You are considering a new product launch. The project will cost $2,200,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 150 units per year; price per unit will be $29,000, variable cost per unit will be $17,500, and fixed costs will be $590,000 per year. The required return on the project is 12 percent, and the relevant tax rate is 34 percent.

You are considering a new product launch. The project will cost $2,200,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 150 units per year; price per unit will be $29,000, variable cost per unit will be $17,500, and fixed costs will be $590,000 per year. The required return on the project is 12 percent, and the relevant tax rate is 34 percent.

  

a.

Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent. What are the upper and lower bounds for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios? (Negative amount should be indicated by a minus sign. Round your NPV answers to 2 decimal places. (e.g., 32.16))

Scenario	Unit Sales	Variable Cost	Fixed Costs	NPV
Base		$	$	$
Best
Worst

b.	Evaluate the sensitivity of your base-case NPV to changes in fixed costs. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places. (e.g., 32.161))

ΔNPV/ΔFC

$

  

c.	What is the cash break-even level of output for this project (ignoring taxes)? (Round your answer to 2 decimal places. (e.g., 32.16))

  

Cash break-even

  

d-1	What is the accounting break-even level of output for this project? (Round your answer to 2 decimal places. (e.g., 32.16))

  

Accounting break-even

d-2	What is the degree of operating leverage at the accounting break-even point? (Round your answer to 3 decimal places. (e.g., 32.161))

  

Degree of operating leverage

Explanation:

a.

The base-case, best-case, and worst-case values are shown below. Remember that in the best-case, sales and price increase, while costs decrease. In the worst-case, sales and price decrease, and costs increase.

Using the tax shield approach, the OCF and NPV for the base case estimate is:

  

OCFbase = [($29,000 – 17,500)(150) – $590,000](0.66) + 0.34($2,200,000/4)

OCFbase = $936,100

NPVbase = –$2,200,000 + $936,100(PVIFA12%,4)

NPVbase = $643,262.72

The OCF and NPV for the worst case estimate are:

OCFworst = [($29,000 – 19,250)(135) – $649,000](0.66) + 0.34($2,200,000/4)

OCFworst = $627,385

  

NPVworst = –$2,200,000 + $627,385(PVIFA12%,4)

NPVworst = –$294,412.58

  

And the OCF and NPV for the best case estimate are:

OCFbest = [($29,000 – 15,750)(165) – $531,000](0.66) + 0.34($2,200,000/4)

OCFbest = $1,279,465

  

NPVbest = –$2,200,000 + $1,279,465(PVIFA12%,4)

NPVbest = $1,686,182.18

b.

To calculate the sensitivity of the NPV to changes in fixed costs we choose another level of fixed costs. We will use fixed costs of $600,000. The OCF using this level of fixed costs and the other base case values with the tax shield approach, we get:

OCF = [($29,000 – 17,500)(150) – $600,000](0.66) + 0.34($2,200,000/4)

OCF = $929,500

And the NPV is:

NPV = –$2,200,000 + $929,500(PVIFA12%,4)

NPV = $623,216.22

  

The sensitivity of NPV to changes in fixed costs is:

ΔNPV/ΔFC = ($643,262.72 – 623,216.22)/($590,000 – 600,000)

ΔNPV/ΔFC = –$2.005

For every dollar FC increases, NPV falls by $2.005.

c.

The cash breakeven is:

QC = FC/(P – v)

QC = $590,000/($29,000 – 17,500)

QC = 51.30

d.

The accounting breakeven is:

QA= (FC + D)/(P – v)

QA = [$590,000 + ($2,200,000/4)]/($29,000 – 17,500)

QA = 99.13

At the accounting breakeven, the DOL is:

DOL = 1 + FC/OCF

DOL = 1 + ($590,000/$550,000) = 2.073

For each 1% increase in unit sales, OCF will increase by 2.073%.

