RossFCF8ce SM Ch11

8/13/2019 RossFCF8ce SM Ch11

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CHAPTER 11

PROJECT ANALYSIS AND EVALUATIONLearning 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.LO How to determine and interpret cash, accounting, and financial break-even points.LO! How the degree of operating leverage can affect the cash flows of a project.LO" How managerial options affect net value.

Ans#ers t$ C$nce%ts Revie# an& Critica' T(in)ing *+esti$ns

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 e amined over a broad range of values. With a

scenario analysis, all variables are e amined for a limited range of values.

, (LO3) !ccounting break-even is unaffected "ta es are #ero at that point$.%ash break-even is lower "assuming a ta credit$.Financial break-even will be higher "because of ta es paid$.

!, (LO3) &t is true that if average revenue is less than average cost, the firm is losing money. This much ofthe statement is therefore correct. !t the margin, however, accepting a project with a marginal revenuein e cess of its marginal cost clearly acts to increase operating cash flow.

", (LO5) The option to abandon reflects our ability to shut down a project if it is losing money. 'ince thisoption acts to limit losses, we will underestimate ()* if we ignore it.

/, (LO5) This is a good e ample of the option to e pand. 0, (LO4) &t makes wages and salaries a fi ed cost, driving up operating leverage.

, (LO4) Fi ed costs are relatively high because airlines are relatively capital intensive "and airplanes aree pensive$. 'killed employees such as pilots and mechanics mean relatively high wages which, becauseof union agreements, are relatively fi ed. +aintenance e penses are significant and relatively fi ed aswell.

, (LO5) With oil, for e ample, we can simply stop pumping if prices drop too far, and we can do so

uickly. The oil itself is not affected it just sits in the ground until prices rise to a point where pumpingis profitable. iven the volatility of natural resource prices, the option to suspend output is veryvaluable.

13, -LO14 2. /uro 0isney1s e perience illustrates that profitability is everybody2s concern. Finance and

marketing are strongly connected because revenues are the single most important determinant of cashflow and profitability, and marketing is responsible, in large part, for revenue production. !s we haveseen in many places, revenue projections are a key part of many types of financial analysis such

projections are best developed in cooperation with marketing.

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S$'+ti$ns t$ *+esti$ns an& Pr$b'e5s

NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. ue to space and readability constraints! when these intermediate steps are included in this solutionsmanual! rounding may appear to have occurred. "owever! the final answer for each problem is foundwithout 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, so3

Total variable costs per unit 4 567.89 : ;.9=

b. The total costs include all variable costs and fi ed costs. We need to make sure we areincluding all variable costs for the number of units produced, so3

Total costs 4 *ariable costs : Fi ed costsTotal costs 4 56=.>="?97,777$ : 59=7,777Total costs 4 5@,=>>,;77

c. The cash breakeven, that is the point where cash flow is #ero, is3

A% 4 59=7,777 B "58

+inimum acceptable total revenue 4 @,777"5@8.;@$+inimum acceptable total revenue 4 5?=>,?@7

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

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, -LO2. The base-case, best-case, and worst-case values are shown below. Demember that in the best-case, sales and price increase, while costs decrease. &n the worst-case, sales and price decrease, andcosts increase.

Enit'cenario Enit 'ales Enit )rice *ariable %ost Fi ed %osts

ase 9@,777 56,877.77 5??7.77 5>,6@,777

Worst =?,?@7 56,6.77 58,89@,777

!, -LO1. !n estimate for the impact of changes in price on the profitability of the project can be foundfrom the sensitivity of ()* with respect to price3 ()*B ). This measure can be calculated by findingthe ()* 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-casevalues.

