CHAPTER 11
PROJECT ANALYSIS AND EVALUATION
Answers to Concepts Review and Critical Thinking Questions
1.
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.
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.
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.
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.
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.
This is a good example of the option to expand.
7.
It makes wages and salaries a fixed cost, driving up operating leverage.
8.
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.
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. The implication is that they will face hard capital rationing.
11. 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.
Solutions to Questions and Problems
Basic
1.
a.
b.
c.
Total variable costs = $0.74 + 2.61 = $3.35
Total costs = variable costs + fixed costs = $3.35(300,000) + $610,000 = $1,615,000
QC = $610,000 / ($7.00 – 3.35) = 167,123 units
QA = ($610,000 + 150,000) / ($7.00 – 3.35) = 208,219 units
2.
Total costs = ($10.94 + 32)(140,000) + $800,000 = $6,811,600
Marginal cost = cost of producing one more unit = $42.94
Average cost = total cost/total quantity = $6,811,600/140,000 = $48.65
367
Minimum acceptable total revenue = 10,000($42.94) = $429,400.
Additional units should be produced only if the cost of producing those units can be recovered.
3.
Unit sales
Price/unit
Variable cost/unit
Fixed costs
Scenario
Base
Best
Worst
Unit Sales
90,000
103,500
76,500
Base Case
90,000
$1,850
$160.00
$7,000,000
Lower Bound
76,500
$1,572.50
$136.00
$5,950,000
Unit Price
$1,850
$2,127.50
$1,572.50
Unit
Variable Cost
$160.00
$136.00
$184.00
Upper Bound
103,500
$2,127.50
$184.00
$8,050,000
Fixed Costs
$7,000,000
$5,950,000
$8,050,000
4.
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: NPV/P. 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.
a.
b.
c.
D = $924,000/6 = $154,000 per year
QA = ($800,000 + 154,000)/($34 – 19) = 63,600 units
DOL = 1 + FC/OCF = 1 + FC/D = 1 + [$800,000/$154,000] = 6.195
OCFbase = [(P – v)Q – FC](1 – t) + tD
= [($34 – 19)(130,000) – 800,000](0.65) + 0.35($154,000) = $801,400
NPVbase = –$924,000 + $801,400(PVIFA15%,6) = $2,108,884.43
Say Q = 135,000:
OCFnew = [($34 – 19)(135,000) – 800,000](0.65) + 0.35($154,000) = $850,150
NPVnew = –$924,000 + $850,150(PVIFA15%,6) = $2,293,377.96
NPV/S = ($2,293,377.96 – 2,108,884.43)/(135,000 – 130,000) = +$36.8987
If sales were to drop by 500 units, then NPV would drop by $36.8987(500) = $18,449.35
v = $18: OCFnew = [($34 – 18)(130,000) – 800,000](0.65) + 0.35($154,000) = $885,900
OCF/v = ($885,900–801,400 )/($18 – 19) = –$84,500
If variable costs fell by $1 then, OCF would rise by $84,500
6.
OCFbest = {[($34)(1.1) – ($19)(0.9)](130K)(1.1) – 800K(0.9)}(0.65) + 0.35(154K) = $1,472,785
NPVbest = –$924,000 + $1,472,785(PVIFA15%,6) = $4,649,729.34
OCFworst = {[($34)(0.9) – ($19)(1.1)](130K)(0.9) – 800K(1.1)}(0.65) + 0.35(154K) = $219,585
NPVworst = –$924,000 + $219,585(PVIFA15%,6) = –$92,984.37
7.
(1): QC = $16M/($2,000 – 1,675) = 49,231
(2): QC = $60,000/($40 – 32) = 7,500
(3): QC = $500/($7 – 2) = 100
QA = ($16M + 7M)/($2,000 – 1,675) = 70,769
QA = ($60,000 + 150,000)/($40 – 32) = 26,250
QA = ($500 + 420)/($7 – 2) = 184
8.
(1): QA = 125,400 = ($175,000 + D)/($34 – 26)
(2): QA = 140,000 = ($3M + 1.25M)/(P – $50)
(3): QA = 5,263 = ($145,000 + 90,000)/($100 – v)
D = $828,200
P = $80.36
v = $55.35
9.
