$4)$ Estimate the beta of the combined entity $($Pampa $+$ CCC$)$ after the merger. Based on your answer, will the merged firms cost of capital to be higher or lower than Pampas current cost of capital? Explain your answer. Hint: Firm beta is a value$-$weighted average of individual betas.

Pampa RV$,$ Inc. is considering the acquisition of Chico Clothing Company $($CCC$)$ for a price of

$9\mathrm{.}75$ per share. The book value of the common stock is

$3,500,000$ and a yield to maturity of $3\mathrm{.}4\%.$ Based on current market valuations, Pampa is currently achieving its target debt to equity ratio. Pampas equity beta is $0\mathrm{.}80.$

CCCs cost of goods sold $($COGS$)$ is expected to be $38\%$ of sales revenues, and selling, general and administrative $($SG&A$)$ expenses are expected to be $12\%$ of revenues. The firm is $100\%$ equity financed and has $100,000$ shares of common stock outstanding. Its equity beta is estimated to be $1\mathrm{.}353.$

CCC has experienced rapid growth over the last ten years. However, your analysis of industry structure suggests that competition in the beauty pageant clothing and accessories market is likely to increase in the next few years. Thus, you forecast that the perpetual growth rate for free cash flows after five years will be a modest $1\mathrm{.}5\%$ per year. The corporate tax rate is $40\%$ for all firms.

Table $1$

Forecast Data for Chico Clothing Company

Year $1$ Year $2$ Year $3$ Year $4$

Sales Revenue

$300,000335,000375,000410,000$

In