$B1.$ HKU is planning the purchase of either machine $A$ or machine $B.$

$($a$)$ The interest rate is $10\%,$ and all cash flows may be treated as end$-$of$-$year cash flows.

Assume that equivalent annual cost is the value of the constant annuity equal to the

total cost of a project. Determine the equivalent annual cost of machine B$.$

$(8$ marks$)$

$($b$)$ If funds equal to the present worth of the cost of purchasing and using machine $A$

over $20$ years were invested at $10\%$ per annum, Determine the value of the investment

at the end of $20$ years would be most nearly.

$(6$ marks$)$

$($c$)$ How much money would have to be placed in a sinking fund each year to replace

machine $B$ at the end of $25$ years if the fund yields $10\%$ annual compound interest

and if the first cost of the machine is assumed to increase at a $6\%$ annual compound

rate? $($Assume the salvage value does not change$).$

$(6$ marks$)$