QA = [$4,000 + ($9,000/3)]/($65 – 33) = 219
NPV = 0 implies $9,000 = OCF(PVIFA16%,3)
QF = ($4,000 + $4,007.32)/($65 – 33) = 250
QC = $4,000/($65 – 33) = 125
OCF = $4,007.32
DOL = 1 + ($4,000/$4,007.32) = 1.998
10. QC = FC/(P–v); 12,000 = $110,000/(P – $20); P = $29.17
QA = (FC+D)/(P–v); 18,000 = ($110,000 + D)/($29.17 – 20); D = $55,060
I = (D)(N); I = 5($55,060) = $275,300
368
OCF = $275,300/(PVIFA18%,5) = $88,034.84
Qf = ($110,000 + 88,034.84)/($29.17 – 20) = 21,596
11. DOL = %OCF/%Q; %OCF = 3[(36,000 – 30,000)/30,000] = 60.00%
The new level of operating leverage is lower since FC/OCF is smaller.
12. DOL = 3 = 1 + $150,000/OCF;
New OCF = $75,000(1.50) = $112,500
OCF = $75,000
New DOL = 1 + ($150,000/$112,500) = 2.333
13. DOL = 1 + ($30,000/$63,000) = 1.47619
%OCF = DOL(%Q) = 1.47619(.042857) = 6.32651%
DOL at 7,300 units = 1 + ($30,000/$66,985.70) = 1.4479
%Q = (7,300 – 7,000)/7,000 = 4.2857%
New OCF = $63,000(1.0632651) = $66,985.70
14. DOL = 3.5 = 1 + FC/OCF; FC = (3.5 – 1)$9,000 = $22,500
%Q = (11,000 – 10,000)/10,000 or (9,000 – 10,000)/10,000 = ±10.0%
%OCF = 3.5(± 10.0%) = ± 35%
OCF at 11,000 units = $9,000(1.35) = $12,150; OCF at 9,000 units = $9,000(0.65) = $5,850
15. DOL at 11,000 units = 1 + $22,500/$12,150 = 2.8519
DOL at 9,000 units = 1 + $22,500/$5,850 = 4.8462
Intermediate
16. a.
b.
c.
IRR = 0%;
IRR = –100%;
IRR = R%;
payback = N years;
payback = Never;
payback < N years;
NPV = I [(1/N)(PVIFAR %,N) – 1]
NPV = – I
NPV = 0
17. OCF @ 110,000 units = [($26 – 18)(110,000) – 185,000](0.66) + 0.34($420,000/3) = $506,300
OCF @ 111,000 units = [($26 – 18)(111,000) – 185,000](0.66) + 0.34($420,000/3) = $511,580
Sensitivity =OCF/Q = ($511,580 – 506,300)/(111,000 – 110,000) = +$5.28
OCF will increase by $5.28 for every additional unit sold.
18. DOL @ 110,000 units = 1 + ($185,000/$506,300) = 1.3654
Qa = [$185,000 + ($420,000/3)]/($26 – 18) = 40,625
DOL @ 40,625 units = 1 + ($185,000/$140,000) = 2.3214
19. a.
b.
c.
d.
20. a.
Sales = 160(1±0.10) = 176, 144; variable costs = $14,000(1±0.10) = $15,400, $12,600
Fixed costs = $150,000(1±0.10) = $165,000, $135,000
OCFbase = [($19,000 – 14,000)(160) – $150,000](0.65) + 0.35($680,000/4) = $482,000
NPVbase = –$680,000 + $482,000(PVIFA15%,4) = $696,099.57
OCFworst = [($19,000 – 15,400)(144) – $165,000](0.65) + 0.35($680,000/4) = $289,210
NPVworst = –$680,000 + $289,210(PVIFA15%,4) = +$145,688.29
OCFbest = [($19,000 – 12,600)(176) – $135,000](0.65) + 0.35($680,000/4) = $703,910
NPVbest = –$680,000 + $703,910(PVIFA15%,4) = $1,329,647.82
Say FC are $160,000:
OCF = [($19,000 – 14,000)(160) – $160,000](0.65) + 0.35($680,000/4) = $475,500
NPV = –$680,000 + $475,500(PVIFA15%,4) = $677,542.21
NPV/FC = ($677,542.21 – 696,099.57)/($160,000 – 150,000) = –1.856
For every dollar FC increase, NPV falls by $1.86.
