Cruz plan for corporate tax is a form of VAT, but there is no collection at each step. From Tax Foundation:
Enacts a broad-based, 16 percent “Business Transfer Tax” or value-added tax. This tax is levied on all business profits, less capital investment. This would include the payroll of business, government, and non-profit institutions, as well as net imports. The tax would exempt from taxation the purchase of health insurance. A business transfer tax is also often known as a subtraction-method value-added tax. While its base is identical in economic terms to that of the credit-invoice VAT seen in many OECD countries, it is calculated from corporate accounts, not on individual transactions.
http://taxfoundation.org/article/details-and-analysis-senator-ted-cruz-s-tax-plan
Does the Cruz VAT incentivize exports and level the ‘stealth vats’ playing field of other countries?