$1.$ Rainbow Co$,$ a medium$-$sized company specialising in the

manufacture and distribution of equipment for babies and small

children, is evaluating a new capital expenditure project. In a joint

venture with another separate company, it has invented a remote

controlled pushchair, one of the first of its kind on the market. It

has been unable to obtain a patent for the invention, but is sure

that it will monopolise the market for the first three years. After

this, it expects to be faced with stiff competition.

The details are set out below.

$(1)$ The project has an immediate cost of K$2,100,000.$

$(2)$ Sales are expected to be K$1,550,000$ per annum for years $1$ to $3,$

falling to K$650,000$ per annum for the two years after that. No

further sales of the product are expected after the end of this fiveyear period.

$(3)$ Cost of sales is $40\%$ of sales.

$(4)$ Distribution costs represent $10\%$ of sales.

$(5)20\%$ of net profits are payable to the joint venture partner the

year after the profits are earned.

$(6)$ The company's cost of capital is $5\%.$

Required

$($a$)$ Calculate the net present value of the project at the company's

required rate of return.

Assume that all cash flows arise annually in arrears unless

otherwise stated. Conclude whether the project is financially viable.

$($b$)$ Calculate the project's internal rate of return $($IRR$)$ to the nearest

percent.

$($c$)$ Calculate the project's simple payback period. Assume all cash

flows arise at the end of the year apart from the immediate investment costs