Qc = $150,000/($19,000 – 14,000) = 30
Qa = [$150,000 + ($680,000/4)]/($19,000 – 14,000) = 64
At this level of output, DOL = 1 + ($150,000/$170,000) = 1.8824
For each 1% increase in unit sales, OCF will increase by 1.8824%.
NPVbase = –$3,500,000 + 840,000(PVIFA16%,10) = $559,911.08
369
b.
c.
21. a.
b.
$2,500,000 = ($140)Q(PVIFA16%,9) ; Q = $2,500,000/[140(4.6065)] = 3,876
Abandon the project if Q < 3,876 units, because NPV(abandonment) > NPV (project CF’s)
The $2,500,000 is the market value of the project. If you continue with the project in one year, you
forego the $2,500,000 that could have been used for something else.
Success: PV future CF’s = $140(7,500)(PVIFA16%,9) = $4,836,871.07
Failure: PV future CF’s = $140(3,500)(PVIFA16%,9) = $2,257,206.50
Expected value of project at year 1 = [($4,836,871.07+2,257,206.50)/2]+840,000= $4,387,039
NPV = –$3,500,000 + (4,387,039)/1.16 = $281,930
If we couldn’t abandon the project, PV future CF’s = $140(3,500)(PVIFA 16%,9) = $2,257,206.50
Gain from option to abandon = $2,500,000 – 2,257,206.50 = $242,793.50
Option is 50% likely to occur: value = (.50)($242,793.50)/1.16 = $104,652.37
22. Success: PV future CF’s = $140(15,000)(PVIFA16%,9) = $9,673,742.14
Failure: from #20, Q = 3,500 < 3,876 so you will abandon the project; PV = $2,500,000
Expected value of project at year 1 = [($9,673,742.14 + 2,500,000)/2] + 840,000 = $6,926,871.07
NPV = –$3,500,000 + (6,926,871.07)/1.16 = $2,471,440.58
If no expansion allowed, PV future CF’s = $140(7,500)(PVIFA16%,9) = $4,836,871.07
Gain from option to expand = $9,673,742.14 – 4,836,871.07 = $4,836,871.07
Option is 50% likely to occur: value =(.50)(4,836,871.07)/1.16 = $2,084,858.22
Challenge
23.
The marketing study and the research and development are both sunk costs and should be ignored.
Sales
New clubs
Exp. clubs
Cheap clubs
Var. costs
New clubs
Exp. clubs
Cheap clubs
$600  50,000 = $30,000,000
$1,000  (– 12,000) = –12,000,000
$300  10,000 =
3,000,000
$21,000,000
$240  50,000 = $12,000,000
$550  (–12,000) = –6,600,000
$100  10,000 = 1,000,000
$6,400,000
The half-year rule has been incorporated into the calculation of the annual CCA.
Year 1
Year 2
Year 3
Sales
$21,000,000
$21,000,000
$21,000,000
Variable costs
6,400,000
6,400,000
6,400,000
Fixed costs
7,000,000
7,000,000
7,000,000
CCA
2,310,000
3,927,000
2,748,900
EBIT
5,290,000
3,673,000
4,851,100
Taxes
2,116,000
1,469,200
1,940,440
Net income
$ 3,174,000
$2,203,800
$2,910,660
To accurately calculate the payback period, we need to estimate the operating cash flows in the first three
years. These can be determined from the relationship:
OCF1 = NI + D = (S – C)(1 – Tc) + D × Tc = $3,174,000 + 2,310,000 = $5,484,000
OCF2 = NI + D = (S – C)(1 – Tc) + D × Tc = $2,203,800 + 3,927,000 = $6,130,800
OCF3 = NI + D = (S – C)(1 – Tc) + D × Tc = $2,910,660 + 2,748,900 = $5,659,560
The initial cost is made up of the cost of the plant and equipment plus the increase in net working capital
= $15.4M + 0.9M = $16.3M
370
Payback period = 2 + 4,685,200/5,659,560 = 2.83 years
To find the NPV and IRR we need the after-tax net revenue each year as well as the present value of the CCA
tax shield and the initial and ending cash flows.
