CHAPTER 3 Problem SolutionsCost Accounting, a managerial emphasis

1. CHAPTER 3 problem solutions 2. COST–VOLUME–PROFIT ANALYSIS 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

NOTATION USED IN CHAPTER 3 SOLUTIONS SP: VCU: CMU: FC: TOI:

Selling price Variable cost per unit Contribution margin per unit Fixed costs Target operating income

3-33

(15–20 min.) CVP analysis, service firm.

1.

Revenue per package Variable cost per package Contribution margin per package

$7,500 6,300 $1,200

Breakeven (packages) = Fixed costs ÷ Contribution margin per package $570,000 $1,200 per package 19. = = 475 tour packages

18.

20. $1, 200 $7,500

Contributi on margin per package Selling price 21.

2.

22.

Contribution margin ratio =

= 24.

26. 3.

Number of tour packages to earn $102,000 operating income

$570,000  $102,000 0.16

Revenues to earn $102,000 OI = 560 tour packages × $7,500 = $4,200,000.

Fixed costs = $570,000 + $19,000 = $589,000

Breakeven (packages) = Fixed costs Breakeven (packages)

30.

= $4,200,000, or

25. $570,000  $102,000   560 tour packages $1,200

Fixed costs Contribution margin per package 29.

= 16%

Revenue to achieve target income = (Fixed costs + target OI) ÷ Contribution margin ratio

23.

27. 28.

=

Contribution margin per package =

$589,000 475 tour packages

31. = 32.

= $1,240 per tour package

Desired variable cost per tour package = $7,500 – $1,240 = $6,260

33. Because the current variable cost per unit is $6,300, the unit variable cost will need to be reduced by $40 ($6,300– $6,260) to achieve the breakeven point calculated in requirement 1. 34. Alternate Method: If fixed cost increases by $19,000, then total variable costs must be reduced by $19,000 to keep the breakeven point of 475 tour packages. 35. 1. 36. 37. 38.

Therefore, the variable cost per unit reduction = $19,000 ÷ 475 = $40 per tour package. Contribution margin per package = $8,200 − $6,300 = $1,900 Breakeven (packages) = Fixed costs ÷ Contribution margin per package = $570,000 ÷ $1,900 per tour package = 300 tour packages

39. Breakeven point in dollars = $8,200 per package × 300 tour packages = $2,460,000 40. The key question for the general manager is: Can Lifetime Escapes sell enough packages at $8,200 per package to earn more total operating income than when selling packages at $7,500. Lowering the breakeven point per se is not the objective. 41. 3.34 (30 min.) CVP, target operating income, service firm. 42. 43. 1. Revenue per child $400 44. Variable costs per child 150 45. Contribution margin per child $250 46. Fixed costs Contributi on margin per child 47. Breakeven quantity = 48. $4,000 $250 49. = = 16 children 50. Fixed costs  Target operating income Contributi on margin per child 51. 2. Target quantity = 52.

$4,000  $5,000 $250 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64.

65. 66. 67. 68.

= 3.

= 36 children

Increase in rent ($2,200 – $1,500) Field trips Total increase in fixed costs Divide by the number of children enrolled Increase in fee per child

$ 700 1,100 $1,800 ÷ 36 $ 50

Therefore, the fee per child will increase from $400 to $450. Alternatively,

New contribution margin per child =

$4,000  $1,800  $5, 000 36

= $300

New fee per child = Variable costs per child + New contribution margin per child = $150 + $300 = $450

69.

3-35

CVP analysis, margin of safety.

1.

70. 71. 72.

Selling price Variable costs per unit: Contribution margin per unit (CMU) 73.

$206 24 $182 Fixed costs Contribution margin per unit

74. 75.

Breakeven point in units =

$327,600 $182 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86.

Breakeven point in units = = 1,800 returns (units) Margin of safety (units) = 3,000* – 1,800 = 1,200 units *$618,000 budgeted revenue÷$206 = 3,000 units Breakeven revenues = $206 × 1,800 = $370,800 Margin of safety percentage = ($618,000−$370,800) ÷ $618,000= 40%

2a. Increase selling price to $224 Selling price Variable costs per unit: Contribution margin per unit (CMU) 87.

$224 24 $200 Fixed costs Contribution margin per unit

88. 89.

Breakeven point in units =

$327,600 $200 90. 91.

Breakeven point in units = = 1,638 returns (units) Breakeven revenues = $224 × 1,638 units = $366,912

92. Margin of safety percentage = ($618,000 − $366,912) ÷ $618,000 = 40.62% 93. This change will not help Arvin achieve its desired margin of safety of 45%. 94. 95. 2b. 96. 97. Selling price $206 98. Variable costs per unit: 24 99. Contribution margin per unit (CMU) $182 100.

Fixed costs Contribution margin per unit 101. 102.

Breakeven point in units =

$327,600 $182 103. Breakeven point in units = = 1,800 returns (units) 104. 105. Breakeven revenues = $206 × 1,800 = $370,800 106. 107. Budgeted revenues = $618,000 × 1.15 = $710,700 108. Margin of safety percentage = ($710,700 − $370,800) ÷ $710,700 = 47.8% 109. This change will help Arvin achieve its desired margin of safety of 45%. 110. 111. 2c. 112. Selling price $206 113. Variable costs per unit $24 – $2): 22 114. Contribution margin per unit (CMU) $184 115. 116. Fixed costs = $327,600 × 1.05 = $343,980 117. Fixed costs Contribution margin per unit 118. Breakeven point in units = 119. $343,980 $184 120. Breakeven point in units = = 1,870 returns/units (rounded up) 121. 122. Breakeven revenues = $206 × 1,870 units = $385,220 123. Margin of safety percentage = ($618,000− $385,220) ÷ $618,000= 37.7% 124. This change will not help Arvin achieve its desired margin of safety of 45%. 125. 126. Options 2a and 2b improve the margin of safety, but only option 2b exceeds the company’s desired margin of safety. Option 2c actually lowers the company’s margin of safety. 127.

