Hamisi Company ltd purchased a packing machine $4$ years ago at a cost of Sh$\mathrm{.}13\mathrm{.}5$ million. The machine had a life of $9$ years at the time of purchase. The company is considering replacing it with a new packing machine costing Sh$\mathrm{.}18$ million with an expected useful life of $5$ years. Due to increased efficiency, the sales are expected to increase by Sh$.2,550,000$ a year, the labor costs would decrease by Sh$.1,260,000$ per year while the maintenance costs would increase at the following rate:

Year Maintenance Costs

$1$

$2$

$3$

$4$

$5150,000$

$330,000$

$405,000$

$435,000$

$504,000$

The salvage value of the new packing machine is estimated at Sh$.2,057,022\mathrm{.}28.$ The market value of the old machine, today, is Sh$\mathrm{.}10\mathrm{.}5$ million. It is estimated to have a zero salvage value after $5$ years. The company$$s tax is $30\%.($Assume depreciation has no effect$).$ The company$$s capital structure is as shown in the following table.

Source of Capital

$100,000$ Ordinary Shares @$100/-10,000,000\mathrm{.}00$

$10\%$ Loan Stock $6,000,000\mathrm{.}00$

$8\%$ Preference Shares $4,000,000\mathrm{.}00$

$20,000,000\mathrm{.}00$

The expected ordinary share dividend was Ksh $31\mathrm{.}20$ per share while the current market price is double the par value. The shares are expected to grow at a constant rate of $5\%$

Required

a$)$ Compute Hamisi Company Ltd$$s average cost of capital $(4$ Marks$)$

b$)$ Hamisi Company ltd prefers NPV approach in appraising their projects. Advise Hamisi ltd on whether the new grinder should be bought. $(6$ Marks$)$