After-tax net revenue year 0 = -$15,400,000 – 900,000 = -$16,300,000
After-tax net revenue years 1-7 = (S – C)(1 – Tc) = ($21,000,000 – 13,400,000)(1 – 0.4) = $4,560,000
Ending cash flows (year 7) = recovery of NWC + salvage value = $900,000 + 2,000,000 = $2,900,000
PV of CCATS = 15,400,000(.3)(.4) x (1 + .5(.14))
.14 + .3
1 + .14
-2,000,000(.3)(.4) x
1
.14 + .3
(1.14) 7
= $3,724,121
NPV = –$16.3M + $4.56M(PVIFA14%,7) + $3,724,121 + $2.9M/1.147 = $8,137,739
To simplify the IRR calculation, it is assumed that CCA tax shield cash flows are as risky as the cash flows for
the company’s overall operations. Accordingly, the appropriate discount rate for these particular cash flows is
the company’s cost of capital. The PV of CCATS is thus the same as for the NPV calculation.
NPV = 0 = –$16.3M + $4.56M(PVIFAIRR%,7) + $3,724,121 + $2.9M/(1 + IRR)7 = 32.17%
A more precise value for the IRR can be obtained using a spreadsheet program like Excel wherein potential
IRR values are input (trial and error) until a solution is obtained. It can be shown that the NPV= 0 when
IRR = 28.944554%.
24.
Unit sales (new)
Price (new)
VC (new)
Fixed costs
Sales lost (expensive)
Sales gained (cheap)
Base Case
50,000
$600
$240
$7,000,000
12,000
10,000
Lower Bound
45,000
$540
$216
$6,300,000
10,800
9,000
Best case
Sales
New clubs
Exp. clubs
Cheap clubs
Var. costs
New clubs
Exp. clubs
Cheap clubs
Year 1
Sales
Variable costs
Fixed costs
CCA
$660  55,000 = $36,300,000
$1,000  (–10,800) = – 10,800,000
$300  11,000 =
3,300,000
$28,800,000
$216  55,000 = $11,880,000
$550  (–10,800) = – 5,940,000
$100  11,000 = 1,100,000
$7,040,000
$28,800,000
7,040,000
6,300,000
2,310,000
371
Upper Bound
55,000
$660
$264
$7,700,000
13,200
11,000
EBIT
13,150,000
Taxes
5,260,000
Net income
$ 7,890,000
To find the NPV we need the after-tax net revenue each year as well as the present value of the CCA tax shield
and the initial and ending cash flows. Compared to the previous problem, only the after-tax net revenue for
years 1-7 change.
After-tax net revenue year 0 = -$15,400,000 – 900,000 = -$16,300,000
After-tax net revenue years 1-7 = (S – C)(1 – Tc) = ($28,800,000 – 13,340,000)(1 – 0.4) = $9,276,000
Ending cash flows (year 7) = recovery of NWC + salvage value = $900,000 + 2,000,000 = $2,900,000
PV of CCATS = $3,724,121
NPV = –$16.3M + $9.276M(PVIFA14%,7) + $3,724,121 + $2.9M/1.147 = $28,361,385
Worst case
Sales
New clubs
Exp. clubs
Cheap clubs
Var. costs
New clubs
Exp. clubs
Cheap clubs
$540  45,000 = $24,300,000
$1,000  (– 13,200) = – 13,200,000
$300  9,000 =
2,700,000
$13,800,000
$264  45,000 = $11,880,000
$550  (– 13,200) = – 7,260,000
$100  9,000 =
900,000
$5,520,000
To find the NPV we need the after-tax net revenue each year as well as the present value of the CCA tax shield
and the initial and ending cash flows. Compared to the previous problem, only the after-tax net revenue for
years 1-7 change.