In each of the following cases, calculate the accounting break-even and the cash break-even points. Ignore any tax effects in calculating the cash break-even. (Round your answers to 2 decimal places. (e.g., 32.16))

In each of the following cases, calculate the accounting  break-even and the cash break-even points. Ignore any tax effects in calculating the cash break-even. (Round your answers to 2 decimal places. (e.g., 32.16))

 

Case	Unit Price			Unit Variable Cost			Fixed Costs			Depreciation
1	$	3,370		$	2,675		$	8,120,000		$	3,060,000
2		146			81			78,000			350,000
3		31			7			3,700			860

Case	Accounting break-even	Cash break-even
1
2
3

Explanation:

The cash break-even equation is:

QC = FC/(P – v)

And the accounting break-even equation is:

QA = (FC + D)/(P – v)

 

Using these equations, we find the following cash and accounting break-even points:

 

a.	QC = $8,120,000/($3,370 – 2,675)	QA = ($8,120,000 + 3,060,000)/($3,370 – 2,675)
	QC = 11,683.45	QA = 16,086.33

 

b.	QC = $78,000/($146 – 81)	QA = ($78,000 + 350,000)/($146 – 81)
	QC = 1,200.00	QA = 6,584.62

c.	QC = $3,700/($31 – 7)	QA = ($3,700 + 860)/($31 – 7)
	QC = 154.17	QA = 190.00

We are evaluating a project that costs $690,000, has a five-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 71,000 units per year. Price per unit is $75, variable cost per unit is $50, and fixed costs are $790,000 per year. The tax rate is 35 percent, and we require a 15 percent return on this project.

We are evaluating a project that costs $690,000, has a five-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 71,000 units per year. Price per unit is $75, variable cost per unit is $50, and fixed costs are $790,000 per year. The tax rate is 35 percent, and we require a 15 percent return on this project.

   

a-1	Calculate the accounting break-even point.

Break-even point

units

   

a-2	What is the degree of operating leverage at the accountin g break-even point? (Round your answer to 3 decimal places. (e.g., 32.161))

   

DOL

   

b-1	Calculate the base-case cash flow and NPV. (Round your NPV answer to 2 decimal places. (e.g., 32.16))

Cash flow	$
NPV	$

b-2	What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))

ΔNPV/ΔQ

$

  

c.	What is the sensitivity of OCF to changes in the variable cost figure? (Negative amount should be indicated by a minus sign.)

  

ΔOCF/ΔVC

$

Explanation: a.

To calculate the accounting breakeven OCF, we first need to find the depreciation for each year. The depreciation is:

Depreciation = $690,000/5

Depreciation = $138,000 per year

   

And the accounting breakeven is:

QA = ($790,000 + 138,000)/($75 – 50)

QA = 37,120 units

   

To calculate the accounting breakeven, we must realize at this point (and only this point), the OCF is equal to depreciation. So, the DOL at the accounting breakeven is:

DOL = 1 + FC/OCF = 1 + FC/D

DOL = 1 + [$790,000)/$138,000)]

DOL = 6.725

b. 

We will use the tax shield approach to calculate the OCF. The OCF is:

  

OCFbase = [(P – v)Q – FC](1 – T) + TD

OCFbase = [($75 – 50)(71,000) – $790,000](0.65) + 0.35($138,000)

OCFbase = $688,550

Now we can calculate the NPV using our base-case projections. There is no salvage value or NWC, so the NPV is:

NPVbase = –$690,000 + $688,550(PVIFA15%,5)

NPVbase = $1,618,126.39

  

To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at a different quantity. We will use sales of 76,000 units. The NPV at this sales level is:

OCFnew = [($75 – 50)(76,000) – $790,000](0.65) + 0.35($138,000)

OCFnew = $769,800

  

And the NPV is:

NPVnew = –$690,000 + $769,800(PVIFA15%,5)

NPVnew = $1,890,488.99

  

So, the change in NPV for every unit change in sales is:

ΔNPV/ΔS = ($1,618,126.39 – 1,890,488.99)/(71,000 – 76,000)

ΔNPV/ΔS = +$54.473

  

If sales were to drop by 500 units, then NPV would drop by:

NPV drop = $54.473(500) = $27,236.26

You may wonder why we chose 76,000 units. Because it doesn’t matter! Whatever sales number we use, when we calculate the change in NPV per unit sold, the ratio will be the same.

c.

To find out how sensitive OCF is to a change in variable costs, we will compute the OCF at a variable cost of $51. Again, the number we choose to use here is irrelevant: We will get the same ratio of OCF to a one dollar change in variable cost no matter what variable cost we use. So, using the tax shield approach, the OCF at a variable cost of $51 is:

OCFnew = [($75 – 51)(71,000) – 790,000](0.65) + 0.35($138,000)

OCFnew = $642,400

So, the change in OCF for a $1 change in variable costs is:

ΔOCF/ΔVC = ($688,550 – 642,400)/($50 – 51)

ΔOCF/ΔVC = –$46,150

If variable costs decrease by $1 then, OCF would increase by $46,150

Olin Transmissions, Inc., has the following estimates for its new gear assembly project: price = $2,500 per unit; variable costs = $500 per unit; fixed costs = $5.1 million; quantity = 80,000 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?

