If a venture has a constant return to scale, and there is no outside investment, how
do you determine the portion of the entrepreneur total investment that maximizes
her NPV of the venture?
With no outside investors, the larger the scale the more undiversified the entrepreneur is.
order to determine the optimal investment scale, we need to plot the capital market line (CML),
as it measures the opportunity cost of capital for the venture at each level of risk. We also need to
plot the line that represents the total return for the entrepreneur’s investment in the venture,
assuming that the remainder of the entrepreneur wealth is invested in the market portfolio. The
optimal scale for the entrepreneur depends on the entrepreneur’s risk tolerance, which we do not
However, as an approximation, the optimal scale is the allocation of wealth between the
venture and the market portfolio that maximizes the computed net present value of the
Why, if the parties agree about the risk and expected return of a venture, is there a
“double payoff” to the entrepreneur from bringing in an outside investor who is
First, it reduces the entrepreneur’s required investment and enables him to realize some benefits
of diversification. Second, if the entrepreneur and the outside investor agree about the expected
future cash flows and risk, then the investor values the venture more highly than the
entrepreneur, and is willing to accept a smaller share of equity in exchange for a given dollar
Alternatively, the investor will, in effect, make a side payment to the entrepreneur in
exchange for being allowed to participate proportionally in the venture.
Contract provisions that shift diversifiable risk to a well-diversified investor yield
pure gains in the venture’s NPV. Explain why the entrepreneur benefits.
If contract provisions only shift the diversifiable risk, then beta risk of each party is unchanged,
but the entrepreneur’s total risk declines.
Accordingly, risk of the entrepreneur’s investment can
be reduced without altering the entrepreneur’s expected return.
As a result, the value of the
entrepreneur’s financial claim increases.
The shifting diversifiable risk does not change the
value of the a well-diversified investor’s claim on project cash flows.
Test Bank for Entrepreneurial Finance, Smith and Smith 2ed. Copyright 2004