3 Unit Selected Review Problems Solutions
Section 5.2
Added question: 360(.7)(.875)(.95) = $209.475 209.475-199 = 10.475209.475 = .0050005967
= 5.00%
4. Solution:
#
List price (L)
Series of discounts rates
Equivalent discount rate
Net price
Amount of discount
a.
$850.00
10%, 5%
(de)
14.50%
(N)
$726.75
(L N)
$123.25
b.
$697.82
5%, 4%, 3%
11.54%
$617.32
$80.50
c.
$2022.71
%, 2%, 1%
8.32%
$1854.50
$168.21
d.
$625.00
5%, 4%, d%
10.62%
$558.60
$66.40
a.
N = 850 (1 0.10)(1 0.05) = $726.75
Amount of discount = L N = 850 726.75 = $123.25
de = 1 (1 d1)(1 d2) = 1 (1 0.10)(1 0.05) = 1 (0.90)(0.95) = 0.145 = 14.50%
b.
Amount of discount = L N = $80.50
Therefore, L = 80.50 N.
We also know, N = L (1 d1) (1 d2) (1 d3) = L (1 0.05) (1 0.04) (1 0.03) = L (0.88464)
Substituting for N in the previous equation, we get,
L = 80.50 L (0.88464),
L L(0.88464) = 80.50
L(1 0. 88464) = 80.50
Solving for L, we get,
L = 697.815534... = $697.82
Now, amount of discount = 697.815534 ... N = 80.50
N = $617.315534 = $617.32
de = 1 (1 d1)(1 d2) = 1 (1 0.05) (1 0.04) (1 0.03) = 1 (0.95)(0.96)(0.97) = 0.11536 =
11.54
c.
N = L (1 d1) (1 d2) (1 d3) = L (1 0.055)(1 0.02) (1 0.01) = L (0.916839)
1854.50 = L (0.916839) Solving for L, we get,
L = $2022.710639... = $2022.71
Amount of discount = L N = $2022.710639... 1854.50 = $168.210639... = $168.21
de = 1 (1 d1)(1 d2) = 1 (1 0.055) (1 0.02) (1 0.01) = 0.083161 = 8.32%
d.
Amount of discount = L N = $625 558.60 = $66.40
N = L (1 d1) (1 d2) (1 d3)
558.60 = 625(1 0.05) (1 0.04) (1 d%)
0.98 = 1 d%
d% = 0.02
d = 2%
de = (1 d1) (1 d2) (1 d3) = 1 (1 0.05)(1 0.04)(1 0.02) = 0.10624 = 10.62%
#10. Solution:
L=
N = L (1 d) = 408,000 (1 0.05) = $387,600.00
Therefore, the list price and net price of the clothes were $408,000.00 and $387,600.00 respectively.
18. Solution:
N = L (1 d1) (1 d2) (1 d3)
N = 2000 (1 0.15) (1 0.10) (1 0.05) = $1453.50
Amount of discount = L N = 2000 1453.5 = $546.50
Therefore, we would pay $1453.50 for the leather jacket and the total amount of discount would be $546.50.
Section 5.3
4. Solution:
6% discount received on payment made on or before Mar 01 (1st discount period)
3% discount received on payment made after Mar 01 but on or before Mar 16 (2nd discount period)
Net payment due by Mar 31 (credit period)
(a) If paid on Feb 14,
They would receive 6% discount on their invoice as it falls within the first 15 days of the invoice date.
Therefore, they would have to pay: 260,800 (1 0.06) = $245,152.00
(b) If paid on Feb 28,
They would receive 6% discount on their invoice as it falls within the first 15 days of the invoice date.
Therefore, they would have to pay: 260,800 (1 0.06) = $245,152.00
(c) If paid on Mar 02,
They would receive 3% discount on their invoice as it falls after 15 days and before 30 days of the invoice
date.
Therefore, they would have to pay: 260,800 (1 0.03) = $252,976.00
(d) If paid on Mar 31,
Net price has to be paid as it falls after the 30 days of the invoice date.