Olin Transmissions, Inc., has the following estimates for its new gear assembly project: price = $2,500 per unit; variable costs = $500 per unit; fixed costs = $5.1 million; quantity = 80,000 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?

Scenario	Units Sales	Unit Price	Unit Variable cost	Fixed Costs
Base		$	$	$
Best
Worst

Explanation:

Remember that in the best-case, sales and price increase, while costs decrease. In the worst-case, sales and price decrease, and costs increase.

K-Too Everwear Corporation can manufacture mountain climbing shoes for $43.03 per pair in variable raw material costs and $25.45 per pair in variable labor expense. The shoes sell for $140 per pair. Last year, production was 110,000 pairs. Fixed costs were $1,150,000.

K-Too Everwear Corporation can manufacture mountain climbing shoes for $43.03 per pair in variable raw material costs and $25.45 per pair in variable labor expense. The shoes sell for $140 per pair. Last year, production was 110,000 pairs. Fixed costs were $1,150,000.

What were total production costs?

Total production cost

$

What is the marginal cost per pair? (Round your answer to 2 decimal places. (e.g., 32.16))

Marginal cost per pair

$

What is the average cost per pair? (Round your answer to 2 decimal places. (e.g., 32.16))

Average cost per pair

$

   

If the company is considering a one-time order for an extra 9,000 pairs, what is the minimum acceptable total revenue from the order?

  

Total revenue

$

Explanation:

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 = ($43.03 + 25.45)(110,000) + $1,150,000

Total costs = $8,682,800

  

The marginal cost, or cost of producing one more unit, is the total variable cost per unit, so:

Marginal cost = $43.03 + 25.45

Marginal cost = $68.48

The average cost per unit is the total cost of production, divided by the quantity produced, so:

Average cost = Total cost / Total quantity

Average cost = $8,682,800/110,000

Average cost = $78.93

Minimum acceptable total revenue = 9,000($68.48)

Minimum acceptable total revenue = $616,320

Additional units should be produced only if the cost of producing those units can be recovered.

Night Shades Inc. (NSI) manufactures biotech sunglasses. The variable materials cost is $18.50 per unit, and the variable labor cost is $7.00 per unit.

Night Shades Inc. (NSI) manufactures biotech sunglasses. The variable materials cost is $18.50 per unit, and the variable labor cost is $7.00 per unit.

a.	What is the variable cost per unit? (Round your answer to 2 decimal places. (e.g., 32.16))

Variable cost

$

  

b.	Suppose NSI incurs fixed costs of $800,000 during a year in which total production is 350,000 units. What are the total costs for the year?

  

Total cost

$

  

c.	If the selling price is $48.00 per unit, what is the cash break-even point? If depreciation is $600,000 per year, what is the accounting break-even point? (Round your answers to 2 decimal places. (e.g., 32.16))

Cash break-even point	units
Break-even point	units

Explanation:

a.

The total variable cost per unit is the sum of the two variable costs, so:

Total variable costs per unit = $18.50 + 7.00

Total variable costs per unit = $25.50

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 = $25.50(350,000) + $800,000

Total costs = $9,725,000

c.

The cash break even, that is the point where cash flow is zero, is:

QC = $800,000 / ($48.00 – 25.50)

QC = 35,555.56 units

And the accounting breakeven is:

QA = ($800,000 + 600,000) / ($48.00 – 25.50)

QA = 62,222.22 units

Dahlia Enterprises needs someone to supply it with 110,000 cartons of machine screws per year to support its manufacturing needs over the next five years, and you’ve decided to bid on the contract. It will cost you $770,000 to install the equipment necessary to start production; you’ll depreciate this cost straight-line to zero over the project’s life.

Dahlia Enterprises needs someone to supply it with 110,000 cartons of machine screws per year to support its manufacturing needs over the next five years, and you’ve decided to bid on the contract. It will cost you $770,000 to install the equipment necessary to start production; you’ll depreciate this cost straight-line to zero over the project’s life. You estimate that in five years, this equipment can be salvaged for $60,000. Your fixed production costs will be $315,000 per year, and your variable production costs should be $9.30 per carton. You also need an initial investment in net working capital of $65,000. If your tax rate is 34 percent and your required return is 10 percent on your investment, what bid price should you submit? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Bid price

$

Explanation:

To find the bid price, we need to calculate all other cash flows for the project, and then solve for the bid price. The aftertax salvage value of the equipment is:

Aftertax salvage value = $60,000(1 − 0.34) = $39,600

Now we can solve for the necessary OCF that will give the project a zero NPV. The equation for the NPV of the project is:

NPV = 0 = −$770,000 − 65,000 + OCF(PVIFA10%,5) + [($65,000 + 39,600) / 1.105]

Solving for the OCF, we find the OCF that makes the project NPV equal to zero is:

OCF = $770,051.63 / PVIFA12%,5 = $203,137.68

The easiest way to calculate the bid price is the tax shield approach, so:

OCF = $203,137.68 = [(P − v)Q − FC](1 − T) + TD

$203,137.68 = [(P − $9.30)(110,000) − $315,000](1 − 0.34) + 0.34($770,000/5)

P = $14.24

You are evaluating two different silicon wafer milling machines. The Techron I costs $222,000, has a three-year life, and has pretax operating costs of $57,000 per year. The Techron II costs $390,000, has a five-year life, and has pretax operating costs of $30,000 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $34,000. If your tax rate is 35 percent and your discount rate is 9 percent, compute the EAC for both machines.

You are evaluating two different silicon wafer milling machines. The Techron I costs $222,000, has a three-year life, and has pretax operating costs of $57,000 per year. The Techron II costs $390,000, has a five-year life, and has pretax operating costs of $30,000 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $34,000. If your tax rate is 35 percent and your discount rate is 9 percent, compute the EAC for both machines. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

	EAC
Techron I	$
Techron II	$

Which do you prefer?

Techron II

Explanation:

We will need the aftertax salvage value of the equipment to compute the EAC. Even though the equipment for each product has a different initial cost, both have the same salvage value. The aftertax salvage value for both is:

Aftertax salvage value = $34,000(1 − 0.35) = $22,100

To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for Techron I is:

OCF = −$57,000(1 − 0.35) + 0.35($222,000/3) = −$11,150

NPV = −$222,000 − $11,150(PVIFA9%,3) + ($22,100/1.093) = −$233,158.68

EAC = −$233,158.68 / (PVIFA9%,3) = −$92,110.45

And the OCF and NPV for Techron II is:

OCF = −$30,000(1 − 0.35) + 0.35($390,000/5) = $7,800

NPV = −$390,000 + $7,800(PVIFA9%,5) + ($22,100/1.095) = −$345,297.24

EAC = −$345,297.24 / (PVIFA9%,5) = −$88,773.31

The two milling machines have unequal lives, so they can only be compared by expressing both on an equivalent annual basis, which is what the EAC method does. Thus, you prefer the Techron II because it has the lower (less negative) annual cost.

Dog Up! Franks is looking at a new sausage system with an installed cost of $460,000. This cost will be depreciated straight-line to zero over the project’s five-year life, at the end of which the sausage system can be scrapped for $66,000. The sausage system will save the firm $230,000 per year in pretax operating costs, and the system requires an initial investment in net working capital of $25,000. If the tax rate is 30 percent and the discount rate is 8 percent, what is the NPV of this project?

Dog Up! Franks is looking at a new sausage system with an installed cost of $460,000. This cost will be depreciated straight-line to zero over the project’s five-year life, at the end of which the sausage system can be scrapped for $66,000. The sausage system will save the firm $230,000 per year in pretax operating costs, and the system requires an initial investment in net working capital of $25,000. If the tax rate is 30 percent and the discount rate is 8 percent, what is the NPV of this project? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

NPV

$

Explanation:

First we will calculate the annual depreciation of the new equipment. It will be:

Annual depreciation = $460,000/5

Annual depreciation = $92,000

Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus (or plus) the taxes on the sale of the equipment, so:

Aftertax salvage value = MV + (BV − MV)T

Very often the book value of the equipment is zero as it is in this case. If the book value is zero, the equation for the aftertax salvage value becomes:

   

Aftertax salvage value = MV + (0 − MV)T

Aftertax salvage value = MV(1 − T)

We will use this equation to find the aftertax salvage value since we know the book value is zero. So, the aftertax salvage value is:

Aftertax salvage value = $66,000(1 − 0.30)

Aftertax salvage value = $46,200

Using the tax shield approach, we find the OCF for the project is:

OCF = $230,000(1 − 0.30) + 0.30($92,000)

OCF = $188,600

Now we can find the project NPV. Notice we include the NWC in the initial cash outlay. The recovery of the NWC occurs in Year 5, along with the aftertax salvage value.