3-36

1.

(30–40 min.) CVP analysis, income taxes.

Revenues – Variable costs – Fixed costs = Let X = Net income for 2014

Target net income 1  Tax rate X

22,000($35.00) – 22,000($18.50) – $214,500 =

1  0.40

X 0.60 $770,000 – $407,000 – $214,500 = $462,000 – $244,200 – $128,700 = X X = $89,100

Alternatively, Operating income = Revenues – Variable costs – Fixed costs = $770,000 – $407,000 – $214,500 = $148,500

Income taxes = 0.40 × $148,500 = $59,400 Net income = Operating income – Income taxes = $148,500 – $59,400 = $89,100 2.

Let Q = Number of units to break even $35.00Q – $18.50Q – $214,500 = 0 Q = $214,500  $16.50 = 13,000 units

3.

Let X = Net income for 2015 X

25,000($35.00) – 25,000($18.50) – ($214,500 + $16,500)

=

1  0.40 X 0.60

$875,000 – $462,500 – $231,000

= X

$181,500

4.

Let Q = Number of units to break even with new fixed costs of $146,250 $35.00Q – $18.50Q – $231,000 Q = $231,000  $16.50 Breakeven revenues = 14,000  $35.00

5.

0.60 = X = $108,900

= 0 = 14,000 units = $490,000

Let S = Required sales units to equal 2011 net income $89,100 0.60 $35.00S – $18.50S – $231,000 = $16.50S = $379,500 S = 23,000 units Revenues = 23,000 units  $35 = $805,000

6.

Let A = Amount spent for advertising in 2012 $108,450 0.60

$875,000 – $462,500 – ($214,500 + A) = $875,000 – $462,500 – $214,500 – A = $180,750 $875,000 – $857,750 = A A = $17,250

3-37 (25 min.) CVP, sensitivity analysis. 128. 129. Contribution margin per pair of shoes = $70 – $30 = $40 130. Fixed costs = $100,000 131. Units sold = Total sales ÷ Selling price = $350,000 ÷ $70 per pair = 5,000 pairs of shoes 132. 1. Variable costs decrease by 20%; Fixed costs increase by 15%  133. Sales revenues 5,000 $70 $350,000   134. Variable costs 5,000 $30 (1 – 0.20) 120,000 135. Contribution margin 230,000  136. Fixed costs $100,000 1.15 115,000 137. Operating income $115,000 138. 2. Increase advertising (fixed costs) by $30,000; Increase sales 20%   139. Sales revenues 5,000 1.10 $70.00 $385,000   140. Variable costs 5,000 1.10 $30.00 165,000 141. Contribution margin 220,000 142. Fixed costs ($100,000 + $25,000) 125,000 143. Operating income $ 95,000 144. 145. 3. Increase selling price by $10.00; Sales decrease 20%; Variable costs increase by $8   146. Sales revenues 5,000 0.80 ($70 + $10) $320,000   147. Variable costs 5,000 0.80 ($30 + $8) 152,000 148. Contribution margin 168,000 149. Fixed costs 100,000 150. Operating income $ 68,000 151. 4. Double fixed costs; Increase sales by 60%   152. Sales revenues 5,000 1.60 $70 $560,000   153. Variable costs 5,000 1.60 $30 240,000 154. Contribution margin 320,000

155.

Fixed costs $100,000 200,000 Operating income



2

156. $120,000 157. 158. Alternative 4 yields the highest operating income. Choosing alternative 4 will give Derby a 20% increase in operating income [($120,000 – $100,000)/$100,000 = 20%], which is less than the company’s 25% targeted increase. Alternative 1also generates more operating income for Derby, but it too does not meet Derby’s target of 25% increase in operating income. Alternatives 2 and 3 actually result in lower operating income than under Derby’s current cost structure. There is no reason, however, for Derby to think of these alternatives as being mutually exclusive. For example, Derby can combine actions 1 and 4, automate the machining process and decrease variable costs by 20% while increasing fixed costs by 15%. This will result in a 38% increase in operating income as follows: 159.   160. Sales revenue 5,000 1.60 $70 $560,000   161. Variable costs 5,000 1.60 $30 × (1 – 0.20) 192,000 162. Contribution margin 368,000  163. Fixed costs $200,000 1.15 230,000 164. Operating income $138,000 165. 166. The point of this problem is that managers always need to consider broader rather than narrower alternatives to meet ambitious or stretch goals. 167. 168. 169. 3-38 (20–30 min.) CVP analysis, shoe stores. 170. 171. 1. CMU (SP – VCU = $60 – $40) $ 20.00   172. a. Breakeven units (FC CMU = $180,000 $20 per unit) 9,000 173. b. Breakeven revenues   174. (Breakeven units SP = 9,000 units $60 per unit) $540,000 175. 176. 2. Pairs sold 8,000  177. Revenues, 8,000 $60 $480,000  178. Total cost of shoes, 8,000 $37 296,000  179. Total sales commissions, 8,000 $3 24,000

180.

Total variable costs 320,000

181.

Contribution margin 160,000

182.

Fixed costs 180,000

183.

Operating income (loss) $ (20,000)

184. 185. 3. 186.

Unit variable data (per pair of shoes) Selling price $ 60.00 Cost of shoes 37.00 Sales commissions 0

187. 188. 189.

Variable cost per unit $ 37.00

190. 191.

Annual fixed costs Rent $ 30,000

192.

