An internet caf$$ is considering investing in a new photocopying machine to maximize its productive capacity for photocopying documents. The purchase price of the new machine is $ $673,800$ which will have an economic life of five years. There is installation and commissioning cost of $$47,000$ and $$28,000$ respectively. It is estimated that a market exists for $42,500$ bottles of sugar wax locally per annum.

Each bottle of sugar wax will be sold for $$160$ and will cost $$90$ to produce. A previous market research has indicated that the small business could gain $15\%$ of the market in the first three years and $10\%$ in the final two years.

Other relevant information are as follows:

Variable distribution cost of $$8$ each

Annual promotion cost of $2\%$ of sales revenue

Use the straight$-$line method for depreciation. There is a scrap value of $$10,000.$

The required rate of return on debt is $20\%$ and return on equity is $14\%$

Currently the assets of the company are funded by $70\%$ debt and $30\%$ equity

Corporation tax rate is $30\%.$

$***$ Depreciation is an allowable deduction for tax purposes.

Required:

$($a$)$ The annual operating income after tax and the operating cash flows of the project and the net present value $($NPV$).$

$(30$ marks$)$

$($b$)$ Internal Rate of Return and Profitability index of the project.

$(8$ marks$)$

$($c$)$ A Recommendation to the management team to accept or reject the project. $(2$ marks$)$

Question #$2(20$ marks$)$

A company operates using a standard marginal costing system and manufactures one product and management is trying to assess its operations. Standard revenue and cost data is provided for Cinco.

Selling price $,$$$48\mathrm{.}00$

Direct material $A,2\mathrm{.}5kg$ at $$6\mathrm{.}80$ per kg

Direct material B $,1\mathrm{.}5kg$ at $$4\mathrm{.}80$ per kg

Direct labour $,0\mathrm{.}45$ hrs$.$ at $$24\mathrm{.}00$ per hour

Actual data for the twelve$-$month period was as follows:

Sales and production $48,000$ units of the blaster were produced and sold for $$2,323,200$

Direct material A $,121,950kg$ were used at a cost of $$804,870$

Direct material B $,67,200kg$ were used at a cost of $$336,000$

Direct labour Employees worked for $18,900$ hours, but $19,200$ hours were paid at a cost of $$468,480$

Budgeted sales for the period were $50,000$ units of Product Blaster. A recession last year meant that the market for the product declined by $10\%.$

Required:

$($a$)$ Calculate the following variances.

$($i$)$ Sales volume variance.

$(2$ marks$)$

$($ii$)$ Planning and operational variances for sales volume.

$(4$ marks$)$

$($iii$)$ Price, mix and yield variances for each material.

$(10$ marks$)$

$($b$)$ Suggest two possible explanations for the material price and yield variances calculated in part $($a$).$

$(4$ marks$)$