roblem $2\mathrm{.}4.$ In Problem $2\mathrm{.}3,$ assume the first phase $($the R&D phase$)$ has proceeded very well; a successful prototype soap powder was successfully developed at the end of Year $3($at a cost of $$6$ million each year$).$ At the beginning of the fourth year $($before the company begins developing test marketing$),$ a long$-$time rival announces that it will have a similar product available next year.

Trid Soap Company managers feel there is a $75\%$ probability that their product is superior to their competitor$$s product. If the company$$s product is superior, they will earn a net profit of $$12$ million per year; otherwise, the company will lose $$3$ million per year. Trid senior managers are considering the possibility of suspending the project for a year to get more information on their competitor$$s product before launching their new soap powder. If they wait, however, and their product is superior, the life span of the new product would be reduced to $4$ years. What would you recommend in this case $($the cost to launch the new product is still $$5\mathrm{.}5$ million$)?($Assume an annual discount rate of $12\%.)$