Chapter 7 Solutions (7.1-7.33) V18

8/11/2019 Chapter 7 Solutions (7.1-7.33) V18

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Chapter 7: Net Present Value and Capital Budgeting

7.1 a. Yes, the reduction in the sales of the companys other products, referred to as erosion, should be

treated as an incremental cash flow. These lost sales are included because they are a cost (arevenue reduction) that the firm must bear if it chooses to produce the new product.

b. Yes, expenditures on plant and equipment should be treated as incremental cash flows. These arecosts of the new product line. owever, if these expenditures have already occurred, they aresunk costs and are not included as incremental cash flows.

c. No, the research and development costs should not be treated as incremental cash flows. Thecosts of research and development underta!en on the product durin" the past # years are sunkcostsand should not be included in the evaluation of the pro$ect. %ecisions made and costsincurred in the past cannot be chan"ed. They should not affect the decision to accept or re$ect thepro$ect.

d. Yes, the annual depreciation expense should be treated as an incremental cash flow. %epreciationexpense must be ta!en into account when calculatin" the cash flows related to a "iven pro$ect.&hile depreciation is not a cash expense that directly affects cash flow, it decreases a firms netincome and hence, lowers its tax bill for the year. 'ecause of this depreciation tax shield, thefirm has more cash on hand at the end of the year than it would have had without expensin"depreciation.

e. No, dividend payments should not be treated as incremental cash flows. firms decision to pay

or not pay dividends is independent of the decision to accept or re$ect any "iven investmentpro$ect. or this reason, it is not an incremental cash flow to a "iven pro$ect. %ividend policy isdiscussed in more detail in later chapters.

f. Yes, the resale value of plant and equipment at the end of a pro$ects life should be treated as anincremental cash flow. The price at which the firm sells the equipment is a cash inflow, and anydifference between the boo! value of the equipment and its sale price will create "ains or lossesthat result in either a tax credit or liability.

". Yes, salary and medical costs for production employees hired for a pro$ect should be treated asincremental cash flows. The salaries of all personnel connected to the pro$ect must be included ascosts of that pro$ect.

7.* +tem + is a relevant cost because the opportunity to sell the land is lost if the new "olf club is produced.+tem ++ is also relevant because the firm must ta!e into account the erosion of sales of existin" products

when a new product is introduced. +f the firm produces the new club, the earnin"s from the existin" clubswill decrease, effectively creatin" a cost that must be included in the decision. +tem +++ is not relevantbecause the costs of esearch and %evelopment are sun! costs. %ecisions made in the past cannot bechan"ed. They are not relevant to the production of the new clubs. Choice Cis the correct answer.


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7.# -ash low -hart/ear 0 /ear 1 /ear * /ear # /ear

1. 2ales revenue 3 47,000 47,000 47,000 47,000*. 5peratin" costs 3 *,000 *,000 *,000 *,000#. %epreciation 3 *,600 *,600 *,600 *,600. +ncome before tax

13(*8#)93 *,600 *,600 *,600 *,600

6. Taxes at #: 3 ;60 ;60 ;60 ;60


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7. The initial payment, which occurs today (year 0), does not need to be discounted

?@ A 41,00,000

The expected value of his bonus payment is

Cxpected @alue A -0 (?robability of 5ccurrence) 8 -1 (?robability of =onoccurrence) A 4760,000 (0.


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?roduct t A 0 t A 1 3 1 t A 16

evenues 4106,000 4106,0003ore"one rent 1*,000 1*,0003Cxpenditures


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These calculations could also have been performed in a sin"le step

=?@ A 341;0,000 8 4*6,;


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2ince the last cash flow occurs 16 years from today, discount the amount of thecash flow bac! 16 years at 1* percent to determine its present value.

