How do you calcualte Yield To Maturity, given only the coupon rate and current required rate of return?
The yield-to-maturity is similar to an internal rate of return, so the calculations need to take into account the timing of cash flows. So your example calculation 10%/.90 = 11.11% does not work. (That is known as a simple interest convention, which I think is sometimes used in the Japanese bond market.)

The calculation form depends upon the coupon frequency of the bond. For an annual coupon, if we denote the yield as y, then the price of the bond equals (convention of \$100 equals par):
$$p = \sum_{i=1}^8 \frac{10}{(1+y)^i} + \frac{100}{(1+y)^8}.$$

However, I do not know what “required return” in the question refers to (a true internal rate of return?). You would need to find the price of the bond using that “required return,” and then work from the price equation to get the yield.