Week7 Tutorial 7 - Copy PDF

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Chapter 11 (1, 3, 6, 17, 18)

Q1. Night Shades, Inc. (NSI), manufactures biotech sunglasses. The variable materials cost is $11.13 per unit, and the variable labor cost is $7.29 per unit. a. What is the variable cost per unit? b. Suppose the company incurs fixed costs of $875,000 during a year in which total production is 190,000 units. What are the total costs for the year? c. If the selling price is $44.99 per unit, does the company break even on a cash basis? If depreciation is $435,000 per year, what is the accounting break-even point? ANSWER a. The total variable cost per unit is the sum of the two variable costs, so: Total variable costs per unit = $11.13 + 7.29 Total variable costs per unit = $18.42 b. The total costs include all variable costs and fixed costs. We need to make sure we are including all variable costs for the number of units produced, so: Total costs = Variable costs + Fixed costs Total costs = $18.42(190,000) + $875,000 Total costs = $4,374,800 c. The cash break-even, that is the point where cash flow is zero, is: QC = $875,000/($44.99 – 18.42) QC = 32,931.88 units And the accounting break-even is: QA = ($875,000 + 435,000)/($44.99 – 18.42) QA = 49,303.73 units Q3. Sloan Transmission, Inc., has the following estimates for its new gear assembly project: price = $1,440 per unit; variable costs = $460 per unit; fixed costs = $3.9 million; quantity = 85,000 units. Suppose the company believes all of its estimates are accurate only to within +/15 percent. What values should the company use for the four variables given here when it performs its best-case scenario analysis? What about the worst-case scenario? ANSWER The base-case, best-case, and worst-case values are shown below. Remember that in the bestcase, sales and price increase, while costs decrease. In the worst-case, sales and price decrease, and costs increase. Unit Scenario Unit Sales Unit Price Variable Cost Fixed Costs Base 85,000 $1,440 $460 $3,900,000 Best 97,750 1,656 391 3,315,000 Worst 72,250 1,224 529 4,485,000

Q6. We are evaluating a project that costs $786,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 65,000 units per year. Price per unit is $48, variable cost per unit is $25, and fixed costs are $725,000 per year. The tax rate is 22 percent, and we require a 10 percent return on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within +/- 10 percent. Calculate the best-case and worst-case NVP figures. ANSWER

We will use the tax shield approach to calculate the OCF for the best- and worst-case scenarios. For the best-case scenario, the price and quantity increase by 10 percent, so we will multiply the base-case numbers by 1.1, a 10 percent increase. The variable and fixed costs both decrease by 10 percent, so we will multiply the base-case numbers by .9, a 10 percent decrease. Doing so, we get: OCFbest = {[($48)(1.1) – ($25)(.9)](65,000)(1.1) – $725,000(.9)}(1 – .22) + .22($98,250) OCFbest = $1,202,496 The best-case NPV is: NPVbest = –$786,000 + $1,202,496(PVIFA10%,8) NPVbest = $5,629,227.41 For the worst-case scenario, the price and quantity decrease by 10 percent, so we will multiply the base-case numbers by .9, a 10 percent decrease. The variable and fixed costs both increase by 10 percent, so we will multiply the base-case numbers by 1.1, a 10 percent increase. Doing so, we get: OCFworst = {[($48)(.9) – ($25)(1.1)](65,000)(.9) – $725,000(1.1)}(1 – .22) + .22($98,250) OCFworst = $115,956 The worst-case NPV is: NPVworst = –$786,000 + $115,956(PVIFA10%,8) NPVworst = –$167,383.30 Q17. Consider a four-year project with the following information: initial fixed asset investment = $575,000; straight-line depreciation to zero over the four-year life; zero salvage value; price = $29; variable costs = $19; fixed costs = $235,000; quantity sold = 76,000 units; tax rate = 21 percent. How sensitive is OCF to changes in quantity sold? ANSWER Using the tax shield approach, the OCF at 76,000 units will be: OCF = [(P – v)Q – FC](1 – TC) + TCD OCF = [($29 – 19)(76,000) – 235,000](1 – .21) + .21($575,000/4) OCF = $444,937.50 We will calculate the OCF at 77,000 units. The choice of the second level of quantity sold is arbitrary and irrelevant. No matter what level of units sold we choose, we will still get the same sensitivity. So, the OCF at this level of sales is:

OCF = [($29 – 19)(77,000) – 235,000](1 – .21) + .21($575,000/4) OCF = $452,837.50 The sensitivity of the OCF to changes in the quantity sold is: Sensitivity = OCF/Q = ($449,937.50 – 452,837.50)/(76,000 – 77,000) OCF/Q = +$7.90 OCF will increase by $7.90 for every additional unit sold. Q18. In the previous problem, what is the degree of operating leverage at the given level of output? What is the degree of operating leverage at the accounting break-even level of output? ANSWER At 76,000 units, the DOL is: DOL = 1 + FC/OCF DOL = 1 + ($235,000/$444,937.50) DOL = 1.53 And, at the accounting break-even level, the DOL is: DOL = 1 + [$235,000/($575,000/4)] DOL = 2.63...