?@(-16) A 41#,0 #;,6>

10. =et income ;3>9 7>,*00 7>,*00 7;,60 77,1*1 7,;#11. -ash flow fromoperations 10879

16>,*00 16>,*00 16;,60 167,1*1 16,;#

1*. +nvestment1#. Total -ash low

300,0003400,000 416>,*00 416>,*00 416;,60 4167,1*1 416,;#

2ince the initial investment occurs today (year 0), its present value does not need to be ad$usted.

?@(-0) A 3400,000?@(-1) A 416>,*00 B (1.16) A 41#;,#6

?@(-*) A 416>,*00 B (1.16)*A 41*0,#7;?@(-#) A 416;,60 B (1.16)

#A 410,*#?@(-) A 4167,1*1 B (1.16)

A 4;>,;#?@(-6) A 416,;# B (1.16)

6A 47;0

=?@ A ?@(-0) 8 ?@(-1) 8 ?@(-*) 8 ?@(-#) 8 ?@(-) 8 ?@(-6) A $!2",(70


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=?@ A 3400,0008 416>,*00 B (1.16) 8 416>,*00 B (1.16)*8 416;,60 B (1.16)#8 4167,1*1 B (1.16)8 416,;# B (1.16)6

A $!2",(70

#he NPV o the in*est/ent is $!2",(70.

7.7/ear 0 /ear 1 /ear * /ear # /ear /ear 6

1. nnual 2alary 2avin"s 41*0,000 41*0,000 41*0,000 41*0,000 41*0,000*. %epreciation 100,000 100,000 100,000 100,000 100,000#. Taxable +ncome 13 *9 *0,000 *0,000 *0,000 *0,000 *0,000. Taxes 0

=?@ A ?@(-0) 8 ?@(-1) 8 ?@(-*) 8 ?@(-#) 8 ?@(-) 8 ?@(-6) A +$!!,2&2


=?@ A 3400,000 8 411#,*00 B (1.1*) 8 411#,*00 B (1.1*)*8 411#,*00 B (1.1*)# 8411#,*00 B (1.1*)8 47>,*00 B (1.1*)6

A +$!!,2&2

ince the NPV o the co/puter is negati*e, it is not a worthwhile in*est/ent.


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7.;t A 0 t A 13 * t A #

1. evenues 41,000 A 0.#6 D 4* The least amount of money that the firm should as! for the first3year lease payment is the amount that will

ma!e the net present value of the purchase of the buildin" equal to Jero. +n other words, the least that thefirm will char"e for its initial lease payment is the amount that ma!es the present value of future cash flows$ust enou"h to compensate it for its 4,000,000 purchase. +n order to determine this amount, set the netpresent value of the pro$ect equal to Jero. 2olve for the amount of the initial lease payment.

2ince the purchase of the buildin" will occur today (year 0), its present value does not need to bead$usted.

?@(?urchase of 'uildin") A 34,000,000


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2ince the initial lease payment also occurs today (year 0), its present value also does not need to bead$usted. owever, since it will be recorded as revenue for the firm and will be taxed, the inflow must bead$usted to the corporate tax rate.

?@(+nitial Iease ?ayment) A -0(13 0.#)

=ote that in this problem we are solvin" for -0, which is not yet !nown.

The second lease payment represents the first cash flow of a "rowin" annuity. 2ince lease paymentsincrease by three percent each year, the amount of the second payment is the amount of the first paymentmultiplied by 1.0#, ad$usted for taxes, or -0(13 0.


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7.10 The decision to accept or re$ect the pro$ect depends on whether the =?@ of the pro$ect is positive orne"ative.

(in thousands)/ear 0 /ear 1 /ear * /ear # /ear

1. 2ales revenue 3 41,*00 41,*00 41,*00 41,*00

*. 5peratin" costs 3 #00 #00 #00 #00#. %epreciation 3 00 00 00 00

. +ncome before tax13*3#9

3 600 600 600 600

6. Taxes at #6: 3 176 176 176 176

. -han"es in net wor!in"

capital3100 3 3 3 100

10. Total cash flow frominvestment;8>9

3*,100 3 3 3 ##7.6

11. Total cash flow78109

3*,100 7*6 7*6 7*6 1,0


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7.11 To determine the maximum price that HH- should be willin" to pay for the equipment, calculate how hi"hthe price for the new equipment must be for the pro$ect to have an =?@ of Jero. %etermine the cash flowspertainin" to the sale of the existin" equipment, the purchase of the new equipment, the future incrementalbenefits that the new equipment will provide to the firm, and the sale of the new equipment in ei"ht years.

