# Residual Income Question

My question is about the question below. When they solve for the continuing residual value they use the premium over book value and discount it back. However, they say that ROE is 10% after five years. That would make it equal to cost of equity and wouldnt that make the residual income zero going forward? Any help would be appreciated. Thanks. Question: Valdez Plastics is expected to have a return on equity (ROE) of 15 percent for the next five years and 10 percent thereafter, indefinitely. Its current book value per share as of the beginning of year 1 (i.e., the end of year 0) is \$8.50 per share and its required rate of return is 10 percent. The premium over book value at the end of five years is expected to be 40 percent. All earnings are reinvested. The sum of the present values of the residual income estimates over the next five years is \$2.10. The projected ending book value in year 5 is \$17.80. What is the value of Valdez Plastics using these inputs? Applying the finite horizon residual income valuation model: V0 = B0 + sum of discounted RIs + discounted premium = 8.50 + 2.10 + [(0.40)(17.80)/(1.10)5] = \$15.02

i suppose that is why the value [(roe-rr)*BV/9r-g)]is not used because the roe-rr is zero. Otherwise you would have that value [(roe-rr)*BV/(r-g)] added to BV and PV of the 5 year residual income …

But doesnt that imply that residual income is 0 going foward and not a premium to book value? Anyone else have a better explanation?