8. Solution:
2.5% discount received on payment made within 10 days
Net payment is due within 30 days
He paid $1000 during the discount period
Amount credited (CR) = = = $1025.64
Balance = 3000 1025.64 = $1974.36
Therefore, the balance on the invoice is $1974.36.
Section 5.4
4. Solution:
$
%
M
$52.63
M/C = 5.26%
S
$1052.63
M/S = 5.00%
C = $1000
M/S = 5% Therefore, M = 0.05S
S=C+M
Therefore, S = 1000 + 0.05S
Solving, we get S = $1052.63
Therefore, M = 0.05S = $52.6315 = $52.63
Rate of Mark Up on Cost: M/C = = 0.0526 = 5.26%
Therefore, the selling price was $1052.63 and the rate of markup on the cost was 5.26%.
6. Solution:
$
%
M
$0.145S
M/S = 14.50%
S
$5.85
C = $5
M/S = 14.5% = 0.1450
M = 0.145S
M+C=S
0.145S + 5 = S
0.855S = 5
S = $5.847953... = $5.85
Therefore, the selling price of each calendar is $5.85.
8. Solution:
C = $450
E = $50
P = $200
M = P + E = 200 + 50 = $250
S = C + M = 450 + 250 = $700
Rate of Markup on Cost: M/C = = 55.555555% = 55.56%
Therefore, the selling price and amount of markup on the laptop were $700.00 and $250.00 respectively and the rate
of markup was 55.56%.
Section 5.6
12. Solution:
a.
Purchase price of the sculptures = $2400 (1 0.10) (1 0.08) (1 0.06) = $1867.97
C = $1867.97
E = 0.15 C = $280.20
P = 0.2 C = $373.59
M = P + E = 373.59 + 280.20 = $653.79
S = C + M = $1867.97 + $653.79 = $2521.76
Therefore, the regular selling price of the sculptures is $2521.76.
b.
D/S = 15% = 0.15
Therefore, D = 0.15 2521.76 = $378.264 = $378.26
SRed = S D = 2521.76 378.26 = $2143.50
PRed = SRed C E = 2143.50 1867.97 280.20 = $4.67 (net loss)
Therefore, Gabriella will have a net loss of $4.67
c.
Break-even price = C + E = 1867.97 + 280.20 = $2148.17
Therefore, to break-even, her reduced selling price should be $2148.17
Letx be the corresponding rate of markdown
2521.76 (1 x) = 2148.17
1 x = 0.8519
x = 0.1481 = 14.81%
Therefore, the maximum markdown she can offer is 14.81%.
Chapter 5 Review Exercises Pages 168-169
5. Solution:
N = L (1 d1) (1 d2)
N(Toronto) = 11 (1 0.05) (1 0.03) = $10.1365 = $10.14
N(Oakville) = 11.25 (1 0.08) = $10.35
Assume that the additional trade discount rate that the wholesaler in Oakville has to provide is d
$10.14 = $10.35 (1 d)
d = 0.020289... = 2.03%
Therefore, the wholesaler in Oakville must offer an additional discount of 2.03% to match the price of the bag sold
in Toronto.
7. Solution:
de = 1 (1 d1)(1 d2)(1 d3) = 1 (1 0.50) (1 0.25) (1 0.15) = 0.68125 = 68.13%
N = L(1 de) = 900 (1 0.68125) = $286.875 = = $286.88
Therefore, the net price and the single equivalent discount rate are $286.88 and 68.13% respectively.
9. Solution:
5% discount received on payment made on or before August 28 (1st discount period)
2% discount received on payment made after August 28 but on or before September 07 (2nd discount
period)
Net payment due by September 22 (credit period)
(a) If paid on August 28
They would receive 5% discount on their invoice as it falls within the first 10 days of the invoice date.
Therefore, they would have to pay: 45,000(1 0.05) = $42,750.00 to settle the invoice on August 28.
(b) If paid on September 06
They would receive 2% discount on their invoice as it falls in the 2nd discount period.
Therefore, they would have to pay: 45,000(1 0.02) = $44,100.00 to settle the invoice on September 06.
(c) If paid on September 22
Net price has to be paid as it falls after the 20th day of the invoice they date.