2ale of existin" equipmentTo find the after3tax resale value of the equipment, ta!e into consideration the current mar!et value and theaccumulated depreciation. The difference is the amount sub$ect to capital "ains taxes.

?urchase ?rice A 40,000

%epreciation per year A 40,000 B 10 yearsA 4,000 per year

ccumulated %epreciation A 6 years D 4,000 per yearA 4*0,000

=et 'oo! @alue of existin" equipment A ?urchase ?rice E ccumulated %epreciationA 40,000 3 4*0,000A 4*0,000

?@(fter3Tax =et esale @alue) A 2ale ?rice E Tc(2ale ?rice E =et 'oo! @alue)A 4*0,000 3 0.# (4*0,000 E 4*0,000)A 4*0,000

?urchase of new equipmentIetIequal the maximum price that HH- should be willin" to pay for the equipment.

?@(=ew Cquipment) A 34+

Iower operatin" costs'efore3tax operatin" costs are lower by 410,000 per year for ei"ht years if the firm purchases the newequipment. Iower operatin" costs raise net income, implyin" a lar"er tax bill.

+ncreased annual taxes due to hi"her net income A 410,000 D 0.# A 4#,00

+f the firm purchases the new equipment, its net income will be 410,000 hi"her but it will alsopay 4#,00 more in taxes. Therefore, lower operatin" costs increase the firms annual cash flow by 4


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+ncremental %epreciation per year due to new equipment A (4+B6) 3 4,000

+ncremental %epreciation tax shield per year A +ncremental %epreciation per year D T-A(4+B6) 3 4,0009 D 0.#

?@(+ncremental %epreciation Tax 2hield) A 0.#(4+B6) 3 4,0009 60.0;

=ote that since both old and new equipment will be fully depreciated after 6 years, no depreciation taxshield is applicable in years


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%epreciation of =ew Cquipment/ear 1 A (4*;,000,000 D 0.###) A 4>,#*,000/ear * A (4*;,000,000D0.#>>) A 411,17*,000/ear # A (4*;,000,000D0.1;) A 4,1,000/ear A (4*;,000,000D0.1*0) A 4#,#,#*,000 3 4#,000,000 A $),&2',000/ear * A 411,17*,0003 4#,000,000 A $(,!72,000/ear # A 4,1,0003 4#,000,000 A $!,!'',000/ear A 4#,#;A 7".'(

#he internal rate o return o the in*est/ent in new e6uip/ent is 7".'(.

d. =?@ -alculation

=?@ A341,6,7B(1.1)

A $27,772,77

#he net present *alue o the in*est/ent in new e6uip/ent is $27,772,77.


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7.1# =ominal cash flows should be discounted at the nominal discount rate. eal cash flows should be discountedat the real discount rate. ?ro$ect s cash flows are presented in real terms. Therefore, one must compute thereal discount rate before calculatin" the =?@ of ?ro$ect . 2ince the cash flows of ?ro$ect ' are "iven innominal terms, discount its cash flows by the nominal rate in order to calculate its =?@.

=ominal %iscount ate A 0.16+nflation ate A 0.01 8 eal %iscount ate A (18 =ominal %iscount ate) B (18 +nflation ate)eal %iscount ate A 0.106; A10.6;:

?ro$ect s cash flows are expressed in real terms and therefore should be discounted at the real discountrate of 10.6;:.

?ro$ect ?@(-0) A 340,000?@(-1) A 4*0,000 B (1.106;) A 41;,0;

Chapter 7 Solutions (7.1-7.33) V18

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