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CHAPTER 11
PROJECT ANALYSIS AND EVALUATION
Learning Objectives
LO1 How to perform and interpret a sensitivity analysis for a proposed investment.
LO2 How to perform and interpret a scenario analysis for a proposed investment.
LO3 How to determine and interpret cash, accounting, and financial break-even points.
LO4 How the degree of operating leverage can affect the cash flows of a project.
LO5 How managerial options affect net value.
Answers to Concepts Review and Critical Thinking Questions
1. (LO1) Forecasting risk is the risk that a poor decision is made because of errors in projected cash flows.
The danger is greatest with a new product because the cash flows are probably harder to predict.
2. (LO2) With a sensitivity analysis, one variable is examined over a broad range of values. With a
scenario analysis, all variables are examined for a limited range of values.
3. (LO3) Accounting break-even is unaffected (taxes are zero at that point).
Cash break-even is lower (assuming a tax credit).
Financial break-even will be higher (because of taxes paid).
4. (LO3) It is true that if average revenue is less than average cost, the firm is losing money. This much of
the statement is therefore correct. At the margin, however, accepting a project with a marginal revenue
in excess of its marginal cost clearly acts to increase operating cash flow.
5. (LO5) The option to abandon reflects our ability to shut down a project if it is losing money. Since this
option acts to limit losses, we will underestimate NPV if we ignore it.
6. (LO5) This is a good example of the option to expand.
7. (LO4) It makes wages and salaries a fixed cost, driving up operating leverage.
8. (LO4) Fixed costs are relatively high because airlines are relatively capital intensive (and airplanes are
expensive). Skilled employees such as pilots and mechanics mean relatively high wages which, because
of union agreements, are relatively fixed. Maintenance expenses are significant and relatively fixed as
well.
9. (LO5) With oil, for example, we can simply stop pumping if prices drop too far, and we can do so
quickly. The oil itself is not affected; it just sits in the ground until prices rise to a point where pumping
is profitable. Given the volatility of natural resource prices, the option to suspend output is very
valuable.
10. (LO1, 2) Euro Disney's experience illustrates that profitability is everybody’s concern. Finance and
marketing are strongly connected because revenues are the single most important determinant of cash
flow and profitability, and marketing is responsible, in large part, for revenue production. As we have
seen in many places, revenue projections are a key part of many types of financial analysis; such
projections are best developed in cooperation with marketing.
11-1 11-2 Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps.
Due to space and readability constraints, when these intermediate steps are included in this solutions
manual, rounding may appear to have occurred. However, the final answer for each problem is found
without rounding during any step in the problem.
Basic
1. (LO3)
a. The total variable cost per unit is the sum of the two variable costs, so:
Total variable costs per unit = $5.43 + 3.13
Total variable costs per unit = $8.56
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 = $8.56(280,000) + $720,000
Total costs = $3,116,800
c. The cash breakeven, that is the point where cash flow is zero, is:
Q C $720,000 / ($19.99 – 8.56)
Q C 62,992.13 units
And the accounting breakeven is:
Q A ($720,000 + 220,000) / ($19.99 – 8.56)
Q A 82,239.72 units
2. (LO3) 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 = ($24.86 + 14.08)(120,000) + $1,550,000
Total costs = $6,222,800
The marginal cost, or cost of producing one more unit, is the total variable cost per unit, so:
Marginal cost = $24.86 + 14.08
Marginal cost = $38.94
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 = $6,222,800/120,000
Average cost = $51.86
Minimum acceptable total revenue = 5,000($38.94)
Minimum acceptable total revenue = $194,700
Additional units should be produced only if the cost of producing those units can be recovered.
11-3 3. (LO2) 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.
Unit
Scenario Unit Sales Unit Price Variable Cost Fixed Costs
Base 95,000 $1,900.00 $240.00 $4,800,000
Best 109,250 $2,185.00 $204.00 $4,080,000
Worst 80,750 $1,615.00 $276.00 $5,520,000
4. (LO1) An estimate for the impact of changes in price on the profitability of the project can be found
from the sensitivity of NPV with respect to price: ΔNPV/ΔP. This measure can be calculated by finding
the NPV at any two different price levels and forming the ratio of the changes in these parameters.
