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Part $1$

Assume$$ you've generated the following information about the stock of$$ Ben's Banana$$ Splits: The$$ company's latest dividends of $$$$2\mathrm{.}312\mathrm{.}31$ a share are expected to grow to $$$$2\mathrm{.}562\mathrm{.}56$ next$$ year, to $$$$2\mathrm{.}842\mathrm{.}84$ the year after$$ that, and to $$$$3\mathrm{.}153\mathrm{.}15$ in year $3.$ After$$ that, you think dividends will grow at a constant $66\%$ rate.

a$.$ Use the variable growth version of the dividend valuation model and a required return of $1212\%$ to find the value of the stock.

b$.$ Suppose you plan to hold the stock for three$$ years, selling it immediately after receiving the $$$$3\mathrm{.}153\mathrm{.}15$ dividend. What is the$$ stock's expected selling price at that$$ time? As in part a$,$ assume a required return of $1212\%.$

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$$ stock's current market price is actually $$$$45\mathrm{.}1545\mathrm{.}15.$ Based on your analysis from part a$,$ is the stock overvalued or$$ undervalued?

e$.$ A friend of yours agrees with your projections of$$ Ben's Banana Splits future$$ dividends, but he believes that in three$$ years, just after the company pays the $$$$3\mathrm{.}153\mathrm{.}15$dividend$,$ the stock will be selling in the market for $$$$55\mathrm{.}1055\mathrm{.}10.$ Given that$$ belief, along with the$$ stock's current market price from part d$,$ calculate the return that your friend expects to earn on the stock over the next three years