William, a technology expert, is considering a new business venture in developing

skin implant equipment for mobile phones. The first annual sales of $4$ million are

expected to be achieved in $4$ years$$ time if venture goes according to the plan. At

that point, the venture could be offered to outside investors at a multiple of $6$ times

the annual sales. To complete the development, William estimates the venture

requires $300,000$ immediately, $350,000$ in year $1,400,000$ in year $2$ and

$450,000$ in year $3.$ Any capital raised before it is needed can be invested to earn a

$2\mathrm{.}5\%$ annual return.

Required:

$($a$)$ Using hurdle rate of $70\%$ for current investment, determine how much

capital William would need if all the investment is provided now? What

fraction of equity would the outside investors require for the investment? $[20]$

$($b$)($i$)$ Now assume that the investment to develop the equipment is raised in the

year when it is required. Assume that the outside investors use investment

hurdle rates of $70\%$ for current investment, $60\%$ for Year $1,50\%$ for Year

$2$ and $40\%$ for Year $3.$ How much equity would the outside investors

require at each stage?

$[20]$

$($ii$)$ Given the ownership dilution due to future financing rounds, what adjusted

percentage of equity should investors require now at each stage?

$[25]$

$($c$)$ Now assume that the business venture is more successful than originally

forecasted. At the end of year $1,$ the sales forecast in Year $4$ is increased

to $5$ million, at the end of year $2,$ it is increased to $6\mathrm{.}5$ million and at the

end of year $3,$ it is increased to $7$ million. Given that the other

assumptions remain unchanged, what percentage of the equity would the

outside investors ultimately require?