There are numerous factors that affect the price of a new roof. Unfortunately, this makes giving an accurate estimate impossible without inspecting your composite roof. A home with three bedrooms and two bathrooms, a walkable roof pitch, and architectural composition (asphalt) shingles is expected to cost between $12,000 and $15,000. It is possible that your composite roof will cost less, more, or be right in the price range listed above. Because no two houses or roofs are alike, there is no way to determine.