$1.$ Daystream, Inc. is considering adding a new line of toys to its current product line. The new line will require an additional investment of $$100,000$ in raw materials to produce the toys. The project$$s life is $7$ years and the firm estimates sales of $500,000$ packages at a price of $$8$ per unit the first year; but this volume is expected to grow at $15\%$ for the next three years $($year $2$~year $4),12\%$ for the last three years of the project $($year $5$~year $7).$ The price per unit is expected to grow at $6\%$ for the next four years $($year $2$~year $5),$ and then at the historical average rate of inflation of $3\mathrm{.}5\%$ for the last two years $($year $6$~year $7)$ of the project. The variable costs will be $65\%$ of sales and the annual fixed costs will be $$500,000.$ The equipment required to produce the toys will cost $$1,500,000,$ and will require an additional $$150,000$ to have it delivered and installed. This equipment has an expected useful life of $7$ years and will be depreciated using the MACRS $5-$year class life. After $7$ years, the equipment can be sold at a price of $$300,000.$ The cost of capital is $12\%$ and the firm$$s marginal tax rate is $35\%.$ a$.$Calculate the initial investment, annual after$-$tax cash flows for each year, and the terminal cash flow. $(9$ points$)$ b$.$Determine the payback period, discounted payback period, NPV$,$ PI$,$ IRR, and MIRR of the new line of toys. $(9$ points$)$ c$.$The firm is considering three scenarios for the new line of toys. Under the best, base, and worst case scenario the firm will sell $300,000,500,000,$ and $700,000$ packages the first year with the same expected growth rates in units and price described in the problem. What are the payback period, discounted payback period, NPV$,$ PI$,$ IRR, and MIRR under each of these scenarios. $(7$ points$)$ MACRS $5-$Year depreciation $1-20\mathrm{.}00\%2-32\mathrm{.}00\%3-19\mathrm{.}20\%4-11\mathrm{.}52\%5-11\mathrm{.}52\%6-5\mathrm{.}76\%7-0$