Consider a venture to develop a new video game system for babies. The system is designed to be installed in child$-$safety car seats. If everything goes according to the entrepreneur's plan, the venture can achieve sales of $$10$ million in four years. At that point, based on market information for similar companies, the venture could be offered to the public at a multiple of $6$ times annual sales. To complete development of the venture, the entrepreneur anticipates needing $$1$ million in capital immediately, $$1\mathrm{.}5$ million in year $1,$ $$2$ million in year $2,$ and $$3$ million in year $3.$ Capital that is raised in advance of when it is needed can be invested to earn an annual return of $5$ percent.

$$Suppose the investor uses hurdle rates of $75$ percent for current investment, $60$ percent for year$-1$ investment, $45$ percent for year$-2$ investment, and $30$ percent for year$-3$ investment. How much capital does the entrepreneur need if all of the investment is provided now? How much of the equity would the investor require for making such an investment?

$$Now$,$ suppose the investor would make annual contributions of the needed amounts of capital $($in four stages$).$ How much of the equity would the investor require at each stage? Assuming that the venture is successful and that its projections are on target, how much of the equity would the investor ultimately require?

$$Finally$,$ suppose the venture survives but is significantly less successful than the entrepreneur projects it to be$.$ At the time of the year$-1$ investment, the revenue projection is reduced to $$9$ million, at the time of the year$-2$ investment, it is reduced to $$7\mathrm{.}5$ million, and at the time of the year$-3$ investment, it is reduced to $$6$ million. All other assumptions are unchanged. What fraction of the equity would the investor ultimately require? SOLVE THIS ON EXCEL