Salaries, $100,000 + $15,500 115,500

193.

Advertising 40,000 Other fixed costs 10,000 Total fixed costs $ 195,500

194. 195. 196. 197.

CMU, $60 – $37 $ 23

198. unit 199. $60 per unit 200.

 a. Breakeven units, $195,500 $23 per 8,500  b. Breakeven revenues, 8,500 units $510,000

201. 4.

Unit variable data (per pair of shoes)

202.

Selling price $ 60.00 Cost of shoes 37.00 Sales commissions 5.00

203. 204. 205.

Variable cost per unit $ 42.00

206.

Total fixed costs $180,000

207. 208.

CMU, $60 – $42 $ 18.00

 a. Break even units = $180,000 $18 per unit

209. 10,000 210.

b. Break even revenues = 10,000 units



$60 per unit

211. 212. 5.

$600,000 Pairs sold 12,000

213. pair) 214.  $37 per pair) 215.

 Revenues (12,000 pairs $60 per $720,000 Total cost of shoes (12,000 pairs

Sales commissions on first 9,000 pairs (9,000 pairs



444,000 $3 per pair)

27,000 216.

Sales commissions on additional 3,000 pairs  [3,000 pairs ($3 + $2 per pair)]

217. 15,000 218.

Total variable costs 486,000 Contribution margin

219. 234,000 220.

Fixed costs 180,000

221.

Operating income $

54,000

222. 223. Alternative approach: 224. 225. Breakeven point in units = 9,000 pairs 226. Store manager receives commission of $2 on 3,000 (12,000 – 9,000) pairs.

227. Contribution margin per pair beyond breakeven point of 9,000 pairs = $18 ($60 – $40 – $2) per pair.  228. Operating income = 3,000 pairs $18 contribution margin per pair = $54,000. 229.

230. 3-39 (30 min.) CVP analysis, shoe stores (continuation of 3-38). 231. 1. For an expected volume of 10,000 pairs, the owner would be inclined to choose the higherfixed-salaries-only plan because income would be higher by $14,500 compared to the salaryplus-commission plan. 232. 233. . Operating income for salary plan = $23 × 10,000 – $195,500 = $34,500 234. Operating income under commission pan = $20 × 10,000 – $180,000 = $20,000 235. 236. But it is likely that sales volume itself is determined by the nature of the compensation plan. The salary-plus-commission plan provides a greater motivation to the salespeople, and it may well be that for the same amount of money paid to salespeople, the salary-pluscommission plan generates a higher volume of sales than the fixed-salary plan. 237. 238. 2. Let TQ = Target number of units 239. 240. For the salary-only plan, 241. $60TQ – $37TQ – $195,500 = $69,000 242. $23TQ= $264,500 243. TQ= $264,500 ÷ $23 244. TQ = 11,500 units 245. For the salary-plus-commission plan, 246. $60TQ – $40TQ – $180,000 = $69,000 247. $20TQ= $249,000 248. TQ= $249,000 ÷ $20.00 249. TQ = 12,450 units 250. 251. The decision regarding the salary plan depends heavily on predictions of demand. For instance, the salary plan offers the same operating income at 11,500 units as the commission plan offers at 12,450 units. 252.

253. 3. 254. 255. 256. 257. 258. 259. 260. 261.

HighStep Shoe Company Operating Income Statement, 2014  $60) + (1,500 pairs $50)  Cost of shoes, 11,000 pairs $37   Commissions = Revenues 5% = $645,000 0.05 Contribution margin Fixed costs Operating income

Revenues (9,500 pairs



$645,000 407,000

$

32,250 205,750 180,000 25,750

262. 3-40

(40 min.) Alternative cost structures, uncertainty, and sensitivity analysis.

263.

264. 1. Contribution margin per page assuming current fixed leasing agreement

265. = $0.15 – $0.04 – $0.05 = $0.06 per page

266. Fixed costs = $1,200 267. Breakeven point = Fixed costs $1, 200   20,000 pages Contribution margin per page $0.06 per page 268. 269. Contribution margin per page 270. = $0.15 – $0.04a – $0.04 – $.05 = $0.02 per assuming $20 per 500 page page commission agreement 271. 272. Fixed costs = $0 Fixed costs $0   0 pages Contribution margin per page $0.02 per page 273. Breakeven point = 274. (i.e., Deckle makes a profit no matter how few pages it sells) 275. a$20  500 pages = $0.04 per page 276.

x 277. 2. Let denote the number of pages Deckle must sell for it to be indifferent between the fixed leasing agreement and commission based agreement. x 278. To calculate we solve the following equation. x x x x x x 279. $0.15 – $0.04 – $0.05 – $1,200 = $0.15 – $0.04 – $0.04 – $.05 x 280. 281. 282.

$0.06

x

– $1,200 = $0.02

x

x $0.04 = $1,200 x = $1,200 ÷ $0.04 = 30,000 pages

283.

For sales between 0 to 30,000 pages, Deckle prefers the commission-based x x agreement because in this range, $0.02 > $0.06 – $1,200. For sales greater than 30,000 pages, Deckle prefers the fixed leasing agreement because in this range, $0.06 x $1,200 > $.02 .

x

–

284.

285.

3. Fixed leasing agreement

286. Pages Sold 287. (1)

288. Revenue 289. (2) 307. 20,000 $.15=$

290. Variable 291. Costs 292. (3) 308. 20,000 $.09=$

314.

3,000 30,000 $.15=$

1,800 315. 30,000 $.09=$

321.

4,500 40,000 $.15=$

2,700 322. 40,000 $.09=$

328.