", (LO1, 3)a . To calculate the accounting breakeven, we first need to find the depreciation for each year.The depreciation is3

0epreciation 4 5


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'o, the change in ()* for every unit change in sales is3

()*B ' 4 "-59;,>??,8?=.;=$B"=7,777 C =@,777$ ()*B ' 4 :58>.=@

&f sales were to drop by @77 units, then ()* would drop by3

()* drop 4 58>.=@"@77$ 4 5?6,9=@

Lou may wonder why we chose =7,777 units. ecause it doesn2t matterM Whatever salesnumber we use, when we calculate the change in ()* per unit sold, the ratio will be the same.

c. To find out how sensitive G%F is to a change in variable costs, we will compute the G%F ata variable cost of 5>7. !gain, the number we choose to use here is irrelevant3 We will get thesame ratio of G%F to a one dollar change in variable cost no matter what variable cost we use. 'o,using the ta shield approach, the G%F at a variable cost of 5>7 is3

G%Fnew 4 I"58; C >7$"=@,777$ C 9?@,777J"7.;@$ : 7.>@"566@,@77$G%Fnew 4 5?98,6=@

'o, the change in G%F for a 56 change in variable costs is3

G%FB v 4 "5?98,6=@ C ?>@,8?@$B"5>7 C >6$ G%FB v 4 -589,=@7

&f variable costs decrease by 56 then, G%F would increase by 589,=@7

/, -LO2. We will use the ta shield approach to calculate the G%F for the best- and worst-case scenarios.For the best-case scenario, the price and uantity increase by 67 percent, so we will multiply the basecase numbers by 6.6, a 67 percent increase. The variable and fi ed costs both decrease by 67 percent, so

we will multiply the base case numbers by .


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0, -LO . The cash breakeven e uation is3

A% 4 F%B") C v$

!nd the accounting breakeven e uation is3

A ! 4 "F% : 0$B") C v$

Esing these e uations, we find the following cash and accounting breakeven points3

"6$3 A% 4 5,777B"58; C 86$ A! 4 "5=>,777 : 6@7,777$B"58; C86$A% 4 68,;77 A ! 4 88,;77

">$3 A% 4 56,=77B"566 C 8$ A! 4 "56,=77 : 7$B"566 C 8$A% 4 ?8?.9; A ! 4 >=@.=6

, -LO . We can use the accounting breakeven e uation3

A ! 4 "F% : 0$B") C v$

to solve for the unknown variable in each case. 0oing so, we find3

"6$3 A! 4 66?,977 4 "59?7,777 : 0$B"5>< C >7$0 4 56.?+ : 6.6@+$B") C 5?=$) 4 5@>.>;

">$3 A! 4 8,>9@ 4 "56;7,777 : 67@,777$B"5.96

!nd the cash breakeven is3

A% 4 56@,@77B"5;? C 86$A% 4 =>9.6

!t the financial breakeven, the project will have a #ero ()*. 'ince this is true, the initial cost of the project must be e ual to the )* of the cash flows of the project. Esing this relationship, we can find the

G%F of the project must be3

()* 4 7 implies 5?8,777 4 G%F")*&F! 6?K,8 $G%F 4 5=,

Esing this G%F, we can find the financial breakeven is3

AF 4 "56@,@77 : 5=,$B"5;? C 86$ 4 6668.>;

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!nd the 0G of the project is3

0G 4 6 : "56@,@77B5=,$ 4 ?.9.6@

(ow that we know the product price, we can use the accounting breakeven e uation to find thedepreciation. 0oing so, we find the annual depreciation must be3

A ! 4 "F% : 0$B") C v$6>,877 4 "56@7,777 : 0$B"5>9.6@ C ?8$0epreciation 4 5>9.6@ C ?8$AF 4 68,89>.=8

11, -LO!. We know that the 0G is the percentage change in G%F divided by the percentage change inuantity sold. 'ince we have the original and new uantity sold, we can use the 0G e uation to find

the percentage change in G%F. 0oing so, we find3

0G 4 K G%F B K A

'olving for the percentage change in G%F, we get3

K G%F 4 "0G $"K A$K G%F 4 ?.


