Assume you've generated the following information about the stock of Ben's Banana Splits: The company's latest dividends of $$1\mathrm{.}94$ a share are expected to grow to $$2\mathrm{.}15$ next year, to $$2\mathrm{.}39$ the year after that, and to $$2\mathrm{.}65$ in year $3.$ After that, you think dividends will grow at a constant $5\%$ rate

a$.$ Use the variable growth version of the dividend valuation model and a required return of $12\%$ to find the value of the stock.

b$.$ Suppose you plan to hold the stock for three years, selling it immediately after receiving the $$2\mathrm{.}65$ dividend. What is the stock's expected selling price at that time? As in part a$,$ assume a required return of $12\%$

c$.$ Imagine that you buy the stock today paying a price equal to the value that you calculated in part a$.$ You hold the stock for three years, receiving dividends as described above. Immediately after receiving the third dividend, you sell the stock at the price calculated in part b$.$ Use the IRR approach to calculate the expected return on the stock over three years. Could you have guessed what the answer would be before doing the calculation?

d$.$ Suppose the stock's current market price is actually $$32\mathrm{.}00.$ Based on your analysis from part a$,$ is the stock overvalued or undervalued?

e$.$ A friend of yours agrees with your projections of Ben's Banana Splits future dividends, but he believes that in three years, just after the company pays the $$2\mathrm{.}65$ dividend, the stock will be selling in the market for $$53\mathrm{.}42.$ Given that belief, along with the stock's current market price from part $,$ calculate the return that your friend expects to earn on the stock over the next three years