Whenever a sensitivity analysis is performed, all other variables are held constant at their base-case
values.
5. (LO1, 3)
a. To calculate the accounting breakeven, we first need to find the depreciation for each year. The
depreciation is:
Depreciation = $724,000/8
Depreciation = $90,500 per year
And the accounting breakeven is:
Q A ($780,000 + 90,500)/($43 – 29)
Q A 62,179 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 + [$780,000/$90,500]
DOL = 9.619
b. We will use the tax shield approach to calculate the OCF. The OCF is:
OCF base [(P – v)Q – FC](1 – c ) +ct D
OCF base [($43 – 29)(90,000) – $780,000](0.65) + 0.35($90,500)
OCF base $343,675
Now we can calculate the NPV using our base-case projections. There is no salvage value or
NWC, so the NPV is:
NPV base –$724,000 + $343,675(PVIFA 15%,8
NPV base $818,180.22
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 95,000 units. The NPV at this sales level is:
OCF = [($43 – 29)(95,000) – $780,000](0.65) + 0.35($90,500)
new
OCF new= $389,175
And the NPV is:
NPV new= –$724,000 + $389,175(PVIFA 15%,8
NPV new= $1,022,353.35
11-4 So, the change in NPV for every unit change in sales is:
ΔNPV/ΔS = ($1,022,353.35 – 818,180.22)/(95,000 – 90,000)
ΔNPV/ΔS = +$40.835
If sales were to drop by 500 units, then NPV would drop by:
NPV drop = $40.835(500) = $20,417.31
You may wonder why we chose 95,000 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 $30. 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 $30 is:
OCF new= [($43 – 30)(90,000) – 780,000](0.65) + 0.35($90,500)
OCF new= $285,175
So, the change in OCF for a $1 change in variable costs is:
ΔOCF/Δv = ($285,175 – 343,675)/($30 – 29)
ΔOCF/Δv = –$58,500
If variable costs decrease by $1 then, OCF would increase by $58,500
6. (LO2) 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:
OCF best {[($43)(1.1) – ($29)(0.9)](90,000)(1.1) – $780,000(0.9)}(0.65) + 0.35($90,500)
OCF best $939,595
The best-case NPV is:
NPV best –$724,000 + $939,595(PVIFA 15%,8
NPV best $3,492,264.85
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:
OCF worst {[($43)(0.9) – ($29)(1.1)](90,000)(0.9) – $780,000(1.1)}(0.65) + 0.35($90,500)
OCF worst –$168,005
The worst-case NPV is:
NPV worst –$724,000 – $168,005(PVIFA 15%,8
NPV worst –$1,477,892.45
7. (LO3) The cash breakeven equation is:
11-5 Q C FC/(P – v)
And the accounting breakeven equation is:
Q = (FC + D)/(P – v)
A
Using these equations, we find the following cash and accounting breakeven points:
(1): Q =C$14M/($3,020 – 2,275) Q A ($14M + 6.5M)/($3,020 – 2,275)
Q = 18,792 Q = 27,517
C A
(2): Q =C$73,000/($38 – 27) Q A ($73,000 + 150,000)/($38 – 27)
Q C 6,636 Q A 20,273
(3): Q = $1,200/($11 – 4) Q = ($1,200 + 840)/($11 – 4)
C A
Q C 171 Q A 291
8. (LO3) We can use the accounting breakeven equation:
Q = (FC + D)/(P – v)
A
to solve for the unknown variable in each case. Doing so, we find:
(1): Q =A112,800 = ($820,000 + D)/($41 – 30)
D = $420,800
(2): Q =A165,000 = ($3.2M + 1.15M)/(P – $43)
P = $69.36
(3): Q = 4,385 = ($160,000 + 105,000)/($98 – v)
A
v = $37.57
9. (LO3) The accounting breakeven for the project is:
Q = [$9,000 + ($18,000/4)]/($57 – 32)
A
Q A 540
And the cash breakeven is:
Q = $9,000/($57 – 32)
C
Q C 360
At the financial breakeven, the project will have a zero NPV. Since this is true, the initial cost of the
project must be equal to the PV of the cash flows of the project. Using this relationship, we can find the
OCF of the project must be:
NPV = 0 implies $18,000 = OCF(PVIFA 12%,4
OCF = $5,926.22
Using this OCF, we can find the financial breakeven is:
Q F ($9,000 + $5,926.22)/($57 – 32) = 597
And the DOL of the project is:
11-6 DOL = 1 + ($9,000/$5,926.22) = 2.519
10. (LO3) In order to calculate the financial breakeven, we need the OCF of the project. We can use the