6,000 50,000 $.15=$

3,600 329. 50,000 $.09=$

7,500 335. 60,000 $.15=$

4,500 336. 60,000 $.09=$



306. 20,000

313. 30,000

320. 40,000

327. 40,000

   

334. 60,000 341. Expected value of fixed leasing agreement

346. 347.

    

9,000 342.

293. Fixe d 294. Cost s 295. (4) 309. $1,2 00

296. Operating 297. Income 298. (Loss) 299. (5) = (2) – (3) – (4)

310. $

300. Proba bility 301. (6)

350. Revenue 351. (2)

352. Variable 353. Costs 354. (3)



0

311. 0.20

312. $

0

317. $ 600

318. 0.20

319. 120

324. $1,200

325. 0.20

326. 240

331. $1,800

332. 0.20

333. 360

338. $2,400

339. 0.20

340.

316. $1,2 00 323. $1,2 00 330. $1,2 00 337. $1,2 00

5,400 343.

344.

355. Operating Income 356. (4) = (2) – (3)

357. Proba bility 358. (5)

480

345. $1,200

Commission-based leasing agreement:

348. Pa ges Sol d 349. (1)

302. Expecte d 303. Operati ng 304. Income 305. (7)=(5) (6)

359. Expected Operating Income 360. (6)=(4)



(5) 361. 2 0,000 367. 3 0,000 373. 4 0,000 379. 5 0,000

362. 20,000 $.15=$

363. 20,000 $.13=

3,000 368. 30,000 $.15=$

$2,600 364. $400 369. 30,000 $.13=

365. 0.20

366. $ 80

4,500 374. 40,000 $.15=$

$3,900 370. $600 375. 40,000 $.13=

371. 0.20

372. 120

6,000 380. 50,000 $.15=$

$5,200 376. $800 381. 50,000 $.13=

377. 0.20

378. 160

7,500 386. 60,000 $.15=$

$6,500 382. $1,000 387. 60,000 $.13=

383. 0.20

384. 200

389. 0.20 393.

390. 240 394. $800

    

   

385. 6 0,000 9,000 391. Expected value of commission based agreement



$7,800 388. $1,200 392.

395.

396. Deckle should choose the fixed cost leasing agreement because the expected value is higher than under the commission-based leasing agreement. The range of sales is high enough to make the fixed leasing agreement more attractive. 397. 398.

399. 3-41 (20-30 min.) CVP, alternative cost structures. 400. 401. 1. Variable cost per unit = $5 402. Contribution margin per unit = Selling price –Variable cost per unit 403. = $20 – $5 = $15 404. Fixed Costs: 405. Manager’s salary ($40,000 × 1.20 × 0.5) ÷12 $2,000 per month 406. Rent 800 per month 407. Hourly employee wages (2 × 160 hours × $10) 3,200 per month 408. Total fixed costs $6,000 per month 409. 410. Breakeven point = Fixed costs ÷ Contribution margin per unit 411. = $6,000 ÷ $15 = 400 sunglasses (per month) 412. Fixed costs + Target operating income Contribution margin per unit 413. 2. Target number of sunglasses = 414. $6,000 + $4,500  700 sunglasses $15 415. = 416. 417. 3. Contribution margin per unit = Selling price – Variable cost per computer 418. = $20 – 0.15 × $20 – $5 = $12 419. Fixed costs = Manager’s salary + Rent = $2,000 + $800 = $2,800 420. Fixed costs + Target operating income Contribution margin per unit 421. Target number of sunglasses = $2,800 + $4,500  609 sunglasses $12 422. = (rounded up) 423. x 424. 4. Let be the number of sunglasses for which SuperShades is indifferent between paying a monthly rental fee for the retail space and paying an 8% commission on sales. SuperShades will be indifferent when the operating income under the two alternatives are equal. 425. x x x x x 426. $20 − $5 – $6,000 = $20 – $5 − $20 (0.08) − $5,200 x x 427. $15 – $6,000 = $13.40 − $5,200 x 428.$1.60 = $800 x 429. = 500 sunglasses 430.

431. For sales between 0 and 500 sunglasses, SuperShades prefers to pay the 8% commission x x because in this range, $13.40 − $5,200 > $15 – $6,000. For sales greater than 500 x sunglasses, the company prefers to pay the monthly fixed rent of $800 because $15 – x $6,000 > $13.40 − $5,200. 432. 433.

434. 3-42 (30 min.) CVP analysis, income taxes, sensitivity. 435. 436. 1a.To breakeven, Carlisle Engine Company must sell 1,200 units. This amount represents the point where revenues equal total costs. 437. Let Q denote the quantity of engines sold. 438. Revenue = Variable costs + Fixed costs 439. $4,000Q = $1000Q + $4,800,000 440. $3,000Q = $4,800,000 441. Q = 1,600 units 442. Breakeven can also be calculated using contribution margin per unit. 443. Contribution margin per unit = Selling price – Variable cost per unit = $4,000 – $1,000 = $3,000 444. Breakeven = Fixed Costs  Contribution margin per unit 445. = $4,800,000  $3,000 446. = 1,600 units 447. 448. 1b. To achieve its net income objective, Carlisle Engine Company must sell 2,100 units. This amount represents the point where revenues equal total costs plus the corresponding operating income objective to achieve net income of $1,200,000. 449. 450. Revenue = Variable costs + Fixed costs + [Net income ÷ (1 – Tax rate)] 451. $4,000Q = $1,000Q + $4,800,000 + [$1,200,000  (1  0.20)] 452. $4,000Q = $1,000Q + $4,800,000 + $1,500,000 453. Q = 2,100 units 454. 455. 2. None of the alternatives will help Carlisle Engineering achieve its net income objective of $1,200,000. Alternative b, where variable costs are reduced by $300 and selling price is reduced by $400 resulting in 1,750 additional units being sold through the end of the year, yields the highest net income of $1,180,000. Carlisle’s managers should examine how to modify Alternative b to further increase net income. For example, could variable costs be decreased by more than $300 per unit or selling prices decreased by less than $400? Calculations for the three alternatives are shown below. 456. 457. Alternative a 458. Revenues = ($4,000  400) + ($3,400a  2,100) = $8,740,000 459. Variable costs = $1,000  2,500b = $2,500,000 460. Operating income = $8,740,000 $2,500,000  $4,800,000 = $1,440,000 461. Net income = $1,440,000  (1  0.20) = $1,152,000 a 462. $4,000 – ($4,000 × 0.15) ; b400 units + 2,100 units. 463. 464.