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The percentage change in G%F is3

K G%F 4 ?.;6".7;=$KPG%F 4 .6=8< or 6=.8


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10, -LO1. Esing the ta shield approach, the G%F at =@,777 units will be3

G%F 4 I") C v$A C F%J"6 C t%$ : t %"0$G%F 4 I"5?@ C 6;$"=@,777$ C 697,777J"7.;;$ : 7.>8"58?7,777B8$G%F 4 5>;?,877

We will calculate the G%F at =;,777 units. The choice of the second level of uantity sold is arbitraryand irrelevant. (o matter what level of units sold we choose, we will still get the same sensitivity. 'o,the G%F at this level of sales is3

G%F 4 I"5?@ C 6;$"=;,777$ C 697,777J"7.;;$ : 7.>8"58?7,777B8$G%F 4 5>;9,>87

The sensitivity of the G%F to changes in the uantity sold is3

'ensitivity 4 G%FB A 4 "5>;9,>87 C >;?,877$B"=;,777 C =@,777$ G%FB A 4 :5@.

1 , -LO14 24 4 !.a . The base-case, best-case, and worst-case values are shown below. Demember that in the best-

case, sales and price increase, while costs decrease. &n the worst-case, sales and price decrease,and costs increase.

'cenario Enit sales *ariable cost Fi ed costsase 697 57,777est 69=,777

Worst 6;? 567,=97 58=>,777

Esing the ta shield approach, the G%F and ()* for the base case estimate is3

G%F base 4 I"56;,777 C @"56,877,777B8$G%F base 4 5@;9,877

()* base 4 C56,877,777 : 5@;9,877")*&F! 6?K,8 $ ()* base 4 5>?;,8?=

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The G%F and ()* for the worst case estimate are3

G%Fworst 4 I"56;,777 C 67,=97$"6;?$ C 58=>,777J"7.;@$ : 7.>@"56,877,777B8$G%Fworst 4 5>;8,=6;

()* worst 4 C56,877,777 : 5>;8,=6;")*&F! 6?K,8 $ ()* worst 4 C5?7.67

!nd the G%F and ()* for the best case estimate are3

G%F best 4 I"56;,777 C 9,9?7$"69=,777J"7.;@$ : 7.>@"56,877,777B8$G%F best 4 5=7;,;9;.;7

The sensitivity of ()* to changes in fi ed costs is3

()*B F% 4 "5>7;,;9;.;7 C >?;,8?=$B"5887,777 C 8>7,777$ ()*B F% 4 C56.


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.

23, (LO5)a . ()* base 4 C5@,@77,777 :6,;@>,=@7")*&F!68K,6; $ 4 58,9;7,98?.>=

b. 5?,977,777 4 "569


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For the variable costs, we must include the units gained or lost from the e isting clubs. (ote that thevariable costs of the e pensive clubs are an inflow. &f we are not producing the sets anymore, we willsave these variable costs, which is an inflow. 'o3

*ar. costs (ew clubs C5>


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'ales (ew clubs 58.@7 8


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%heap clubs C569@ 67,977 4 C 6,


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%osts 7,777

(et income 5 8,?8@,777

Esing the bottom up G%F calculation, we get3

G%F 4 (& : 0epreciation 4 58,?8@,777 : 8,?77,777G%F 4 59,88@,777

!nd the ()* is3

()* 4 C5??,?69.?9 - 6@,889,;;>.96$B"5977 C 9?@$ ()*B ) 4 56;7,;@=.9?

For every dollar increase "decrease$ in the price of the clubs, the ()* increases "decreases$ by56;7,;@=.9?.

To calculate the sensitivity of the ()* to changes in the uantity sold of the new club, we simply needto change the uantity sold. We will choose @;,777 units, but the choice is irrelevant as the sensitivitywill be the same no matter what uantity we choose.