cash and accounting breakeven points to find this. First, we will use the cash breakeven to find the price
of the product as follows:
Q C FC/(P – v)
13,200 = $140,000/(P – $24)
P = $34.61
Now that we know the product price, we can use the accounting breakeven equation to find the
depreciation. Doing so, we find the annual depreciation must be:
Q A (FC + D)/(P – v)
15,500 = ($140,000 + D)/($34.61 – 24)
Depreciation = $24,394
We now know the annual depreciation amount. Assuming straight-line depreciation is used, the initial
investment in equipment must be five times the annual depreciation, or:
Initial investment = 5($24,394) = $121,970
The PV of the OCF must be equal to this value at the financial breakeven since the NPV is zero, so:
$121,970 = OCF(PVIFA 16%,5
OCF = $37,250.69
We can now use this OCF in the financial breakeven equation to find the financial breakeven sales
quantity is:
Q F ($140,000 + 37,250.69)/($34.61 – 24)
Q F 16,712
11. (LO4) We know that the DOL is the percentage change in OCF divided by the percentage change in
quantity sold. Since we have the original and new quantity sold, we can use the DOL equation to find
the percentage change in OCF. Doing so, we find:
DOL = %ΔOCF / %ΔQ
Solving for the percentage change in OCF, we get:
%ΔOCF = (DOL)(%ΔQ)
%ΔOCF = 3.40[(70,000 – 65,000)/65,000]
%ΔOCF = .2615 or 26.15%
The new level of operating leverage is lower since FC/OCF is smaller.
12. (LO4) Using the DOL equation, we find:
DOL = 1 + FC / OCF
3.40 = 1 + $130,000/OCF
OCF = $54,167
The percentage change in quantity sold at 58,000 units is:
11-7 %ΔQ = (58,000 – 65,000) / 65,000
%ΔQ = –.1077 or –10.77%
So, using the same equation as in the previous problem, we find:
%ΔOCF = 3.40(–10.77%)
%ΔQ = –36.62%
So, the new OCF level will be:
New OCF = (1 – .3662)($54,167)
New OCF = $34,333
And the new DOL will be:
New DOL = 1 + ($130,000/$34,333)
New DOL = 4.786
13. (LO4) The DOL of the project is:
DOL = 1 + ($73,000/$87,500)
DOL = 1.8343
If the quantity sold changes to 8,500 units, the percentage change in quantity sold is:
%ΔQ = (8,500 – 8,000)/8,000
%ΔQ = .0625 or 6.25%
So, the OCF at 8,500 units sold is:
%ΔOCF = DOL(%ΔQ)
%ΔOCF = 1.8343(.0625)
%ΔOCF = .1146 or 11.46%
This makes the new OCF:
New OCF = $87,500(1.1146)
New OCF = $97,531
And the DOL at 8,500 units is:
DOL = 1 + ($73,000/$97,531)
DOL = 1.7485
14. (LO4) We can use the equation for DOL to calculate fixed costs. The fixed cost must be:
DOL = 2.35 = 1 + FC/OCF
FC = (2.35 – 1)$43,000
FC = $58,050
If the output rises to 11,000 units, the percentage change in quantity sold is:
%ΔQ = (11,000 – 10,000)/10,000
%ΔQ = .10 or 10.00%
11-8 The percentage change in OCF is:
%ΔOCF = 2.35(.10)
%ΔOCF = .2350 or 23.50%
So, the operating cash flow at this level of sales will be:
OCF = $43,000(1 + .235)
OCF = $53,105
If the output falls to 9,000 units, the percentage change in quantity sold is:
%ΔQ = (9,000 – 10,000)/10,000
%ΔQ = –.10 or –10.00%
The percentage change in OCF is:
%ΔOCF = 2.35(–.10)
%ΔOCF = –.2350 or –23.50%
So, the operating cash flow at this level of sales will be:
OCF = $43,000(1 – .235)
OCF = $32,895
15. (LO4) Using the equation for DOL, we get:
DOL = 1 + FC/OCF
At 11,000 units
DOL = 1 + $58,050/$53,105
DOL = 2.0931
At 9,000 units
DOL = 1 + $58,050/$32,895
DOL = 2.7647
Intermediate
16. (LO3)
a. At the accounting breakeven, the IRR is zero percent since the project recovers the initial
investment. The payback period is N years, the length of the project since the initial investment is
exactly recovered over the project life. The NPV at the accounting breakeven is:
NPV = I [(1/N)(PVIFA R%,N – 1]
b. At the cash breakeven level, the IRR is –100 percent, the payback period is negative, and the NPV
is negative and equal to the initial cash outlay.
