At Home agreed May 6 to sell itself for $36 a share, noting at the time that the deal included a 40-day “go shop” period and gave Hellman & Friedman a chance to match competing bids should any materialize. At Home’s shares have been hovering above $36 since, suggesting shareholders expect the price tag could rise.

CAS said in the letter the deal “grossly undervalues the company and deprives stockholders of anything resembling a fair premium.” It suggested that a price above $70 a share would be more realistic based on its projections and said it is prepared to try to block the current deal if needed. The deal requires signoff from a majority of its shareholders.

At Home sells furniture, décor and other home goods such as bedding and seasonal decorations in more than 200 stores in 40 states. For the fiscal year ended Jan. 30, At Home posted a narrower loss of $149.7 million compared with the prior year as sales grew.

CAS, launched in 2012 by Clifford Sosin, is a value investor with a concentrated portfolio and about $2 billion under management. In its letter, CAS said it “is not an activist investor that seeks to engage in public disputes.”

Write to Dave Sebastian at dave.sebastian@wsj.com