PRACTICE PROBLEM SET LESSON NO. 10
Problem 1:
The design capacity for engine repair in our company is 80 trucks/day. The effective capacity is 40 engines/day and the actual output is 36 engines/day. Calculate the utilization and efficiency of the operation. If the efficiency for next month is expected to be 82%, what is the expected output? GIVEN: Des ig ign Ca pa pa ci ci ty ty (Dc ) Effectiv ctive e Cap Capac acit ityy (E (Ec) Ac tua l Output (Oa ) Effi c i enc y (Em)
= 80 tr uc ks /d /da y = 40 engin ngine es/d s/day = 36 engi ne nes /da y = 82%
Solution:
Utilization =
Ac tua l Output (Oa ) Des i gn Ca pa c i ty (Dc)
Efficiency
36 80
= Ut ilizat ion =
45%
=
Ac tua l Output (Oa ) Effecti ve Ca pa ci ty (Ec )
Efficiency
=
Ac tua l Output (Oa ) Effec ti ve Ca pa c i ty (Ec)
=
36 40
82%
=
Oa 40
Efficie ncy =
90%
Act ual Out put (Oa) =
Problem 2: Solution:
BEPx
BEPx
=
Fi xed Cos t (F) Pri ce (P) - Va ri a bl e Cos t (V)
=
$1,000 $4 - $2
= $
500.00
BEPs
BEPs
=
=
Fi xed Cos t (F) 1 - Va r i a bl e Cos t (V)/ Pri ce (P)
=
$1,000 1 - (2/4) $
2 ,000 .00
32 .8 0
Problem 3:
Develop the break-even chart for Problem 2.
Break-Even Analysis $5,000
$4,000 $3,000 $2,000
$1,000 $0 0
1 00
2 00
300
400
500
600
700
800
900
1 ,0 0 0
($1,000)
($2,000) T FC
T VC
TC
Sa les
Br eak-Eve n Point (unit s) = 50 50 0 Tota l Fi x ed Cos ts Va ri a bl e Cos t per Uni t Sa l es Pr i c e per Uni t
TFC = VCU = SP U =
Profit Br eak-Eve n Point ($'s) = $2 $2 ,0 0 0
$1,000 $2.00 $4.00
Formulas: BEP (units ) = TFC/(SPU-VCU) TFC/(SPU-VCU) BEP ($'s) = BEP (units) * SPU
Problem 4 & 5:
Jack’s Grocery is manufacturing a “store brand” item that has a variable cost of $0.75 per unit and a selling price of $1.25 per unit. Fixed costs are $12,000. Current volume is 50,000 units. The Grocery can substantially improve the product quality by adding a new piece of equipment at an additional fixed cost of $5,000. Variable cost would increase to $1.00, but their volume should increase to 70,000 units due to the higher quality product. Should the company buy the new equipment? What are the break-even points ($ and units) for the two two processes considered consider ed in Problem 4? BEFORE IMPROVEMENT BEPx
BEPx
=
Fi xed Cos t (F) Pri c e (P) - Va ri a bl e Cos t (V)
=
$1 2,0 00 $1 .25 - $ 0.7 5
= $
2 4,0 00 .00
BEPs
BEPs
=
Fi xed Cos t (F) 1 - Va r i a bl e Cos t (V)/ Pr i c e (P)
=
$ 12 ,00 0 1 - (0 .75 /1 .25 )
=
$
30 ,00 0.0 0
PROFIT
= (P - V) V) x - F ($1 .25 - $ 0.7 5)(50 ,00 0) - 1 2,0 00
PROFIT
= $
PROFIT
= (P - V) V) x - F ($1 .25 - $ 1.0 0)(70 ,00 0) - 1 7,0 00
PROFIT
= $
13,000 .00
AFTER IMPROVEMENT BEPx
BEPx
=
Fi xed Cos t (F) Pri c e (P) - Va ri a bl e Cos t (V)
=
$1 7,0 00 $1 .25 - $ 1.0 0
= $
6 8,0 00 .00
BEPs
BEPs
=
=
Fi xed Cos t (F) 1 - Va r i a bl e Cos t (V)/ Pr i c e (P)
=
$ 17 ,00 0 1 - (1 .00 /1 .25 ) $
85 ,00 0.0 0
50 0.0 0
Therefore, since the profit generated is lesser than the original set-up, it is advised to not buy the equipment and check for another alternate improvement.
Problem 6:
Develop a break-even chart for Problem 4.
Break-Even Analysis (Before Improvement) $80,000 $70,000 $60,000 $50,000 $40,000 $30,000 $20,000 $10,000 $0 ($10,000)
0
6,000
12,000
18,000
24,000
30,000
T FC
T VC
TC
36,000
42,000
48,000
54,000
60,000
($20,000) Sa les
Bre ak-Eve n Point (units) = 24 24,000 Tota l Fi xed Cos ts Va ri a bl e Cos t per Uni t Sa l es Pr i c e per Uni t
TFC = VCU = SPU =
Pr ofit Br e ak-Eve n Point ($'s) = $3 $30,000
$12,000 $0.75 $1.25
Formulas: BEP (uni ts) = TFC/(SPU-VCU) TFC/(SPU-VCU) BEP ($'s) = BEP (units) * SPU
Break-Even Analysis (After Improvement) Improveme nt) $170,000 $153,000 $136,000 $119,000 $102,000 $85,000 $68,000 $51,000 $34,000 $17,000 $0 ($17,000)
0
17,000
34,000
51,000
68,000
85,000
102, 000
T FC
T VC
TC
Sa les
119, 000
136, 000
153, 00 0
170, 000
($34,000)
Bre ak-Eve n Point (units) = 68 68,000 Tota l Fi xed Cos ts Va ri a bl e Cos t per Uni t Sa l es Pr i c e per Uni t
TFC = VCU = SPU =
$17,000 $1.00 $1.25
Pr ofit Br e ak-Eve n Point ($'s) = $8 $85,000 Formulas: BEP (uni ts) = TFC/(SPU-VCU) TFC/(SPU-VCU) BEP ($'s) = BEP (units) * SPU
Problem 7:
Good News! You are going to receive $6,000 in each of the next 5 years for sale of used machinery. A bank is willing to lend you the present value of the money in the meantime at discount of 10% per year. How much cash do you receive now? Solution: YEAR
PF
1
0 .9 09
2
0 .8 26
3
0 .7 51
4
0 .6 83
5
0 .6 21
N PF
3.79
PV = 6000 * 3.79
PV = $ 22,740.00