c. The definition of the financial breakeven is where the NPV of the project is zero. If this is true,
then the IRR of the project is equal to the required return. It is impossible to state the payback
period, except to say that the payback period must be less than the length of the project. Since the
discounted cash flows are equal to the initial investment, the undiscounted cash flows are greater
than the initial investment, so the payback must be less than the project life.
11-9 17. (LO1) Using the tax shield approach, the OCF at 110,000 units will be:
OCF = [(P – v)Q – FC](1 – t ) + t (D)
C C
OCF = [($32 – 19)(110,000) – 210,000](0.66) + 0.34($490,000/4)
OCF = $846,850
We will calculate the OCF at 111,000 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 = [($32 – 19)(111,000) – 210,000](0.66) + 0.34($490,000/4)
OCF = $855,430
The sensitivity of the OCF to changes in the quantity sold is:
Sensitivity = ΔOCF/ΔQ = ($846,850 – 855,430)/(110,000 – 111,000)
ΔOCF/ΔQ = +$8.58
OCF will increase by $8.58 for every additional unit sold.
18. (LO4) At 110,000 units, the DOL is:
DOL = 1 + FC/OCF
DOL = 1 + ($210,000/$846,850)
DOL = 1.2480
The accounting breakeven is:
Q A (FC + D)/(P – v)
Q A [$210,000 + ($490,000/4)]/($32 – 19)
Q A 25,576
And, at the accounting breakeven level, the DOL is:
DOL = 1 + [$210,000/($490,000/4)]
DOL = 2.7143
19. (LO1, 2, 3, 4)
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.
Scenario Unit sales Variable cost Fixed costs
Base 190 $11,200 $410,000
Best 209 $10,080 $369,000
Worst 171 $12,320 $451,000
Using the tax shield approach, the OCF and NPV for the base case estimate is:
OCF base [($18,000 – 11,200)(190) – $410,000](0.65) + 0.35($1,700,000/4)
OCF base $722,050
NPV base –$1,700,000 + $722,050(PVIFA 12%,4
NPV base $493,118.10
11-10 The OCF and NPV for the worst case estimate are:
OCF worst [($18,000 – 12,320)(171) – $451,000](0.65) + 0.35($1,700,000/4)
OCF worst $486,932
NPV worst –$1,700,000 + $486,932(PVIFA 12%,4
NPV worst –$221,017.41
And the OCF and NPV for the best case estimate are:
OCF best [($18,000 – 10,080)(209) – $369,000](0.65) + 0.35($1,700,000/4)
OCF = $984,832
best
NPV best –$1,700,000 + $984,832(PVIFA 12%,4
NPV best $1,291,278.83
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 $420,000. The OCF using this level of fixed costs and the other
base case values with the tax shield approach, we get:
OCF = [($18,000 – 11,200)(190) – $420,000](0.65) + 0.35($1,700,000/4)
OCF = $715,550
And the NPV is:
NPV = –$1,700,000 + $715,550(PVIFA 12%,4
NPV = $473,375.32
The sensitivity of NPV to changes in fixed costs is:
ΔNPV/ΔFC = ($493,118.10 – 473,375.32)/($410,000 – 420,000)
ΔNPV/ΔFC = –$1.974
For every dollar FC increase, NPV falls by $1.974.
