### Question Description

A venture investor, BKAngel, is considering investing in a software venture opportunity. However, the rate of return to be realized next year is likely to vary with the economic climate that actually occurs. Following are three possible economic outcomes, the probability that each one will occur, and the rate of return projected for each outcome:

Economic Probability of Rate of

Climate Occurrence Return

Recession .25 -20.0%

Normal .50 15.0%

Rapid Growth .25 30.0%

1. What is the expected rate of return on the software venture?

2. Calculate the variance and standard deviation of the rates of return for the software venture?

3. Calculate the coefficient of variation of the rates of return for the software venture. If the coefficient of variation of rates of return for BKAngel’s prior venture investments is 1.5, would the software venture be considered as being less or more risky?

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Expected return = ??

Standard deviation = ??

Coefficient of variation = standard deviation / expected return = ??

Voice River, Inc. has successfully moved through its early life cycle stages and now is well into its rapid growth stage. However by traditional standards this provider of media-on-demand is still considered to be a relatively small venture.

The interest rate on long-term US government securities is currently 7 percent. Voice River’s management has observed that over the long-run the average annual rate of return on small firm stocks has been 17.3 percent while the annual returns on long-term U.S. government securities has averaged 5.7 percent.

Management views Voice River as being an average small company venture at its current life cycle stage.

1. Determine the historical average annual market risk premium for small firm common stocks.

Avg. historical MRP = (Avg. historical return) – (Avg. historical risk free rate) = ??

2. Use the capital asset pricing model (CAPM) to estimate the cost of common equity capital for Voice River.

Note that beta = 1, as against the small firm stocks = 1.

CAPM = (rf) + (MRP) x (B) = ??

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