Case Study $-$ Planning Ahead

Precision Machining Corporation has been growing steadily over the past decade. Demand for the company$$s products continues to rise, so management has decided to expand the production facility; $$2800000$ has been set aside for this over the next four years.

Management has developed two different plans for expanding over the next four years: Plan A and Plan B$.$ Plan A would require equal amounts of $$750000,$ one year from now, two years from now, three years from now, and four years from now. Plan B would require $$300000$ now, $$700000$ one year from now, $$900000$ two years from now, and $$975000$ four years from now.

The company has decided to fund the expansion with only the $$2800000$ and any interest it can earn on it$.$ Before deciding which plan to use, the company asks its treasurer to predict the rates of interest it can earn on the $$2800000.$ The treasurer expects that Precision Machining Corporation can invest the $$2800000$ and earn interest at a rate of $4\mathrm{.}5\%$ p$.$a$.$ compounded semi$-$annually during Year $1,5\mathrm{.}0\%$ p$.$a$.$ compounded semi$-$annually during Years $2$ and $3,$ and $5\mathrm{.}5\%$ p$.$a$.$ compounded semi$-$annually during Year $4.$ The company can withdraw part of the money from this investment at any time without penalty.

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Question #:$\_\_\_\_\_\_\_1\_\_\_\_\_\_\_(10$ Marks$)$

Case Study $-$ Planning Ahead

Precision Machining Corporation has been growing steadily over the past decade. Demand for the company$$s products continues to rise, so management has decided to expand the production facility; $$2800000$ has been set aside for this over the next four years.

Management has developed two different plans for expanding over the next four years: Plan A and Plan B$.$ Plan A would require equal amounts of $$750000,$ one year from now, two years from now, three years from now, and four years from now. Plan B would require $$300000$ now, $$700000$ one year from now, $$900000$ two years from now, and $$975000$ four years from now.

The company has decided to fund the expansion with only the $$2800000$ and any interest it can earn on it$.$ Before deciding which plan to use, the company asks its treasurer to predict the rates of interest it can earn on the $$2800000.$ The treasurer expects that Precision Machining Corporation can invest the $$2800000$ and earn interest at a rate of $4\mathrm{.}5\%$ p$.$a$.$ compounded semi$-$annually during Year $1,5\mathrm{.}0\%$ p$.$a$.$ compounded semi$-$annually during Years $2$ and $3,$ and $5\mathrm{.}5\%$ p$.$a$.$ compounded semi$-$annually during Year $4.$ The company can withdraw part of the money from this investment at any time without penalty.

$$

Question #:$\_\_\_\_\_\_\_1\_\_\_\_\_\_\_(10$ Marks$)$

a$.$ Could Precision Machining Corporation meet the cash requirement of Plan A by investing the $$2800000$ as described above? $($Use $$now$$ as the focal date.$)$

b$.$ What is the exact difference between the cash required and the cash available from the investment?

Question #:$\_\_\_\_\_\_\_2\_\_\_\_\_\_\_(10$ Marks$)$

c$.$ Could Precision Machining Corporation meet the cash requirement of Plan B by investing the $$2800000$ as described above? $($Use $$now$$ as the focal date.$)$

d$.$ What is the exact difference between the cash required and the cash available from the investment?

Question #:$\_\_\_\_\_\_\_3\_\_\_\_\_\_\_(10$ Marks$)$

a$.$ Suppose Plan A was changed so that it required equal amounts of $$750000$ now, one year from now, two years from now, and four years from now. Could Precision Machining Corporation meet the cash requirements of the new Plan A by investing the $$2800000$ as described above? $($Use $$now $$ as the focal date.$)$

b$.$ What is the difference between the cash required and the cash available from the investment?

Question #:$\_\_\_\_\_\_\_4\_\_\_\_\_\_\_(10$ Marks$)$

Suppose the treasurer found another way to invest the $$2800000$ that earned interest at a rate of $4\mathrm{.}9\%$ compounded quarterly for the next five years.

a$.$ Could the company meet the cash requirements of the original Plan A with this new investment? $($Show all your calculations.$)$

b$.$ Could the company meet the cash requirements of Plan B with this new investment? $($Show all your calculations.$)$

c$.$ If the company could meet the cash requirements of both plans, which plan would the treasurer recommend? In other words, which plan would have the lower present value?