Therefore, would have to pay $45,000.00 to settle the invoice on September 22.
13. Solution:
$
P
$18.00
+M
E
$6.00
$24.00
S
$84.00
%
0.1C =40.00%
M/C
M/S = 28.57%
C = $60
E = 10% of cost
Therefore, E = 0.1 60 = $6.00
M/C = 0.4
Therefore, M = 0.4 60 = $24.00
S = C + M = 60 + 24 = $84.00
Rate of Markup on Selling Price M/S =
P = M E = 24 6 = $18.00
Therefore, Profit = $18.00
Therefore, the selling price, rate of markup on selling price, and profit per pair of shoe sold were $84.00, 28.57%
and $18.00 respectively.
15. Solution:
S = $4
M/C = 0.8
Therefore, M = 0.8C
S=C+M
Therefore, we have 4 = C + 0.8C = 1.8C
$
%
+M
E
$1.78
M/C = 80.00%
S
$4.00
P
Therefore, C = = $2.222222 = $2.22
Amount of Markup M = 0.8C = 0.8 2.22 = $1.776 = $1.78
Therefore, the cost of coffee powder per kg was $2.22 and the amount of markup was $1.78.
17. Solution:
C = $25
M/C = 0.8
Therefore, M = 0.8C = 0.8 25 = $20.00
S = C + M = 25 + 20 = $45.00 (regular selling price)
Markdown rate D/S = 20% = 0.2
Therefore, D = 0.2S = 0.2 45 = $9.00
Discounted selling price SRed = S D = 45 9 = $36.00
Therefore, the regular and discounting selling prices are $45.00 and $36.00 respectively.
19. Solution:
a.
Purchase price of the printer = $150(1 0.15)(1 0.10) = $114.75
Therefore, C = $114.75
E = 0.3C = 0.3 114.75 = $34.425 = $34.43
P = 0.25C = 0.25 114.75 = $28.6875 = $28.69
M = P + E = 28.69 + 34.43 = $63.12
S = C + M = 114.75 + 63.12 = $177.87 (regular selling price)
Therefore, the regular selling price of the printer is $177.87.
b.
Markdown Rate D/S = 0.2
Therefore, D = 0.2S = 0.2 177.87 = $35.574 = $35.57
Discounted selling price SRed = S D = 177.87 35.57 = $142.30
PRed = SRed C E = 142.3 114.75 34.43 = $6.88
Therefore, he has a net loss of $6.88
c.
Break-even price = C + E = 114.75 + 34.43 = $149.18
Therefore, to break-even, his reduced selling price should be $149.18. Let the corresponding markdown
rate be x
177.87 (1 x) = 149.18
1 x= 0.838702...
x= 0.161297... = 16.13%
Therefore, the maximum markdown he can offer is 16.13%
Chapter 5: Self-Test Page 170
1. Solution:
a.
N = L (1 d1) (1 d2) (1 d3)
1077.30 = L (1 0.4)(1 0.1)(1 0.05)
Solving, we get L = $2100.00
Therefore, the list price of the item is $2100.00
b.
de = 1 (1 d1)(1 d2)(1 d3)
= 1 (1 0.4)(1 0.1)(1 0.05) = 0.487 = 48.70%
7. Solution:
Discount period starts from date of invoice which is July 9
2.5% discount received on payment made on or before July 19 (1st discount period)
1.5% discount received on payment made after July 19, but on or before August 3 (2 nd discount period)
Net payment is due by August 23 (credit period)
a.
She made the first payment of $4000 on July 19, which falls within the first discount period
Therefore, Amount credited (CR) = = = $4102.564103... = $4102.56
Therefore, balance after 1st payment = 70,000 4102.56 = $65,897.44
b.
She made the second payment of $2000 on August 3, which falls within the second discount period
Therefore, Amount credited (CR) = = = $2030.456853... = $2030.46
Therefore, balance after 2nd payment = 65,897.44 2030.46 = $63,866.98
c.
The final payment on August 23 does not lie in any discount period.
Therefore, the payment that will settle the invoice on August 23 is the balance amount, which is $63,866.98.