We will calculate the sales and variable costs first. 'ince we will lose sales of the e pensive clubs andgain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new projectwill be3

'ales (ew clubs 59?@ @;777 4 58;,?77,777/ p. clubs 56,677 "C67,777$ 4 C66,777,777%heap clubs 5867 6?,777 4 8,


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Ta es >,@@?,777 (et income 5 @,>?9,777

Esing the bottom up G%F calculation, we get3

G%F 4 (& : 0epreciation 4 5@,>?9,777 : 8,?77,777G%F 4 578,[email protected]; - 6@,789,;;>.96$B"@;,777 C @@,777$ ()*B A 4 56,?@;.7@

For an increase "decrease$ of one set of clubs sold per year, the ()* increases "decreases$ by 59@;.7@.

2/, -LO .a. First we need to determine the total additional cost of the hybrid. The hybrid costs more to

purchase and more ownership costs each year, so the total additional cost is3

Total additional cost 4 5@,@;@ : ; "5>77$Total additional cost 4 5=>;@

(e t, we need to determine the cost per kilometre for each vehicle. The cost per km is the litres ofgasoline per 677 km multiplied by the cost per litre and divided by 677, or3

%ost per km for traditional 4 ";.=$ 56.>@ B 677%ost per km for traditional 4 57.7


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Total kms driven 4 ; "6@,777$Total kms driven 4 ,777,777,777 B ?8@.>8

b. &n this case the cash flows are a perpetuity. 'ince we know the cash flow per plane, we need todetermine the annual cash flow necessary to deliver a ?7 percent return. Esing the perpetuitye uation, we find3

)* 4 % BD 56>,777,777,777 4 % B .?7% 4 5?,;77,777,777

This is the total cash flow, so the number of planes that must be sold is the total cash flow divided by the cash flow per plane, or3

(umber of planes 4 5?,;77,777,777 B 5@?,?79,9>@.>8 (umber of planes 4 8


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'o3

AF 4 IF% : "G%F C t % V 0$JB") C v$AF 4 N5@77,777 : I56,6=7,>?9.9"5=77,777$JOB"587,777 C ?7,777$AF 4 =7.?? =6

c. !t the accounting break-even point, the net income is #ero. This using the bottom up definition ofG%F3

G%F 4 (& : 0

We can see that G%F must be e ual to depreciation. 'o, the accounting breakeven is3

A ! 4 NF% : I"0 C t %0$B"6 C t$JOB") C v$A ! 4 "F% : 0$B") C v$A ! 4 "F% : G%F$B") C v$

The ta rate has cancelled out in this case.

2 , (LO4) The 0G is e pressed as3

0G 4 K G%F B K A0G 4 NI"G%F 6 C G%F7$BG%F7J B I"A6 C A7$BA7JO

The G%F for the initial period and the first period is3

G%F6 4 I") C v$A 6 C F%J"6 C t%$ : t %0

G%F7 4 I") C v$A 7 C F%J"6 C t%$ : t %0

The difference between these two cash flows is3

G%F6 C G%F7 4 ") C v$"6 C t%$"A6 C A7$

0ividing both sides by the initial G%F we get3

"G%F6 C G%F7$BG%F7 4 ") C v$" 6C t%$"A6 C A7$ B G%F7

Dearranging we get3

I"G%F6 C G%F7$BG%F7JI"A6 C A7$BA7J 4 I") C v$"6 C t %$A7JBG%F7 4 IG%F 7 C t%0 : F%"6 C t$JBG%F70G 4 6 : IF%"6 C t$ C t %0JBG%F7

3, (LO2)a . We can calculate the G%F year-by-year, allowing for the half-year rule and a %%! that iscalculated on a declining balance basis.