After-tax net revenue year 0 = -$15,400,000 – 900,000 = -$16,300,000
After-tax net revenue years 1-7 = (S – C)(1 – Tc) = ($13,800,000 – 13,220,000)(1 – 0.4) = $348,000
Ending cash flows (year 7) = recovery of NWC + salvage value = $900,000 + 2,000,000 = $2,900,000
PV of CCATS = $3,724,121
NPV = –$16.3M + $0.348M(PVIFA14%,7) + $3,724,121 + $2.9M/1.147 = -$9,924,601
25. Price = $700
Sales
New clubs
Exp. clubs
Cheap clubs
Var. costs
New clubs
Exp. clubs
Cheap clubs
Year 1
Sales
Variable costs
Fixed costs
CCA
$700  50,000 = $35,000,000
$1,000  (– 12,000) = –12,000,000
$300  10,000 =
3,000,000
$26,000,000
$240  50,000 = $12,000,000
$550  (–12,000) = –6,600,000
$100  10,000 = 1,000,000
$6,400,000
$26,000,000
6,400,000
7,000,000
2,310,000
372
EBIT
10,290,000
Taxes
4,116,000
Net income
$ 6,174,000
To find the NPV we need the after-tax net revenue each year as well as the present value of the CCA tax shield
and the initial and ending cash flows. Compared to the previous problem, only the after-tax net revenue for
years 1-7 change.
After-tax net revenue year 0 = -$15,400,000 – 900,000 = -$16,300,000
After-tax net revenue years 1-7 = (S – C)(1 – Tc) = ($26,000,000 – 13,400,000)(1 – 0.4) = $7,560,000
Ending cash flows (year 7) = recovery of NWC + salvage value = $900,000 + 2,000,000 = $2,900,000
PV of CCATS = $3,724,121
NPV = –$16.3M + $7.56M(PVIFA14%,7) + $3,724,121 + $2.9M/1.147 = $21,002,654
NPV/P = ($21,002,654 – 8,137,739)/($700 – 600) = $128,649.15
For every dollar increase (decrease) in the price of the clubs, the NPV increases (decreases) by $128,649.15.
Quantity = 49,000
Sales
New clubs
Exp. clubs
Cheap clubs
Var. costs
New clubs
Exp. clubs
Cheap clubs
Year 1
Sales
Variable costs
Fixed costs
CCA
EBIT
Taxes
Net income
$600  49,000 = $29,400,000
$1,000  (– 2,000) = –12,000,000
$300  10,000 =
3,000,000
$20,400,000
$240  49,000 = $11,760,000
$550  (–12,000) = –6,600,000
$100  10,000 = 1,000,000
$6,160,000
$20,400,000
6,160,000
7,000,000
2,310,000
4,930,000
1,972,000
$ 2,958,000
To find the NPV we need the after-tax net revenue each year as well as the present value of the CCA tax shield
and the initial and ending cash flows. Compared to the previous problem, only the after-tax net revenue for
years 1-7 change.
After-tax net revenue year 0 = -$15,400,000 – 900,000 = -$16,300,000
After-tax net revenue years 1-7 = (S – C)(1 – Tc) = ($20,400,000 – 13,160,000)(1 – 0.4) = $4,344,000
Ending cash flows (year 7) = recovery of NWC + salvage value = $900,000 + 2,000,000 = $2,900,000
PV of CCATS = $3,724,121
NPV = –$16.3M + $4.344M(PVIFA14%,7) + $3,724,121 + $2.9M/1.147 = $7,211,465
NPV/Q = ($7,211,465 – 8,137,739)/(49,000 – 50,000) = $926.27
For an increase (decrease) of one set of clubs sold per year, the NPV increases (decreases) by $926.27.
