Question

I have two questions that need to be answered, I can't figure them out:

1) Steve Coleman has just won the state lottery and has the following three payout options for

afterminus?tax

prize? money:1.

$ 152 comma 000$152,000

per year at the end of each of the next six years2.

$ 318 comma 000$318,000

?(lump sum) now3.

$ 500 comma 000$500,000

?(lump sum) six years from now

The annual discount rate is? 9%. Compute the present value of the second option.? (Round to nearest whole? dollar.)

Present value of? $1:

	?8%	?9%	?10%
1	0.926	0.917	0.909
2	0.857	0.842	0.826
3	0.794	0.772	0.751
4	0.735	0.708	0.683
5	0.681	0.650	0.621
6	0.630	0.596	0.564
7	0.583	0.547	0.513

A.

$ 100 comma 000$100,000

B.

$ 400 comma 000$400,000

C.

$ 652 comma 000$652,000

D.

$ 318 comma 000$318,000

2) Smash Company has? 4,000 machine hours available annually to manufacture badminton racquets. The following information is available for the two different racquets produced by? Smash:

Pro
Unit sales price	?$400
Unit variable costs	?$100
Annual demand	?2,000 units
Machine time	1.5 hours per unit
Mid
Unit sales price	?$100
Unit variable costs	?$70
Annual demand	?5,000 units
	2 hours per unit

How many units of each racquet should be manufactured for the company to maximize its operating? income?

A.

?2,000 units of Pro and 500 units of Mid

B.

?2,000 units of Pro and? 5,000 units of Mid

C.

?2,000 units of Pro and? 1,500 units of Mid

D.

?5,000 units of Mid and 500 units of Pro

Answer 1

Solution 1:

Present value of second option = Amount to be received lump sum today = $318,000

Hence option D is correct.

Solution 2:

Computation of contribution margin per machine hour
Particulars	Pro	Mid
Selling price per unit	$400.00	$100.00
Variable cost per unit	$100.00	$70.00
Contribution margin per unit	$300.00	$30.00
Machine time per unit (In hour)	$1.50	$2.00
Contribution margin per machine hour	$200.00	$15.00

As contribution margin per hour for Pro is higher therefore available machine hour will be first utilized in production of Pro racquets. Therefore

Total unit to be producted for pro = 2000 unit

Total hour required to produce 2000 units of pro = 2000*1.5 = 3000 hours

Remaining machine hours = 4000 - 3000 = 1000

Remaining machine hours will be utilize to product mid racquet and total production of mid product = 1000/2= 500 units

Therefore in order to maximize operating income, 2000 units of Pro and 500 unti of Mid should be manufactured.

Hence option A is correct.