Healthcare is becoming increasingly automated with the development and deployment of care robots. There are many benefits to care robots but they also pose many challenging ethical issues. This paper takes care robots for the elderly as the subject of analysis, building on previous literature in the domain of the ethics and design of care robots. Using the value sensitive design (VSD) approach to technology design, this paper extends its application to care robots by integrating the values of care, values that are specific to AI, and higher-scale values such as the United Nations Sustainable Development Goals (SDGs). The ethical issues specific to care robots for the elderly are discussed at length alongside examples of specific design requirements that work to ameliorate these ethical concerns.