Donna Is Considering the Option of Becoming a Co-Owner in a Business

question 13

Essay

Donna is considering the option of becoming a co-owner in a business. Her investment choices are to hold a risk free asset that has a return of R_j and co-ownership of the business, which has a rate of return of R_b and a level of risk of σ_b. Donna's marginal rate of substitution of return for risk
(
/
) is
=
where RP is Donna's portfolio rate of return and σP is her optimal portfolio risk. Donna's budget constraint is given by
RP = Rj +
σP. Solve for Donna's optimal portfolio rate of return and risk as a function of R_j, R_{b and} σ_b. Suppose the table below lists the relevant rates of returns and risks. Use this table to determine Donna's optimal rate or return and risk.
Investment Rate of Return Risk
Risk Free 0.06 0
Business 0.25 0.39

---

Definitions:

Net Income

The profit of a company after all expenses and taxes have been deducted from revenues.

Upstream Intra-Entity Profits

Profits realized from transactions between a parent company and its subsidiary, where the subsidiary sells to the parent.

Mutual Ownership

Refers to an arrangement where entities are owned by their members who share profits or benefits.

Consolidated Balance Sheet

A financial statement that shows the financial position of a parent company and its subsidiaries as if they were a single entity.