NPV = −$460,000 − 25,000 + $188,600(PVIFA8%,5) + [($46,200 + 25,000) / 1.085]

NPV = $316,482.64

Keiper, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $2.49 million. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate $2,010,000 in annual sales, with costs of $705,000. The tax rate is 34 percent and the required return on the project is 16 percent. What is the project’s NPV?

Keiper, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $2.49 million. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate $2,010,000 in annual sales, with costs of $705,000. The tax rate is 34 percent and the required return on the project is 16 percent. What is the project’s NPV? (Round your answer to 2 decimal places. (e.g., 32.16))

NPV

$

Explanation:

Using the tax shield approach to calculating OCF (Remember the approach is irrelevant; the final answer will be the same no matter which of the four methods you use.), we get:

OCF = (Sales − Costs)(1 − T) + T(Depreciation)

OCF = ($2,010,000 − 705,000)(1 − 0.34) + 0.34($2,490,000/3)

OCF = $1,143,500

Since we have the OCF, we can find the NPV as the initial cash outlay plus the PV of the OCFs, which are an annuity, so the NPV is:

NPV = −$2,490,000 + $1,143,500(PVIFA16%,3)

NPV = $78,174.69

Keiper, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $2.76 million. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate $2,100,000 in annual sales, with costs of $795,000. If the tax rate is 34 percent, what is the OCF for this project?

Keiper, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $2.76 million. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate $2,100,000 in annual sales, with costs of $795,000. If the tax rate is 34 percent, what is the OCF for this project? (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567.)

OCF

$

Explanation:

Using the tax shield approach to calculating OCF (Remember the approach is irrelevant; the final answer will be the same no matter which of the four methods you use.), we get:

OCF = (Sales − Costs)(1 − T) + T(Depreciation)

OCF = ($2,100,000 − 795,000)(1 − 0.34) + 0.34($2,760,000/3)

OCF = $1,174,100

Consider an asset that costs $712,000 and is depreciated straight-line to zero over its eight-year tax life. The asset is to be used in a five-year project; at the end of the project, the asset can be sold for $184,000. If the relevant tax rate is 35 percent, what is the aftertax cash flow from the sale of this asset?

Consider an asset that costs $712,000 and is depreciated straight-line to zero over its eight-year tax life. The asset is to be used in a five-year project; at the end of the project, the asset can be sold for $184,000. If the relevant tax rate is 35 percent, what is the aftertax cash flow from the sale of this asset?

Aftertax salvage value

$

Explanation:

The asset has an eight-year useful life and we want to find the BV of the asset after five years. With straight-line depreciation, the depreciation each year will be:

Annual depreciation = $712,000/8

Annual depreciation = $89,000

So, after five years, the accumulated depreciation will be:

Accumulated depreciation = 5($89,000)

Accumulated depreciation = $445,000

The book value at the end of Year 5 is thus:

BV5 = $712,000 − 445,000

BV5 = $267,000

The asset is sold at a loss to book value, so the depreciation tax shield of the loss is recaptured.

Aftertax salvage value = $184,000 + ($267,000 − 184,000)(0.35)

Aftertax salvage value = $213,050

To find the taxes on salvage value, remember to use the equation:

Taxes on salvage value = (BV − MV)T

This equation will always give the correct sign for a tax inflow (refund) or outflow (payment).

A piece of newly purchased industrial equipment costs $984,000 and is classified as seven-year property under MACRS. The MACRS depreciation schedule is shown in Table 10.7. Calculate the annual depreciation allowances and end-of-the-year book values for this equipment. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places. (e.g., 32.16))

A piece of newly purchased industrial equipment costs $984,000 and is classified as seven-year property under MACRS. The MACRS depreciation schedule is shown in Table 10.7. Calculate the annual depreciation allowances and end-of-the-year book values for this equipment. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places. (e.g., 32.16))

Year	Beginning Book Value	Depreciation	Ending book Value
1	$	$	$
2	$	$	$
3	$	$	$
4	$	$	$
5	$	$	$
6	$	$	$
7	$	$	$
8	$	$	$

Explanation:

The ending book value for any year is the beginning book value minus the depreciation for the year. Remember, to find the amount of depreciation for any year, you multiply the purchase price of the asset times the MACRS percentage for the year. The beginning book values and MACRS percentages are:

Year	Beginning Book Value				MACRS
1	$	984,000.00				0.1429
2		843,386.40				0.2449
3		602,404.80				0.1749
4		430,303.20				0.1249
5		307,401.60				0.0893
6		219,530.40				0.0892
7		131,757.60				0.0893
8		43,886.40				0.0446