Smitty Nursing Homes Ltd is cash rich because of several consecutive good years. One of the alternative

uses for the excess funds is an acquisition. Linda Wade, Smitty's treasurer, has been asked to place a

value on a potential target, Hill Long Term Care, a small chain in an adjacent state. The table below

indicates Wade's estimates of Hill's earnings potential if it came under Smitty's management $($in millions

of dollars$).$ The interest expense here includes the interest on Hill's existing debt and on new debt

expected to be issued over time to help finance expansion within the new $"$H Division," the code name

given to the target firm. The retentions represent earnings that will be reinvested within the H Division

to help finance its growth.

Security analysts estimate Hill's beta to be $1\mathrm{.}3.$ The acquisition would not change Hill's capital structure

or tax rate, and its optimal capital structure is $40$ percent debt and $60$ percent equity. Wade estimates the

risk$-$free rate to be $9$ percent and the market risk premium to be $4$ percent. She also estimates that net

cash flows after Year $4$ will grow at a constant rate of $6$ percent. Smitty's tax rate is $21$ percent. Wade

has assembled the following forecasted data:

Year $1$ Year $2$ Year $3$ Year $4$

Net revenues $$60\mathrm{.}0$ $$90\mathrm{.}0$ $$112\mathrm{.}5$ $$127\mathrm{.}5$

Cash expenses $$43\mathrm{.}5$ $$61\mathrm{.}5$ $$78\mathrm{.}0$ $$90\mathrm{.}0$

Depreciation $$4\mathrm{.}5$ $$6\mathrm{.}0$ $$7\mathrm{.}5$ $$9\mathrm{.}0$

Earnings before interest and taxes $$12\mathrm{.}0$ $$22\mathrm{.}5$ $$27\mathrm{.}0$ $$28\mathrm{.}5$

Interest $$3\mathrm{.}0$ $$4\mathrm{.}5$ $$4\mathrm{.}5$ $$6\mathrm{.}0$

Earnings before taxes $$9\mathrm{.}0$ $$18\mathrm{.}0$ $$22\mathrm{.}5$ $$22\mathrm{.}5$

Taxes $(40$ percent$)$ $$3\mathrm{.}6$ $$7\mathrm{.}2$ $$9\mathrm{.}0$ $$9\mathrm{.}0$

Net profit $$5\mathrm{.}4$ $$10\mathrm{.}8$ $$13\mathrm{.}5$ $$13\mathrm{.}5$

Estimated retentions $$0\mathrm{.}0$ $$15\mathrm{.}0$ $$12\mathrm{.}0$ $$9\mathrm{.}0$

a$.$ What is the equity value of Hill using the free cash flow to equityholders $($FCFE$)$ method?

b$.$ Wade is quite confident of the estimated cash flows in the table above but is aware of the limitations of

the constant growth model. How sensitive is the equity value of Hill to different values of the constant

growth rate of the net cash flows after Year $4?($Hint: Graph the equity value at different values of g$,$

from $2$ to $12$ percent.$)$

c$.$ Assume Hill has $10$ million shares outstanding. These shares are traded relatively infrequently, but

the last trade, made several weeks ago, was at a price of $$16$ per share.

$-$ Should Smitty make an offer for Hill?

$-$ If so$,$ what is the range of how much Smitty should offer per share of Hill?

$-$ Construct a table that shows the gain$/$loss per share for Smitty and Hill over the range of offer per

share $($in one$-$dollar increments$),$ and graph the results.