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 Rb = 0 and Rb = 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 Rb , Rb 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 = RH - Ψ0(eM) 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 = RH - Ψ0 (eM). 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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