Question $3$

Driver plc is fully financed by $2\mathrm{.}5$ million equity shares with a current $($cum$-$div$)$ market value of $2\mathrm{.}29$ each. The current dividend of $0\mathrm{.}16$ per share is about to be paid. The firm has been paying a constant dividend of $0\mathrm{.}16$ per share for several years.

The finance director of Driver has proposed that the firm invests $1$ million now in more efficient machinery, which will save the firm $227,500$ per year in perpetuity.

The first saving will be in one year. To obtain the funds for investment, Driver can make a onetime reduction in the current dividend to $0\mathrm{.}06$ per share. Alternatively, Driver could raise external finance through a rights issue. Issue costs associated with the rights issue will be $25,000.$

The market is semi$-$strong form efficient, and there are no taxes.

$($a$)$ Demonstrate that the total present value of the cash inflows from the project is ${}_{3\mathrm{.}25}$ million.

$(3$ marks$)$

$($b$)$ If the firm funds the project by reducing the current dividend, what will be the ex$-$div price per share after the project acceptance?

$(4$ marks$)$

$($c$)$ If the firm funds the project by a $1$ for $5$ rights issue priced at $2$ per share, what will be the ex$-$div equilibrium price per share after the project acceptance?

$(5$ marks$)$

$($d$)$ A representative shareholder concerned only about her wealth owns $250$ shares in Driver before the rights issue. What change in her wealth will result from:

$($i$)$ taking up the rights and receiving a full dividend?

$($ii$)$ receiving a reduced dividend with no rights issue?

Are the two wealth outcomes the same? Explain why or why not.

$(6$ marks$)$

$($e$)$ Assume now that Driver chooses to fund the project by cutting the current dividend to $0\mathrm{.}06$ per share. All income from capital gains is taxed at a rate c; all income from dividends is taxed at a rate $d.$ Assume also that the rates $c$ and $d$ are the same, and the inflation rate is zero. There are no other market imperfections.

For next year and the foreseeable future, Driver can pay a constant dividend of either $0\mathrm{.}06$ or $0\mathrm{.}16$ per share. Will the shareholder in part $($d$)$ be indifferent between the two payout policies? Carefully explain your reasoning.

$(7$ marks$)$