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.

Answer 1

(1)(a) Yes Precision machining corporation meet the cash requirement of Plan A by investing the $2800000 as described.

(b)Difference = $112296.59

(2) (a)So Precision Machining Corporation not meet the cash requirements of Plan B by investing the $2800000 as described.

(3)(a) Yes Precision Machining Corporation meet the cash requirements of the new Plan A by investing the $2800000 as described.

(b)Difference = $112296.59

(a)Yes the company meet the cash requirements of the original Plan A with this new investment.

(b) Yes the company meet the cash requirements of Plan B with the new investment

(c) Plan first has lower present value then plan second.

Explanation:

Total amount for expand the production facility = $2800000

Total amount required for plan A = $300000 + 4 * 700000 = $3100000

For calculation of interest we use formula =P[(1+r)ⁿ -1]

where

P = principle amount

r= rate of interest

n = Number of compounding period

Interest for first year

P = $2800000

r = 4.5/100 = 0.045

n = 1

interest = 2800000[(1+0.045)¹ -1]= $126000

Interest for second and third year

P=2800000+126000 = $2926000

r= 5.0/100=0.05

n = 3

Interest = 2926000[(1+0.05)³ -1]= $461210.75

Interest for fourth year

P = 2926000+461210.75 = $3387210.75

r=.055

n = 1

Interest=3387210.75[(1+0.055)^1-1] = $186296.59

Total amount after investment Precision machining corporation have = $3112296.59

1(a) Yes Precision machining corporation meet the cash requirement of Plan A by investing the $2800000 as described.

(b)Difference = $3112296.59 - $3100000 = $112296.59

(2) (a)Cash requirement of plan B = 4*$975000 = $3900000

So Precision Machining Corporation not meet the cash requirements of Plan B by investing the $2800000 as described.

(b) difference = $3900000 - $3112296.59 = $ 787703.41

(3)(a) required amount = $750000 *4 = $3000000

available amount = $3112296.59

Yes Precision Machining Corporation meet the cash requirements of the new Plan A by investing the $2800000 as described.

(b)Difference = $3112296.59- $3000000= $112296.59

(4)We have P = $2800000

r = 0.049

n = 9

Interest = 2800000[(1+0.049)^9 - 1]= $1506628..65

(a) Total amount required for plan A = $300000 + 4 * 700000 = $3100000

Available amount after new investment = 2800000+ 1506628.65 = $4306628.65

Yes the company meet the cash requirements of the original Plan A with this new investment.

(b) Amount requirement of plan B = 4*$975000 = $3900000.

Available amount after new investment = 2800000+ 1506628.65 = $4306628.65

Available amount > Required amount

So, Yes the company meet the cash requirements of Plan B with the new investment

(c) Plan first has lower present value then plan second.