26. a. From the tax-shield definition of OCF:
OCF = [ (P–v)Q – FC ](1–Tc) + TcD ; (OCF–TcD)/(1–Tc) = (P–v)Q – FC
{FC + [(OCF– Tc D)/(1–Tc)] }/(P–v) = Q
b. Qcf = {$500,000+[– 0.4(700,000)/0.6]}/(40,000–20,000) = 1.67
373
Qacc = {$500,000+[(700,000–700,000(0.4))/0.6]}/(40,000–20,000) = 60
OCFfinc = $3,500,000/PVIFA20%,5 = $1,170,328.96; thus Qfinc = 99.19
c. At the accounting break-even point, net income = 0, so OCF = NI+D = D
Qacc = {FC+[(D–TcD)/(1–Tc)]}/(P–v) = (FC+D)/(P–v) = (FC+OCF)/(P–v)
The tax rate has cancelled out in this case.
27.
DOL = %OCF / %Q = {[(OCF1 – OCF0)/OCF0] / [(Q1 – Q0)/Q0]}
OCF1 = [(P – v)Q1 – FC](1 – Tc) + TcD; OCF0 = [(P – v)Q0 – FC](1 – Tc) + Tc D;
OCF1 – OCF0 = (P – v)(1 – Tc)(Q1 – Q0)
(OCF1 – OCF0)/OCF0 = (P – v)( 1– Tc)(Q1 – Q0) / OCF0 ;
[(OCF1 – OCF0)/OCF0]/[(Q1 – Q0)/Q0] = [(P – v)(1 – Tc)Q0]/OCF0 =
[OCF0 – TcD + FC(1 – Tc)]/OCF0 ;
DOL = 1 + [FC(1 – Tc) – TcD]/OCF0
28. a.
We can calculate the OCF year-by-year, allowing for the half-year rule and a CCA that is calculated on a
declining balance basis.
CCA1 = (1,500,000/2)(.2) = $150,000
CCA2 = (1,350,000)(.2) = $270,000
CCA3 = (1,080,000)(.2) = $216,000
CCA4 = (864,000)(.2) = $172,800
CCA5 = (691,200)(.2) = $138,240
OCF1
OCF2
OCF3
OCF4
OCF5
= [($230 – 200)(35,000) – 300,000](0.62) + 0.38($150,000) = $522,000
= [($230 – 200)(35,000) – 300,000](0.62) + 0.38($270,000) = $567,600
= [($230 – 200)(35,000) – 300,000](0.62) + 0.38($216,000) = $547,080
= [($230 – 200)(35,000) – 300,000](0.62) + 0.38($172,800) = $530,664
= [($230 – 200)(35,000) – 300,000](0.62) + 0.38($138,240) = $517,531
To find the NPV we need the after-tax net revenue each year as well as the present value of the CCA tax
shield and the initial and ending cash flows.
After-tax net revenue year 0 = -$1,500,000 – 450,000 = -$1,950,000
After-tax net revenue years 1-5 = (S – C)(1 – Tc) = ($8,050,000 – 7,300,000)(1 – 0.38) = $465,000
Ending cash flows (year 5) = recovery of NWC + salvage value = $450,000 + 500,000 = $950,000
PV of CCATS = 1,500,000(.2)(.38) x (1 + .5(.13))
.13 + .2
1 + .13
-500,000(.2)(.38) x
1
.13 + .2
(1.13)5
= $263,084.
NPV = –$1,950,000 + $465,000(PVIFA13%,5) + $263,084 + $950,000/1.13 5 = $464,218
b.
Item
Initial cost ($)
Salvage value ($)
Price ($)
NWC ($)
Base case
1,500,000
500,000
230
450,000
Worst case
1,725,000
425,000
207
472,500
Best case
1,275,000
575,000
253
427,500
CCA1,worst = (1,725,000/2)(.2) = $172,500.
Proceed in the same way to calculate the CCA in each of the remaining 4 years.
OCF1,worst = {[207 – 200](35,000) – 300,000}(0.62) + 0.38($172,500)
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= $31,450
Proceed in the same way to calculate the OCF in each of the remaining 4 years.
To find the NPV in the worst-case scenario, we need the after-tax net revenue each year as well as the
present value of the CCA tax shield and the initial and ending cash flows based on the worst-case
assumptions.
