = Ψ⁰(eM) in case of success, where eM is the second
best effort defined in Lemma 1. Entrepreneurial effort is e = eM.

If a good signal is observed at date 2, then the entrepreneur’s payoffs are
the same as in Lemma 2:

(i) for W ≤ W, the entrepreneur’s payoffs are R_b = 0 and R_b = Ψ⁰(eCP)

(ii) for W > IW, the entrepreneur’s payoffs are RL = b and RH = b +
_Ψ0_(eCP₎

Entrepreneurial effort is e = eCP, i.e. the third best level of effort.

Proof. This result is immediate since the venture capitalist’s program can
be split in two separate programs: the optimal levels of RL, RH,e are found
by solving a program which is formally identical to the second best optimum,
whereas the optimal levels of R_b , R_b and e are the solution to a program which
is identical to the third best optimum. ■

We provide an interpretation for the optimal financial contract that is con-
sistent with the evidence on the modes of financing observed in venture capital
deals.

Proposition 5 There exists a convertible debt contract, {D₀,D₁ ,s} , that im-
plements the optimal financial contract of Lemma 4. The venture capitalist
initially takes debt D0 = R^H - Ψ⁰(e^M) in Firm 1. If and only if a good signal
occurs then part of the debt is automatically converted into an equity stake
_Ψ0_(eCP₎

s = 1 — rh _-rL , so that the venture capitalist is left with a debt position D₁.
The post-conversion debt position is decreasing in W:

(i) if W ≤ W, then D₁ = RL

(ii) if W >W, then D₁ = RL - ^bψH(^-R)) where b = W - IW.

Proof. If a bad signal occurs, then the venture capitalist is left with a debt
claim D₀ = R^H - Ψ⁰ (e^M). But, according to Lemma 1, this financial claim
implements the contract RL = 0 , RH = Ψ⁰(eM). If a good signal occurs, part of

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