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.

Questions

1.

2.

3.

a. Could Precision Machining Corporation meet the cash requirement of Plan A 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?

a. Could Precision Machining Corporation meet the cash requirements of Plan B by investing the $2 800 000 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?

a. 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.)

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

the treasurer found another way to invest the $2 800 000 that earned interest at a rate of 4.9%

4. Suppose

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?

Answer 1

1. (a) Present value of cash payments for Plan A:

PV of $750 000 one year from now = 750 000(1.0225^-2) = $17 356

PV of $750 000 two years from now = 750 000(1.0225^-2)(1.025^-2) = 682 790

PV of $750 000 three years from now=750 000(1.0225^-2)(1.025^-2) = 649 889

PV of $750 000 four years from now = 750 000(1.0225^-2) (1.025^-2) (1.025^-2)(1.0275^-2) = 615 567 Total present value of payments = $2 665 602

Since the present value of the cash payment is less than $2 800 000, the cashrequirements of Plan A can be met by the investment.

(b) The difference between the investment and the present value of the cash payments = 2 800 000 − 2 665 602 = $134 398.

The accumulated value of the difference after four years =134 398(1.0225²) (1.025²) (1.025²) (1.0275²) = 163 748

The difference between the cash required and the cash available from the

investment is $163 748.

2. (a) Present value of cash payments for Plan B:

PV of $300 000 now = $300 000

PV of $700 000 one year from now = 750000(1.0225^-2) = 717 356

PV of $700 000 two years fromnow = 900000(1.0225^-2) (1.025^-2) = 819 348

PV of $975 000 four years from now

975 000(1.0225^-2) (1.025^-2) (1.025^-2) (1.0275^-2) = 800 237

Total present value of payments = $2 636 941

Since the present value of the cash payments is less than $2 800 000, thecash requirements of Plan B can be met by the investment.

(b) The difference between the investment and the present value of the cash payments = 2 800 000 − 2 636 941 = $1 630 59.

The accumulated value of the difference after four years =163 059(1.0225²) (1.025²) (1.025²) (1.0275²)

The difference between the cash required and the cash available from the investment is $198 669.

3. (a) Present value of cash payments for Plan A:

PV of $750 000 now = $750 000

PV of $750 000 one year from now = 750000(1.0225^-2) = 717 356

PV of $750 000 two year fromnow = 750 000 (1.0225^-2) (1.025^-2) = 682 790

PV of $750 000 four years from now =

750 000(1.0225^-2) (1.025^-2) (1.025^-2) (1.0275^-2) = 615 567

Total present value of payments = $2 765 713

Since the present value of the cash payments is less than $2 800 000, thecash requirements of Plan A can be met by the investment.

(b) The difference between the investment and the present value of the cash payments = 2 800 000 − 2 765 713 = $34 287.

The accumulated value of the difference after five years =

34 287(1.0225²) (1.025²) (1.025²) (1.0275²) = $41 775.

The difference between the cash required and the cash available from the investment is $41 775.

4. (a) Present value of cash payments for Plan A = 0.049/4 = 0.01225

PV of $750 000 one year from now = 750 000(1.01225^-4) =$714 349

PV of $750 000 two years from now = 750 000(1.01225^-8) = 680 392

PV of $750 000 three years from now = 750 000(1.01225^-12) = 648 049

PV of $750 000 four years from now = 750 000(1.01225^-16) = 617 244

Total present value of payments = $2 660 034

Since the present value of the cash payments is less than $2 800 000, thecash requirements of Plan A can be met by the investment.

(b) Present value of cash payments for Plan B = 0.049/4 = 0.01225

PV of $300 000 now = $300 000

PV of $700 000 one year from now = 700 000(1.01225^-4) = 666 725

PV of $900 000 two years from now = 900 000(1.01225^-8) = 816 470

PV of $975 000 four years from now = 975 000(1.01225^-16) = 802 417

Total present value of payments = $2 585 612

Since the present value of the cash payments is less than $2 800 000, thecash requirements of Plan B can be met by the investment.

(c) The treasurer should recommend Plan B, since it has the lower present value

($2 660 034 − $2 585 612).