After-tax net revenue year 0 = -$1,725,000 – 472,500 = -$2,197,500
After-tax net revenue years 1-5 = (S – C)(1 – Tc) = ($7,245,000 – 7,300,000)(1 – 0.38) = -$34,100
Ending cash flows (year 5) = recovery of NWC + salvage value = $472,500 + 425,000 = $897,500
PV of CCATS = 1,725,000(.2)(.38) x (1 + .5(.13))
.13 + .2
1 + .13
-425,000(.2)(.38) x
1
.13 + .2
(1.13)5
= $321,296
NPVworst = –$2,197,500 – $34,100(PVIFA13%,5) + $321,296 + $897,500/1.135 = -$1,509,015
CCA1,best = (1,275,000/2)(.2) = $127,500.
Proceed in the same way to calculate the CCA in each of the remaining 4 years.
OCF1,best = {[253 – 200](35,000) – 300,000}(0.62) + 0.38($127,500)
= $1,012,550
Proceed in the same way to calculate the OCF in each of the remaining 4 years.
To find the NPV in the best-case scenario, we need the after-tax net revenue each year as well as the
present value of the CCA tax shield and the initial and ending cash flows based on the best-case
assumptions.
After-tax net revenue year 0 = -$1,275,000 – 427,500 = -$1,702,500
After-tax net revenue years 1-5 = (S – C)(1 – Tc) = ($8,855,000 – 7,300,000)(1 – 0.38) = $964,100
Ending cash flows (year 5) = recovery of NWC + salvage value = $427,500 + 575,000 = $1,002,500
PV of CCATS = 1,275,000(.2)(.38) x (1 + .5(.13))
.13 + .2
1 + .13
-575,000(.2)(.38) x
1
.13 + .2
(1.13)5
= $204,871
NPVbest = –$1,702,500 + $964,100(PVIFA13%,5) + $204,871 + $1,002,500/1.135 = $2,437,451
29. Q = 36,000: OCF1 = [($230 – 200)(36,000) – 300,000](0.62) + 0.38($150,000) = $540,600
The OCF for each of the remaining four years of the project can be found in the same way.
OCF/Q = ($540,600 – 522,000)/(36,000 – 35,000) = +$18.60
To find the NPV we need the after-tax net revenue each year as well as the present value of the CCA tax shield
and the initial and ending cash flows.
After-tax net revenue year 0 = -$1,500,000 – 450,000 = -$1,950,000
After-tax net revenue years 1-5 = (S – C)(1 – Tc) = ($8,280,000 – 7,500,000)(1 – 0.38) = $483,600
Ending cash flows (year 5) = recovery of NWC + salvage value = $450,000 + 500,000 = $950,000
PV of CCATS = $263,084.
375
NPV = –$1,950,000 + $483,600(PVIFA13%,5) + $263,084 + $950,000/1.13 5 = $529,639
NPV/Q = ($529,639 – 464,218)/(36,000 – 35,000) = +$65.42
You wouldn’t want Q to fall below the point where NPV = 0:
$464,218 = $65.42(Q) ; Q = 7,096; Qmin = 35,000 – 7,096 = 27,904
0  0.38 150,000 
OCF - T x D
300 ,000 
1 - 0.38
1
T

 6,935 .48
30. For year 1: At Qc, OCF1 = 0: Q c 
P-v
230 - 200
For year 1: Qa = [$300,000 + $150,000]/($230 – 200); Qa = 15,000
From #29, Qf = 27,904
FC 
31. For year 1: DOL1 = 1 + [$300,000(1 – 0.38) – 0.38($150,000)]/ $522,000 = 1.24713
Thus a 1% rise leads to a 1.24713% rise in OCF. If Q rises to 36,000, then
Q = (36,000 – 35,000)/35,000 = 2.857%, so %OCF = 2.857%(1.24713) = 3.563%
From #29, OCF/OCF = ($540,600 – 522,000)/$522,000 = 0.03563
In general, if Q rises by 1 unit, OCF rises by 3.563%.
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