$1.$ Bene plc is considering five project proposals. They are summarised

below:

Project Initial

investment

$(000)$

Annual revenue

$(000)$

Annual fixed

costs

$(000)$

Year $12341234$

A $1112121254422$

B $31171617174334$

C $45252525253333$

D $12201816144321$

E $18121226262233$

Variable costs are $10\%$ of annual revenue. Only $35,000$ is available in

cash and the directors intend to limit the capital expenditure over the next

$12$ months to this amount. The projects are independent and perfectly

divisible, none of them can be postponed.

Assume:

$-$ The cash flows are confined to within the lifetime of each project.

$-$ The cost of capital is $11\%.$

$-$ No inflation.

$-$ No risk.

$-$ No tax.

$-$ All cash flows occur on anniversary dates.

$1$a$)$ Calculate the expected net present values of the five projects.

$1$b$)$ Assuming no capital rationing, indicate which projects should be

selected and calculate the total net present value of the selected

projects.

$1$c$)$ Assume that a single period constraint of $35,000$ has been imposed.

What is the maximum net present value available if projects are selected

on the basis of net present value alone?

$1$d$)$ Now calculate benefit cost ratios and profitability indexes for the five

projects. Indicate which projects would be selected on the basis of

benefit cost ratio, and calculate the total net present value of the

selected projects. Demonstrate that the profitability index would produce

the same choice.

$1$e$)$ Indicate which projects would be selected under the above capital

constraint, if the projects were non$-$divisible.

$1$f$)$ Indicate which projects would be selected if projects D and E were

mutually exclusive $($assuming all projects are perfectly divisible$).$