LOS m: Explain and apply methods to account for risk in venture capital.

Q1. A private equity investor expects to realize a return on her venture capital investment in two years and expects to sell the firm for $30 million. She estimates that a discount rate of 30% is reasonable but expects that there is a 20% probability of failure in any given year. The post-money value of her investment today, adjusted for failure, is closest to:

A)   $11.20.

B)   $14.20.

C)   $11.36.

Q2. The founders of a small technology firm are seeking a $3 million venture capital investment from prospective investors. The founders project that their firm could be sold for $25 million in 4 years. The private equity investors deem a discount rate of 25% to be appropriate, but believe there is a 20% chance of failure in any year.
The adjusted pre-money valuation (PRE) of the technology firm is closest to (in millions):

A)   $4.19.

B)   $7.24.

C)   $1.19.

Q3. A private equity investor calculates a discount rate of 40% for valuing a company. The investor, however, believes that there is a 20% chance that the company will fail in any one year. The most appropriate adjusted discount rate the investor should use is:

A)   75.0%.

B)   48.0%.

C)   50.0%.

Q4. The least likely factor affecting venture capital firm valuation is the:

A)   private equity firm’s initial investment.

B)   bargaining power of the venture capital and private equity firms.

C)   probability of failure.

Q5. A private equity investor is considering an investment in a venture capital firm, and is looking to calculate the firm’s terminal value. The investor determines that there is equal likelihood of the following:

1. Expected firm earnings are $2.5 million with a P/E ratio of 8.
2. Expected firm earnings are $3.0 million with a P/E ratio of 10.

The firm’s expected terminal value, and the analysis used by the investor, respectively, is:

              Terminal value                Analysis

A)      $2.75 million                 Sensitivity

B)       $50 million                  Scenario

C)      $25 million                    Scenario

LOS m: Explain and apply methods to account for risk in venture capital. fficeffice" />

Q1. A private equity investor expects to realize a return on her venture capital investment in two years and expects to sell the firm for $30 million. She estimates that a discount rate of 30% is reasonable but expects that there is a 20% probability of failure in any given year. The post-money value of her investment today, adjusted for failure, is closest to:

A)   $11.20.

B)   $14.20.

C)   $11.36.

Correct answer is C)

The investor must first adjust the discount rate for the probability of failure:

r* = (1 + r) / (1 ? q) ? 1, where r is the unadjusted discount rate, and q is the probability of failure.

r* = (1 + 0.30) / (1 ? 0.20) ? 1 = 0.625

To determine the post-money valuation, the projected future value must then be discounted at the adjusted discount rate:

POST = FV / (1 + r*)^N = ($30 million) / (1.625)² = $11.36 million

Q2. The founders of a small technology firm are seeking a $3 million venture capital investment from prospective investors. The founders project that their firm could be sold for $25 million in 4 years. The private equity investors deem a discount rate of 25% to be appropriate, but believe there is a 20% chance of failure in any year.
The adjusted pre-money valuation (PRE) of the technology firm is closest to (in millions):

A)   $4.19.

B)   $7.24.

C)   $1.19.

Correct answer is C)

The general formula for determining the pre-money value (PRE) is to first discount the exit (sale) value at the appropriate discount rate to its present value. This value is called the post-money value (POST). The pre-money value is the post-money value less the investment (INV):
POST = FV / (1+r)ffice:smarttags" />^N
PRE = POST ? INV
This would yield a PRE value of $7.24 million when using the unadjusted discount rate of 25%. This rate, however, must be adjusted for the possibility of failure in any particular year. This is calculated as follows:
r* = (1 + r) / (1 ? q) ? 1, where r is the unadjusted discount rate and q is the probability of failure.
The discount rate adjusted for failure is then:
r* = (1 + 0.25) / (1 ? 0.20) ? 1 = 0.5625 or 56.25%
The pre value is then calculated as:
POST* = $25 / (1.5625)4 = $4.19 million.
PRE* = $4.19 ? $3.0 = $1.19 million.

Q3. A private equity investor calculates a discount rate of 40% for valuing a company. The investor, however, believes that there is a 20% chance that the company will fail in any one year. The most appropriate adjusted discount rate the investor should use is:

A)   75.0%.

B)   48.0%.

C)   50.0%.

Correct answer is A)

The discount rate adjusted for the probability of failure is calculated as follows:
r* = (1 + 0.40) / (1 ? 0.20) ? 1 = 0.75 or 75%

Q4. The least likely factor affecting venture capital firm valuation is the:

A)   private equity firm’s initial investment.

B)   bargaining power of the venture capital and private equity firms.

C)   probability of failure.

Correct answer is A)

The probability of failure is often factored in to adjust the discount rate (IRR) which could significantly affect firm valuation. The bargaining power between the two parties affects the final price paid for the venture capital firm. The private equity firm’s initial investment has no direct bearing on venture capital firm valuation.

Q5. A private equity investor is considering an investment in a venture capital firm, and is looking to calculate the firm’s terminal value. The investor determines that there is equal likelihood of the following:

1. Expected firm earnings are $2.5 million with a P/E ratio of 8.
2. Expected firm earnings are $3.0 million with a P/E ratio of 10.

The firm’s expected terminal value, and the analysis used by the investor, respectively, is:

              Terminal value                Analysis

A)      $2.75 million                 Sensitivity

B)       $50 million                  Scenario

C)      $25 million                    Scenario

Correct answer is C)

The investor is using scenario analysis to determine the venture capital firm’s terminal value. The terminal value under each scenario is calculated by multiplying the expected earnings by the P/E ratio:
Scenario 1: $2.5 million × 8 = $20 million
Scenario 2: $3.0 million × 10 = $30 million
The expected terminal value is then the weighted value under each scenario:
Expected terminal value = (0.50)($20 million + $30 million) = $25 million.

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