Questions: An analyst has determined that the appropriate EV/EBITDA for Rainbow Company is 10.2. The analyst has also collected the following forecasted information for Rainbow Company: EBITDA = 22,000,000 Market value of debt = 56,000,000 Cash = 1,500,000 The value of equity for Rainbow Company is closest to: A. 169,000,000. B. 224,000,000. C. 281,000,000.

To determine the value of equity for Rainbow Company, we can use the EV/EBITDA multiple provided by the analyst. The formula for Enterprise Value (EV) using the EV/EBITDA multiple is:

\[ \text{EV} = \text{EBITDA} \times \text{EV/EBITDA multiple} \]

Given:

• EBITDA = \$22,000,000
• EV/EBITDA multiple = 10.2

First, calculate the Enterprise Value (EV):

\[ \text{EV} = 22,000,000 \times 10.2 = 224,400,000 \]

The Enterprise Value (EV) is the total value of the company, which includes both debt and equity, minus cash. The formula to find the value of equity is:

\[ \text{Equity Value} = \text{EV} - \text{Market Value of Debt} + \text{Cash} \]

Given:

• Market Value of Debt = \$56,000,000
• Cash = \$1,500,000

Now, calculate the Equity Value:

\[ \text{Equity Value} = 224,400,000 - 56,000,000 + 1,500,000 \]

\[ \text{Equity Value} = 169,900,000 \]

The value of equity for Rainbow Company is closest to \$169,000,000.

Therefore, the answer is A: \$169,000,000.

Explanation for each option:

• A. \$169,000,000: This is the closest value to the calculated equity value of \$169,900,000.
• B. \$224,000,000: This option is incorrect as it represents the Enterprise Value, not the equity value.
• C. \$281,000,000: This option is incorrect as it is higher than the calculated equity value and does not match the given data.