Irving Ship Building is planning a major expansion of its present production facility. The total cost of

the project is estimated at $$20$ million over the next seven years. Of this, $$4$ million is to be spent in

the first year, $$3$ million in the second, $$2$ million in each of the third, fourth, fifth, and sixth years,

and $$5$ million in the seventh year.

$($a$)$ Assuming that all expenditures occur at the end of the year, and Irving$$s discount rate is $15\%,$

what is the present value of the cost of this project? $(5$ marks$)$

$($b$)$ If revenues for the project are expected to start in year $3$ at $$1$ million, then increase to $$2$ million

for year $4,$ $$3$ million for year $5,$ and $$4$ million for years $6$ and $7.$ Would you approve the project

given the $15\%$ internal rate of return and seven$-$year return period?

$($c$)$ Would your conclusion change if the time horizon was shortened to an eight$-$year term $($assume

there are no costs in year $8,$ and revenues continue at $$4$ million$)?$