Question

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; $2,600,000 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 $700,000, now, one year from now, two years from now, and four years from
now. Plan B would require $300,000 now, $730,000 one year from now, $900,000 two years from now, and
$975,000 four years from now.
The company has decided to fund the expansion with only the $2,600,000 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 $2,600,000. The treasurer expects that Precision Machining Corporation can invest the $2,600,000 and earn
interest at a rate of 4.5% p.a. compounded semi-annually during Year 1,5.0% p.a. compounded semi-annually
during Years 2 and 3, and 5.5% p.a. compounded semi-annually during Year 4. The company can withdraw part
of the money from this investment at any time without penalty.

Answer 1

Plan A

Explanation:

The attached spreadsheet shows the investment results for the two plans. (Amounts are in thousands.)

The "invested" column represents the amount that will be earning interest for the year beginning at the given time. The interest multiplier for the year is (1+r/2)^2, representing the growth factor for interest at rate r compounded semi-annually.

The "withdrawn" amount is taken out after the previous year's interest is credited.

Plan B cannot be funded using the given investment strategy. It falls short by about $22 thousand in year 4

The appropriate choice is Plan A.