465. 466. 467. 468. 469. 470. 471. 472. 473. 474. 475. 476. 477. 478. 479. 480.

Alternative b Revenues = ($4,000  400) + ($3,600a  1,750) = $7,900,000 Variable costs = ($1,000  400) + (700b  1,750) = $1,625,000 Operating income = $7,900,000  $1,625,000  $4,800,000 = $1,475,000 Net income = $1,475,000  (1  0.20) = $1,180,000 a b $4,000 – 400 ; $1,000 – $300. Alternative c Revenues = ($4,000  400) + ($2,800a  2,200) = $7,760,000 Variable costs = $1,000  2,600b = $2,600,000 Operating income = $7,760,000 $2,600,000  $4,320,000c = 840,000 Net income = $840,000  (1  0.20) = $672,000 a $4,000 – ($4,000 0.30); b400 units + 2,200nits; c$4,800,000 – ($4,800,000  0.10)

481. 3-43 (30 min.) Choosing between compensation plans, operating leverage. 482. 483. 1. We can recast BioPharm’s income statement to emphasize contribution margin, and then use it to compute the required CVP parameters. 484. 485. BioPharm Corporation 486.

489. 492. 497. 502. 507. 512. 517. 522. 527. 532. 537. 542.

547. 548. 555. 556.

487. Income Statement for the Year Ended December 31, 2014 488. 491. Using Own Sales 490. Using Sales Agents Force 494. $32,0 496. $32,0 00,00 00,00 Revenues 493. 0 495. 0 Variable Costs 498. 499. 500. 501. 503. $12,1 505. $12,1 60,00 60,00 Cost of goods sold—variable 0 504. 0 506. 509. 18,5 511. 16,3 508. 6,40 60,00 510. 4,16 20,00 Marketing commissions 0,000 0 0,000 0 514. 13,44 516. 15,68 Contribution margin 513. 0,000 515. 0,000 Fixed Costs 518. 519. 520. 521. 523. 3,750, 525. 3,750, Cost of goods sold—fixed 000 524. 000 526. 529. 7,4 528. 3,66 10,00 530. 5,90 531. 9,65 Marketing—fixed 0,000 0 0,000 0,000 534. $ 536. $ 6,030, 6,030, Operating income 533. 000 535. 000 538. 539. 540. 541. Contribution margin 543.  percentage ($13,440,000  $32,000,000; $15,680,000 $32,000,000) 544. 42% 545. 546. 49% 550. 553. Breakeven revenues $17,6 $19,6  42,85 93,87 ($7,410,000 0.42; $9,650,000 7 8  0.49) 549. 551. 552. 554. Degree of operating leverage 557.  ($13,440,000 $6,030,000; 558. 560.  $15,680.000 $6,030,000) 2.23 559. 2.60

561. 562. 2. The calculations indicate that at sales of $32,000,000, a percentage change in sales and contribution margin will result in 2.23 times that percentage change in operating income if BioPharm continues to use sales agents and 2.60 times that percentage change in operating income if BioPharm employs its own sales staff. The higher contribution margin per dollar of sales and higher fixed costs gives BioPharm more operating leverage, that is, greater

benefits (increases in operating income) if revenues increase but greater risks (decreases in operating income) if revenues decrease. BioPharm also needs to consider the skill levels and incentives under the two alternatives. Sales agents have more incentive compensation and, hence, may be more motivated to increase sales. On the other hand, BioPharm’s own sales force may be more knowledgeable and skilled in selling the company’s products. That is, the sales volume itself will be affected by who sells and by the nature of the compensation plan. 563.

564. 3. 565. Fixed marketing costs

Variable costs of marketing = 16% of Revenues = $5,900,000 Variable Fixed marketing marketing Variable Fixed costs costs manuf. costs manuf. costs 566. Operating income = Revenues     567. Denote the revenues required to earn $6,030,000 of operating income by R, then 568.

569. R  0.38R  $3,750,000  0.16R  $5,900,000 = $6,030,000 570. R  0.38R  0.16R = $6,030,000 + $3,750,000 + $5,900,000 571. 0.46R = $15,680,000 572. R = $15,680,000 0.46 = $34,086,957 573. 3.44(15–25 min.) Sales mix, three products. 574. 1. Sales of A, B, and C are in ratio 20,000 : 100,000 : 80,000. So for every 1 unit of A, 5 (100,000 ÷ 20,000) units of B are sold, and 4 (80,000 ÷ 20,000) units of C are sold. 575. 576. Contribution margin of the bundle = 1  $3 + 5  $2 + 4  $1 = $3 + $10 + $4 = $17 $255,000 $17 577. Breakeven point in bundles = = 15,000 bundles 578. Breakeven point in units is: 579. Product 580. 15,000 bundles × 1 unit per A: bundle 581. 15,000 units 582. Product 583. 15,000 bundles × 5 units per B: bundle 584. 75,000 units 585. Product 586. 15,000 bundles × 4 units per 587. 60,000 C: bundle units 588. Total number of units to breakeven 589. 150,000 units 590. 591. Alternatively, Let Q = Number of units of A to break even 5Q = Number of units of B to break even 4Q = Number of units of C to break even Contribution margin – Fixed costs = Zero operating income $3Q + $2(5Q) + $1(4Q) – $255,000 $17Q Q 5Q 4Q Total 592.

