You should bring your data into long (i.e. molten) format to use it with ggplot2:
library("reshape2")
mdf <- melt(mdf, id.vars="Company", value.name="value", variable.name="Year")
And then you have to use aes( ... , group = Company ) to group them:
ggplot(data=mdf, aes(x=Year, y=value, group = Company, colour = Company)) +
geom_line() +
geom_point( size=4, shape=21, fill="white")