c. The cash breakeven is:
QC= FC/(P – v)
Q C $410,000/($18,000 – 11,200)
Q C 60
d. The accounting breakeven is:
Q A (FC + D)/(P – v)
Q A [$410,000 + ($1,700,000/4)]/($18,000 – 11,200)
Q = 123
A
At the accounting breakeven, the DOL is:
DOL = 1 + FC/OCF
DOL = 1 + ($410,000/$425,000) = 1.9647
For each 1% increase in unit sales, OCF will increase by 1.9647%.
11-11 For the 1st printing of the textbook, please note the following amendment to the question printed in the
textbook:
20. ‘$165 net cash flow’ should read ‘$145 net cash flow’.
20. (LO5)
a. NPV base= –$3,900,000 + 906,250(PVIFA 14%,11 = $1,041,539.30
b. $2,700,000 = ($145)Q(PVIFA ) ; Q = $2,700,000/[145(5.2161)] = 3,570
14%,10
Abandon the project if Q < 3,570 units, because NPV(abandonment) > NPV (project CF’s)
c. The $2,700,000 is the market value of the project. If you continue with the project in one year,
you forego the $2,700,000 that could have been used for something else.
21. (LO5)
a. Success: PV future CF’s = $145(7,700)(PVIFA 14%,10 = $5,823,793.12
Failure: PV future CF’s = $145(3,500)(PVIFA 14%,10= $2,647,178.69
Expected value of project at year 1 = [(5,823,793.12+ 2,647,178.69)/2] + 906,250 = 5,141,735.90
NPV = –$3,900,000 + (5,141,735.90)/1.14
= $610,294.65
b. If we couldn’t abandon the project, PV future CF’s = $145(3,500)(PVIFA 14%,10 = $2,647,178.69
Gain from option to abandon = $2,700,000 – 2,647,178.69 = $52,821.31
Option is 50% likely to occur: value = (.50)($ 52,821.31)/1.14 = $23,167.24
22. (LO5)
Success: PV future CF’s = $145(15,400)(PVIFA 14%,10= $11,647,586.24
Failure: from #20, Q = 3,500 < 3,570 so you will abandon the project; PV = $2,700,000
Expected value of project at year 1 = [(11,647,586.24+2,700,000)/2] + 906,250 = $8,080,043.12
NPV = –$3,900,000 + (8,080,043.12)/1.14
= $3,187,757.12
If no expansion allowed, PV future CF’s = $145(7,700)(PVIFA 14%,10= $5,823,793.12
Gain from option to expand = $11,647,586.24 –5,823,793.12 = $5,823,793.12
Option is 50% likely to occur: value =(.50)( 5,823,793.12)/1.14 = $2,554,295.23
23. (LO1, 2) The marketing study and the research and development are both sunk costs and should be
ignored. We will calculate the sales and variable costs first. Since we will lose sales of the expensive
clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the
new project will be:
Sales
New clubs $750 × 51,000 = $38,250,000
Exp. clubs $1,200 × (–11,000) = –13,200,000
Cheap clubs $420 × 9,500 = 3,990,000
$29,040,000
11-12 For the variable costs, we must include the units gained or lost from the existing clubs. Note that the
variable costs of the expensive clubs are an inflow. If we are not producing the sets anymore, we will
save these variable costs, which is an inflow. So:
Var. costs
New clubs –$330 × 51,000 = –$16,830,000
Exp. clubs –$650 × (–11,000) = 7,150,000
Cheap clubs –$190 × 9,500 = –1,805,000
–$11,485,000
The pro forma income statement will be:
Sales $29,040,000
Variable costs 11,485,000
Fixed Costs 8,100,000
Depreciation 3,200,000
EBT $6,255,000
Taxes 2,502,000
Net income $3

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