= 0 = $255,000 = 15,000 ($255,000 ÷ $17) units of A = 75,000 units of B = 60,000 units of C = 150,000 units

593. 2.

Contribution margin: A: 20,000 $ 60,000 B: 100,000  $2 C: 80,000 80,000 Contribution margin Fixed costs

594.



$3

200,000 

$1

$340,000 255,000 Operating income $ 85,000

3.

Contribution margin A: 20,000  $3 $ 60,000 B: 80,000  $2 160,000 C: 100,000  $1 100,000 Contribution margin $320,000 Fixed costs 255,000 595. Operating income $ 65,000 596. 597. Sales of A, B, and C are in ratio 20,000 : 80,000 : 100,000. So for every 1 unit of A, 4 (80,000 ÷ 20,000) units of B and 5 (100,000 ÷ 20,000) units of C are sold. 598. 599. Contribution margin of the bundle = 1  $3 + 4  $2 + 5  $1 = $3 + $8 + $5 = $16 $255,000 $16 600. Breakeven point in bundles = = 15,938 bundles (rounded up) 601. Breakeven point in units is: 602. Product 603. 15,938 bundles × 1 unit per A: bundle 604. 15,938 units 605. Product 606. 15,938 bundles × 4 units per B: bundle 607. 63,752 units 608. Product 609. 15,938 bundles × 5 units per 610. 79,690 C: bundle units 611. Total number of units to breakeven 612. 159,380 units 613. 614. Alternatively, Let Q = Number of units of A to break even 4Q = Number of units of B to break even 5Q = Number of units of C to break even Contribution margin – Fixed costs = Breakeven point $3Q + $2(4Q) + $1(5Q) – $255,000 $16Q Q 4Q 5Q Total

= 0 = $255,000 = 15,938 ($255,000 ÷ $16) units of A (rounded up) = 63,752 units of B = 79,690 units of C = 159,380 units

Breakeven point increases because the new mix contains less of the higher contribution margin per unit, product B, and more of the lower contribution margin per unit, product C. 615. 616.

617. 3-45 (40 min.) Multi-product CVP and decision making. 618. 1. Faucet filter: 619. Selling price $100 620. Variable cost per unit 35 621. Contribution margin per unit $ 65 622. 623. Pitcher-cum-filter: 624. Selling price $120 625. Variable cost per unit 30 626. Contribution margin per unit $ 90 627. 628. Each bundle contains two faucet models and three pitcher models. 629.   630. So contribution margin of a bundle = 2 $65 + 3 $90 = $400 631. 632. Breakeven Fixed costs $1, 200, 000 point in =   3, 000 bundles Contribution margin per bundle $400 bundles 633. 634. 635. 636. 637. 638. 639. 640. 641. 642. 643. 644.

Breakeven point in units of faucet models and pitcher models is:  Faucet models: 3,000 bundles 2 units per bundle = 6,000 units  Pitcher models: 3,000 bundles 3 units per bundle = 9,000 units Total number of units to breakeven 15,000 units Breakeven point in dollars for faucet models and pitcher models is:  Faucet models: 6,000 units $100 per unit = $ 600,000  Pitcher models: 9,000 units $120 per unit = 1,080,000 Breakeven revenues $1,680,000

Alternatively, weighted average contribution margin per unit = Breakeven point =

$1,200,000  15, 000 units $80

2  15,000 units = 6,000 units 5 3 Pitcher-cum-filter: 15, 000 units  9, 000 units 5 Faucet filter:

Breakeven point in dollars 645.

 Faucet filter: 6,000 units $100 per unit = $600,000

(2  $65) + (3  $90) = $80 5

646.

 Pitcher-cum-filter: 9,000 units $120 per unit = $1,080,000

647. 2. Faucet filter: 648. Selling price $100 649. Variable cost per unit 30 650. Contribution margin per unit $ 70 651. Pitcher-cum-filter: 652. Selling price $120 653. Variable cost per unit 20 654. Contribution margin per unit $100 655. 656. Each bundle contains two faucet models and three pitcher models. 657.   658. So contribution margin of a bundle = 2 $70 + 3 $100 = $440 659. 660. Breakeven Fixed costs $1, 200, 000  $208, 000 point in =   3, 200 bundles Contribution margin per bundle $440 bundles 661. 662. 663. 664. 665. 666. 667. 668. 669. 670. 671.

Breakeven point in units of faucet models and pitcher models is:  Faucet models: 3,200 bundles 2 units per bundle = 6,400 units  Pitcher models: 3,200 bundles 3 units per bundle = 9,600 units Total number of units to breakeven 16,000 units Breakeven point in dollars for faucet models and pitcher models is:  Faucet models: 6,400 bundles $100 per unit = $ 640,000  Pitcher models: 9,600 bundles $120 per unit = 1,152,000 Breakeven revenues $1,792,000

Alternatively, weighted average contribution margin per unit = Breakeven point =

$1,200,000 + $208,000  16, 000 units $88

(2  $70) + (3  $100) = $88 5

2  16,000 units = 6,400 units 5 3 Pitcher-cum-filter: 16, 000 units  9, 600 units 5 Faucet filter:

Breakeven point in dollars: 672. 673. 674.