%%! 6 4 ">,;77,777B?$".?$ 4 5>;7,777%%! ? 4 ">,?87,777$".?$ 4 5;89,777%%! > 4 "?,@


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G%F? 4 I"5?97 C 69@$"?@,777$ C 9@7,777J"7.;7$ : 7.87"5;89,777$ 4 56,6=8,?77G%F> 4 I"5?97 C 69@$"?@,777$ C 9@7,777J"7.;7$ : 7.87"5@69,877$ 4 56,6??,>;7G%F8 4 I"5?97 C 69@$"?@,777$ C 9@7,777J"7.;7$ : 7.87"5868,=?7$ 4 56,797,999G%F@ 4 I"5?97 C 69@$"?@,777$ C 9@7,777J"7.;7$ : 7.87"5>>6,==;$ 4 56,78=,=67.87

To find the ()* we need the after-ta net revenue each year as well as the present value of the%%! ta shield and the initial and ending cash flows.

&nitial %ash Flow year 7 4 -5>,;77,777 C >;7,777 4 -5>,$@

4 5=@;,=>=.7;

()* 4 C5>,,;77,777 8,687,777 >,7;7,777'alvage value "5$ @77,777 8?@,777 @=@,777

)rice "5$ ?97 ?@? >79 (W% "5$ >;7,777 >=9,777 >8?,777

%%! 6,worst 4 "8,687,777B?$".?$ 4 5868,777)roceed in the same way to calculate the %%! in each of the remaining 8 years.G%F6,worst 4 NI?@? C 69@J"?@,777$ C 9@7,777O"7.;7$ : 7.87"5868,777$

4 5;;7,;77)roceed in the same way to calculate the G%F in each of the remaining 8 years.

To find the ()* in the worst-case scenario, we need the after-ta net revenue each year as well asthe present value of the %%! ta shield and the initial and ending cash flows based on the worst-case assumptions.

&nitial %ash Flow year 7 4 -58,687,777 C >=9,777 4 -58,@69,777!fter-ta net revenue years 6-@ 4 I"' C %$-F%J "6 C T c$ 4 I"5;,>77,777 C 8,;?@,777$ C 9@7,777J

"6 C 7.87$ 4 8


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8?@,777".?$".87$ 6.6> : .?

"6.6>$@

4 599,7;7,777B?$".?$ 4 5>7;,777)roceed in the same way to calculate the %%! in each of the remaining 8 years.G%F6,best 4 NI>79C 69@J"?@,777$ C 9@7,777O"7.;7$ : 7.87"5>7;,777$

456,8@=,877)roceed in the same way to calculate the G%F in each of the remaining 8 years.

To find the ()* in the best-case scenario, we need the after-ta net revenue each year as well asthe present value of the %%! ta shield and the initial and ending cash flows based on the best-case assumptions.

!fter-ta net revenue year 7 4 -5>,7;7,777 C >8?,777 4 -5>,87?,777!fter-ta net revenue years 6-@ 4 I"' C %$ C F%J "6 C T c$ 4 I"5=,=77,777 C 8,;?@,777$ C9@7,777J "6 C 7.87$ 4 6,>>@,777

/nding cash flows "year @$ 4 recovery of (W% : salvage value 4 5>8?,777 : @=@,777 45;7,777$ 4 56,66;,777

The G%F for each of the remaining four years of the project can be found in the same way. 'ensitivity per 6,777 ton change in A is calculated as3

G%FB A 4 "56,66;,777 C 6,7@


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&nitial %ash Flow year 7 4 -5>,;77,777 C >;7,777 4 -5>,K,@$ : 5=@;,=>=.7; : 59;7,777B6.6> @ 4 5;9?,?@?

From Auestion S>6, A f 4 >;,>@7.8;

, -LO!.For year 63 0G 6 4 6 : I59@7,777"6 C 7.87$ C 7.87"5>;7,777$JB 56,7@8@;

Thus a 6K rise in uantity A leads to a 6.>8@;K rise in G%F. &f A rises to ?;,777, then

A 4 "?;,777 C ?@,777$B?@,777 4 8K, so K G%F 4 8K"6.>8@;$ 4 @.>9?8K

From Auestion S>6, G%FBG%F 4 "56,66;,777 C 6,7@9?8K

&n general, if A rises by 6,777 units, G%F rises by @,>9?8K.

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RossFCF8ce SM Ch11

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