The stock of ABC limited is expected to issue $$1$ of dividend next year. Analyst forecast suggests that the dividend will continue to drop by $2\%$ because of bad

performance caused by inflation. After examine ABC limited carefully, you decide the appropriate discount rate for this firm should be $4\%.$

a$)$ How much are you willing to pay to buy the stock of ABC limited if the dividend drops at $2\%$ forever? $(1$pt$)$

b$)$ All other information unchanged, now suppose the performance of ABC limited recovers in year $4$ and distribute $$1$ in year $4.$ After year $4,$ new forecast estimate that dividend will continue to grow by $2\%$ forever. How much are you willing to pay to buy the stock of ABC limited now?