What was done mathematically to get $10,000 to the left of the equal sign in the 4th equation above? What was done mathematically to get the $1,200 ($10,000 x 0.12 = $1,200) on the numerator area and 0.12 (12/100 = 0.12) on the denominator of the fraction that you see at the very bottom? Or, why does the last step look like V = $1,200/0.12, V = $10,000? Can you show me the step by step work with explanations too, please? Thank you very much!

Suppose investors have invested $10,000 in common equity in a company. Given the risk of the company, the investors expect to earn a 12% return, and they expect the company to pay out 100% of income in dividends each year. The required income of the company each period is as follows: RE X BV -1 = 0.12 x $10,000 = $1,200 Suppose the investors forecast that the company will generate exactly $1,200 in comprehensive income each year. The investors should compute the residual income of the firm as follows: CI. - (R; X BV,-1) = $1,200 (0.12 * $10,000) = $0 Using the residual income approach, investors would value this firm based on book value plus expected future residual income as follows: Vo = BV. + CI, - (REX BV-1) (1 + Rp)' $1,200 -(0.12 x $10,000) = $10,000+ (1 +0.12) $0 = $10,000 + = $10,000 (1 +0.12) I=1 I=1 In this case, the firm's expected future income exactly equals the required income neces- sary to cover the cost of equity capital. So residual income is zero and the value of the firm is equal to the book value of common equity invested in the firm. The value of the firm under the residual income model is identical to the value determined using the div- idends valuation model, which would value the company as a stream of dividends in perpetuity with no growth as follows: $1,200 Vo = = $10,000 0.12