 Faucet filter: 6,400 units $100 per unit = $640,000  Pitcher-cum-filter: 9,600 units $120 per unit = $1,152,000

x 3. Let be the number of bundles for Crystal Clear Products to be indifferent between the old and new production equipment. 675. x 676. Operating income using old equipment = $400 – $1,200,000 677. x 678. Operating income using new equipment = $440 – $1,200,000 – $208,000 679. 680. At point of indifference: x x 681. $400 – $1,200,000 = $440 – $1,408,000 x x 682. $440 – $400 = $1,408,000 – $1,200,000 x 683. $40 = $208,000 x 684. = $208,000 ÷ $40 = 5,200 bundles 685.

686.

 Faucet models = 5,200 bundles 2 units per bundle = 10,400 units  Pitcher models = 5,200 bundles 3 units per bundle = 15,600 units Total number of units 26,000 units

687. 688. 689. 690. Let x be the number of bundles, 691. 692. When total sales are less than 26,000 units (5,200 bundles), $400x  $1,200,000 > $440x  $1,408,000, 693. so Crystal Clear Products is better off with the old equipment. 694. 695. When total sales are greater than 26,000 units (5,200 bundles), $440x  $1,408,000 > $400x  $1,200,000,

so Crystal Clear Products is better off buying the new equipment. 696. 697. At total sales of 24,000 units (4,800 bundles), Crystal Clear Products should keep the old production equipment. 698. 699. Check   700. $400 4,800 – $1,200,000 = $720,000 is greater than $440 4,800 – $1,408,000 = $704,000. 701. 702. 3-46 (20–25 min.) Sales mix, two products. 703. 1. Sales of standard and deluxe carriers are in the ratio of 187,500 : 62,500. So for every 1 unit of deluxe, 3 (187,500 ÷ 62,500) units of standard are sold. Contribution margin of the bundle = 3  $10 + 1  $20 = $30 + $20 = $50 $2, 250, 000 $50 705. Breakeven point in bundles = = 45,000 bundles 706. Breakeven point in units is: 707. Standard 708. 45,000 bundles × 3 units per 709. 135,000 carrier: bundle units 710. Deluxe 711. 45,000 bundles × 1 unit per 712. 45,000 carrier: bundle units 713. Total number of units to breakeven 714. 180,000 units 704.

Alternatively, Let Q = Number of units of Deluxe carrier to break even

3Q

= Number of units of Standard carrier to break even

Revenues – Variable costs – Fixed costs = Zero operating income $28(3Q) + $50Q – $18(3Q) – $30Q – $2,250,000 = $84Q + $50Q – $54Q – $30Q = $50Q = Q = 3Q =

0 $2,250,000 $2,250,000 45,000 units of Deluxe 135,000 units of Standard

The breakeven point is 135,000 Standard units plus 45,000 Deluxe units, a total of 180,000 units. 2a.

Unit contribution margins are: Standard: $28 – $18 = $10; Deluxe: $50 – $30 = $20 715. If only Standard carriers were sold, the breakeven point would be: 716. $2,250,000  $10 = 225,000 units.

717. 2b.

If only Deluxe carriers were sold, the breakeven point would be: $2,250,000  $20 = 112,500 units

3. Operating income = Contribution margin of Standard + Contribution margin of Deluxe - Fixed costs

= 200,000($10) + 50,000($20) – $2,250,000 = $2,000,000 + $1,000,000 – $2,250,000 = $750,000 Sales of standard and deluxe carriers are in the ratio of 200,000 : 50,000. So for every 1 unit of deluxe, 4 (200,000 ÷ 50,000) units of standard are sold. Contribution margin of the bundle = 4  $10 + 1  $20 = $40 + $20 = $60 $2, 250, 000 $60 719. Breakeven point in bundles = = 37,500 bundles 720. Breakeven point in units is: 721. Standard 722. 37,500 bundles × 4 units per 723. 150,000 carrier: bundle units 724. Deluxe 725. 37,500 bundles × 1 unit per 726. 37,500 carrier: bundle units 727. Total number of units to breakeven 728. 187,500 units 718.

Alternatively, Let Q = Number of units of Deluxe product to break even 4Q = Number of units of Standard product to break even $28(4Q) + $50Q – $18(4Q) – $30Q – $2,250,000 $112Q + $50Q – $72Q – $30Q

= 0 = $2,250,000

$60Q = $2,250,000 Q = 37,500 units of Deluxe 4Q = 150,000 units of Standard The breakeven point is 150,000 Standard +37,500 Deluxe, a total of 187,500 units. The major lesson of this problem is that changes in the sales mix change breakeven points and operating incomes. In this example, the budgeted and actual total sales in number of units were identical, but the proportion of the product having the higher contribution margin declined. Operating income suffered, falling from $875,000 to $750,000. Moreover, the breakeven point rose from 180,000 to 187,500 units. 729. 730.

731. 3-47 732. 733. 734. 735. 736. 737. 738. 739. 740. 741. 742.

(20 min.) Gross margin and contribution margin.  1. Ticket sales ($24 525 attendees) $12,600  Variable cost of dinner ($12a 525 attendees)$6,300  Variable invitations and paperwork ($1b 525) 525 Contribution margin Fixed cost of dinner 9,000 Fixed cost of invitations and paperwork 1,975 Operating profit (loss)

743. 2. 744.

a b

10,975 $ (5,200)

$6,300/525 attendees = $12/attendee $525/525 attendees = $1/attendee Ticket sales ($24



1,050 attendees)  Variable cost of dinner ($12 1,050 attendees)  Variable invitations and paperwork ($1 1,050) Contribution margin Fixed cost of dinner Fixed cost of invitations and paperwork Operating profit (loss)

$25,200 $12,600

745. 1,050 746. 747. 9,000 748. 1,975 749. 750. 751. 3-48 (30 min.) Ethics, CVP analysis. 752. 753. 1. Contribution margin percentage = Revenues  Variable costs Revenues $4, 000, 000  $2, 400, 000 $4,000,000 754.

