Question

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; $2 800 000 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 $750 000, one year from now, two years from now, three years from now, and four years from now. Plan B would require $300 000 now, $700 000 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 $2 800 000 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 $2 800 000. The treasurer expects that Precision Machining Corporation can invest the $2 800 000 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.
a) Could Precision Machining Corporation meet the cash requirement of Plan B by investing the $2 800 000 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?
c) Suppose Plan A was changed so that it required equal amounts of $750 000 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 $2 800 000 as described above? (Use “now ” as the focal date.)
d) What is the difference between the cash required and the cash available from the investment. e ) Suppose the treasurer found another way to invest the $2 800 000 that earned interest at a rate of 4.9% compounded quarterly for the next five years.
Could the company meet the cash requirements of the original Plan A with this new investment? (Show all your calculations.)
f)Could the company meet the cash requirements of Plan B with this new investment? (Show all your calculations.)
g)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?

Answer 1

a. Yes, Precision Machining Corporation can meet the cash requirement of Plan B. Let's make necessary calculations. The company requires $300000 for expansion right now so remaining amount $2500000 (2800000 less 300000), the company will invest at 4.5% compounded semi annualy for 1st year. Note that formula for annual compounding is principle amount * (1+r)^n, where r is intrest rate and n is time period in year. since it is semi annual compounding, we will divide intrest rate r by 2 and multiply time period n by 2.
At end of 1st year, company will receive $2613765.625 (2500000*1.0225^2). Out of this amount, it will need $700000 at that time. It will invest remaining amount $1913765.625 at 5% semi annually compounded for 2nd year.
At end of 2nd year, company will receive $2010650 (1913765.625*1.025^2). Out of this amount, it will need $900000 and invest remaining amount $1110650 at 5% compounded intrest semi annualy for third year and 5.5% for 4th year.
At end of 3rd year, company will receive $1166877 (1110650*1.025^2). the company does not require cash at end of 3rd year in plan B so it will invest entire amount at 5.5% intrest semi annually compounded in 4th year.
At end of 4th year, it will receive $1231938 (1166877*1.0275^2). out of this, it will need $975000.

B. Exact difference between cash available at end of 4th year and cash required at end of 4th year is (1231938 - 975000) = $256938.

C. Yes, The company can meet cash requirement according to new plan A. let's make calculations. Now, company has $2800000 and requires $750000 immediately. It will invest remaining amount at 4.5% intrest compounded semi annualy.
At end of 1st year, it will receive $2143288 (2050000*1.0225^2). out of which it will require $750000 and invest remaining amount at 5% intrest compounded semi annualy for 2nd year.
At end of 2nd year, it will receive $1463823 (1393288*1.025^2). Out of which it will require $750000 and invest remaining amount at 5% compounded semi annually for 3rd year and 5.5% for 4th year.
At end of 3rd year, it will receive $749960 (713823*1.025^2). It doesn't require any cash at end of 3rd year, so it will invest entire amount at 5.5% compounded semi annualy in 4th year.
At end of 4th year, it will receive $791775 (749960*1.0275^2. Out of this amount, it will require $750000.

D. Difference between cash available and cash required is (791775 - 750000) = $41775.