11. Solution:
M/S = 0.4
M = 0.4S which means that S = 2.5M
But S = C + M
2.5M = C + M
1.5M = C
Rearranging, we get, M/C = 0.666666 = 66.67%
Therefore, the markup as a percentage of the cost of the phone is 66.67%.
Section 7.2
6. Solution:
a. Assume that she
needs to sell x paintings to break-even.
TC = FC + TVC
FC = 4450 + 50 + 5000 + 2000 = $11,500.00 per month
VC = 1000 + 25 = $1025.00
TVC = VC
x = 1025x
TC = 11,500 + 1025x
TR = S x = 1600x
At break-even TR = TC
Therefore, 1600x = 11,500 + 1025x
575x = 11,500
x = 20
Therefore, she needs to sell 20 paintings to break-even.
b. She wants her net profit (net income) to be $23,000.00
Therefore, NI = $23,000.00
But NI = TR TC
Therefore, 23000 = 1600x (11,500 + 1025x)
575x = 34,500
x = = 60
x = 60 paintings
Therefore, she would have to sell 60 paintings in a month to make the desired profits.
7. Review Exercises
1. Solution:
a. Let x be the number of bouquets to be sold per month to break-even.
S = $14, FC = $2700, VC = $8.50, x =?
TR = S x = 14x
TVC = VC x = 8.5x
TC = FC + TVC = 2700 + 8.5x
At break-even TR = TC
Therefore 14x = 2700 + 8.5x
5.5x = 2700
x = = 490.909090 (rounded off to 491)
Therefore, the break-even number of bouquets to be sold per week is 491.
b. We have x = 900 bouquets
TR = S x = 14 900 = $12,600.00
TC = FC + TVC = 2700 + 8.5 900 = $10,350.00
NI = TR TC = 12,600 10,350 = $2250.00
Therefore, the net income in that week is $2250.00.
c. Let x be the number of bouquets to be sold
NI = $1000
TR = S x = 14x
TC = FC + TVC = 2700 + 8.5x
NI = TR TC = 14x (2700 + 8.5x) = 5.5x 2700
Therefore, we have 1000 = 5.5x 2700
5.5x = 3700
x = = 672.727272 (rounded off to 673)
Therefore, the number of bouquets to be sold to get the desired profit is 673.
9. Solution:
a.
TR = $86,400 per month, x = 320 cameras, VC = $150 per unit, FC = $54,000 per month
S=?
TR = S x
86,400 = 320S
S = = $270.00
Therefore, the selling price of each camera is $270.00
b.
Let x be the new break-even number
New FC = 54,000 6000 = $48,000.00
TR = S x = 270x
TC = FC + TVC = 48,000 + 150x
At break-even, TR = TC
Therefore, 270x = 48,000 + 150x
120x = 48,000
x = = 400
Therefore, the new break-even point is 400.
d.
Break-even point as percentage of maximum capacity =
Therefore, the new break-even point as a percentage of the maximum capacity is 66.67%.
11. Solution:
a.
S = $105 per unit, FC = $180,000, VC = $75 per unit
Annual sales (Total Revenue) TR = $840,000
But TR = S x
Therefore, x =
TC = FC + TVC = 180,000 + 75 8000 = $780,000.00
NI = TR TC = 840,000 780,000 = $60,000.00
Therefore, their net income that year was $60,000.00.
b.
Let the number of units they require to sell in order to have the desired income be x
TR = S x = 105x
TC = FC + TVC = 180,000 + 75x
NI = TR TC = 105x (180,000 + 75x) = 30x 180,000
But it is given that NI = 75,000
Therefore, we have 75,000 = 30x 180,000
30x = 255,000
x=
Therefore, they must sell 8500 units in order to make the desired income.
c.
New variable costs = 75 + 5 = $80 per unit
Let the corresponding break-even volume be x
TR = S x = 105x
TC = FC + TVC = 180,000 + 80x
At break-even, TR = TC
Therefore, 105x = 180,000 + 80x
25x = 180,000
x = = 7200
Therefore, the new break-even number of items is 7200.