= $1,600,000 $4,000,000

755. 756. Fixed costs Contributi on margin percentage

757. 758.

6,825 5,775

= = 40% Breakeven revenues =

=

$1,728,000 0.40

= $4,320,000

13,650 11,550 10,975 $ 575

759. 2.

If variable costs are 52% of revenues, contribution margin percentage equals 48% (100%  52%)

760.

Fixed costs Contributi on margin percentage 761.

Breakeven revenues

= $1,728,000 0.48

762. = = $3,600,000 763. 764. 3. Revenues $4,000,000 765. Variable costs (0.52  $4,000,000) 2,080,000 766. Fixed costs 1,728,000 767. Operating income $ 192,000 768. 769. 4. Incorrect reporting of environmental costs with the goal of continuing operations is unethical. In assessing the situation, the specific “Standards of Ethical Conduct for Management Accountants” (described in Exhibit 1-7) that the management accountant should consider are listed below. 770.

771. Competence 772. Clear reports using relevant and reliable information should be prepared. Preparing reports on the basis of incorrect environmental costs to make the company’s performance look better than it is violates competence standards. It is unethical for Madden not to report environmental costs to make the plant’s performance look good. 773. 774. Integrity 775. The management accountant has a responsibility to avoid actual or apparent conflicts of interest and advise all appropriate parties of any potential conflict. Madden may be tempted to report lower environmental costs to please Buckner and Hewitt and save the jobs of his colleagues. This action, however, violates the responsibility for integrity. The Standards of Ethical Conduct require the management accountant to communicate favorable as well as unfavorable information. 776.

777. Credibility 778. The management accountant’s Standards of Ethical Conduct require that information should be fairly and objectively communicated and that all relevant information should be disclosed. From a management accountant’s standpoint, underreporting environmental costs to make performance look good would violate the standard of objectivity. 779. 780. Madden should indicate to Buckner that estimates of environmental costs and liabilities should be included in the analysis. If Buckner still insists on modifying the numbers and reporting lower environmental costs, Madden should raise the matter with one of Buckner’s superiors. If after taking all these steps, there is continued pressure to understate environmental costs, Madden should consider resigning from the company and not engage in unethical behavior.

781. 782.

783. 3-49 784.

(35 min.)

Deciding where to produce.

785.

786. Peoria 787. Moline 790. $150.0 792. $150. 789. 0791. 00 794. 795. 796. 797. 799. $72.00800. 801. $88.00802. 805. 86.0 807. 102. 804. 14.00 0 806. 14.00 00 809. 810. 64.00 811. 812. 48.00 814. 815. 816. 817. 819. 30.00820. 821. 15.00822. 825. 49.0 827. 29. 824. 19.00 0 826. 14.50 50 830. $ 832. $ 829. 15.00 831. 18.50 834. 835. 836. 837.

788. Selling price 793. Variable cost per unit 798. Manufacturing 803. Marketing and distribution 808. Contribution margin per unit (CMU) 813. Fixed costs per unit 818. Manufacturing 823.

Marketing and distribution

828. Operating income per unit 833. 838. CMU of normal production (as shown above) 843. CMU of overtime production 844. ($64 – $3; $48 – $8) 849. 854. 1. 859. Annual fixed costs = Fixed cost per unit Daily production rate capacity 860. ($49





839.



845. 850. 855.

840. $64841.

842. $48

846. 61847. 852. 857.

848. 40 853. 858.

851. 856.

Normal annual



400 units 240 days;   861. $29.50 320 units 240 days)



862. $4,704,0 00863.

866. Breakeven volume = FC CMU of normal   production ($4,704,000 $64; $2,265,600 867. 7 48) 3,500 868. units 871. 872. 873. 876. 2. 877. 878. 881. Units produced and sold 882. 96,000883. 886. Normal annual volume (units) 888. 96,0 887. (400 × 240; 320 × 240) 00889. 892. Units over normal volume (needing 893. overtime) 0894. 897. CM from normal production units (normal  annual volume CMU normal production) 899. $6,144,0 898. (96,000 × $64; 76,800 × 48) 00900. 903. CM from overtime production units 905.  904. (0; 19,200 $40) 0906. 910. 6,144,00 909. Total contribution margin 0911. 914. Total fixed costs 915. 4,704,0916.

864. $2,265,600865.

869.

47, 200 870. units 874. 875. 879. 880. 884. 96,000885. 890.

76,800891.

895.

19,200896.

901. $3,686,400902. 907.

768,000908.

912. 4,454,400913. 917. 2,265,600918.

919. Operating income 924. Total operating income

00 920. $1,440,0 00921. 922. $2,188,800923. 926. $3,628, 925. 800927. 928.

929. 930. 3. The optimal production plan is to produce 120,000 units at the Peoria plant and 72,000 units at the Moline plant. The full capacity of the Peoria plant, 120,000 units (400 units × 300 days), should be used because the contribution from these units is higher at all levels of production than is the contribution from units produced at the Moline plant. 931.

932. Contribution margin per plant: 933. Peoria, 96,000 × $64 $ 6,144,000 934. Peoria 24,000 × ($64 – $3) 1,464,000 935. Moline, 72,000 × $48 3,456,000 936. Total contribution margin 11,064,000 937. Deduct total fixed costs 6,969,600 938. Operating income $ 4,094,400 939. 940. The contribution margin is higher when 120,000 units are produced at the Peoria plant and 72,000 units at the Moline plant. As a result, operating income will also be higher in this case because total fixed costs for the division remain unchanged regardless of the quantity produced at each plant. 941. 942.