Fundamentals of corporate finance brealey chapter 08 using discounted cash flow analysis make investment decision

While depreciation is a non-cash expense, it still has an impact on net cash flow because of its impact on taxes.. In Canada, such tax savings can be generated by capital cost allowance

Solutions to Chapter 8 Using Discounted Cash-Flow Analysis to Make Investment Decisions

A General Note: Many of the questions, for which solutions are provided below, require

only that the NPV or IRR or some other evaluation criterion be calculated These

questions have not asked that you make a decision based on such criteria In Chapter 7,

we discussed the decision rules when we use these criteria For instance, a positive NPV project should be accepted whereas a project with a negative NPV should be rejected These decision rules should generally be kept in mind while working on the solutions below

1 Net income = ($74  42  10) )  35  ($74  42  10) ) = $22  $7.7 = $14.3 million

= $32  65 + 35  $10) = $24.3 million

= $1,50) 0) + $1,0) 0) 0)  $2,0) 0) 0) = $2,50) 0)

b Cash flow = $36,0) 0) 0)  $24,0) 0) 0) + $2,50) 0) = $14,50) 0)

3 Net income = ($7  4  1)  40)  ($7  4  1) = $2  $0) 8 = $1.2 million

 Revenues  cash expenses  taxes paid = $3  $0) 8 = $2.2 million

= $3  60) + 40)  $1 = $2.2 million

4 While depreciation is a non-cash expense, it still has an impact on net cash flow because of its impact on taxes Every dollar of depreciation reduces taxable income

by one dollar, and thus reduces taxes owed by $1 times the firm’s marginal tax rate

In Canada, such tax savings can be generated by capital cost allowance (CCA) which, for most assets, is computed using the written-down value method CCA is computed for asset classes rather than for individual assets Also, in the first year ofthe asset’s life, the half-year rule becomes applicable The various unique features

of the declining balance CCA system make it quite different from straight-line depreciation Compared with straight-line depreciation, declining balance CCA

will move the tax benefits in time, and thus provide a different present value of the tax shield, thereby altering the value of the project.

5 Gross revenues from new chip = 12 million  $25 = $30) 0) million

Cost of new chip = 12 million  $8 = $96 million

Lost sales of old chip = 7 million  $20) = $140) million

Saved costs of old chip = 7 million  $6 = $42 million

Increase in cash flow = (30) 0) – 96) – (140) – 42) = $10) 6 million

7 a Net Profit + Depreciation = $45,50) 0) + $10) ,0) 0) 0) = $55,50) 0)

b The cash that could have been realized by selling the art.

positive, we do not have to worry about CCA recapture If, however, overall UCC becomes negative, we consider CCA recapture The firm’s after-tax

proceeds from the sale are $20) ,0) 0) 0) – PV of CCA tax shield lost - (0) 35 x amount of CCA recapture, if applicable).

c If no other assets exist in Class 46 and the equipment is sold after 3 years, the adjusted cost of disposal is the sale price of $20) ,0) 0) 0) Subtracting this amount from the UCC of asset class 46 ($16,660) - $20) ,0) 0) 0) = -$3,340) ), we arrive at a negative balance, and thus recaptured depreciation This amount is now addedback to taxable income and the UCC of the asset class becomes zero

At the time of sale, the present value of tax shields lost as a result of the sale

0)

35 0) 30) 0) 660) , 16

, where r is the cost of

capital

The firm’s after-tax proceeds from the sale are thus $20) ,0) 0) 0) – (0) 35 x 3,340) ) – PV of tax shields lost = $18,831 – PV of CCA tax shields lost

proposed project, then the incremental cash outflow from allocating the space

to the project is effectively zero The incremental cost of the space used should be based on the cash flow given up by allocating the space to this project rather than some other use

rental income that the firm could earn if it allowed another firm to use the space This is the opportunity cost of the space

13 Cash flow = Net income + depreciation – increase in NWC

1.2 = 1.2 + 5 – NWC

NWC = $0) 5 million

14 Cash flow = profit – increase in inventory

= $10) ,0) 0) 0) – $1,0) 0) 0) = $9,0) 0) 0)

15 NWC20) 0) 7 = $32 + $25 – $12 = $45 million

NWC20) 0) 8 = $35 + $30) – $25 = $40) million

Net working capital has decreased by $5 million

16 Depreciation per year = $40) /5 = $8 million

Book value of old equipment = $40) – (3  $8) = $16 million

Sales price = $18 million

After-tax cash flow = $18 – 35  ($18 – $16) = $17.3 million

17 CCA calculation for the new capital investment (figures in thousands of dollars):

18 a The UCC increases by $6,0) 0) 0) to the extent of the purchase of the new washer

but decreases by $2,0) 0) 0) to the extent of sale of the old washer The net effect is

an UCC increase of $4,0) 0) 0) CCA calculations are as follows:

All dollar values should be interpreted as incremental results from making the

Now we consider the effect of the CCA tax shield on Bottoms Up’s cash

flows

After-tax Cash Flow from

Operations (excl CCA) 0) 90) 0) 90) 0) 90) 0) 90) 0) 90) 0) 90) 0) Cash Flow from Sale of Old

Total Cash Flow (excl CCA) -4,0) 0) 0) 90) 0) 90) 0) 90) 0) 90) 0) 90) 0) 90) 0)

Total Project Cash Flow -4,0) 0) 0) 1,140) 1,30) 8 1,186 1,10) 0) 1,0) 40) 998

present value of cash flows excluding the CCA tax shield:

PV = -4,0) 0) 0) + 90) 0) x annuity factor(15%, 6 years) = -$594.4

Second, we calculate the present value of the CCA tax shield:

PV of CCA tax shield =

 t

c c

r r

d

SdT r

r d

5.0) 1

, where S = 0)

=

15 0) 1

15 0) 5 0) 1 3 0) 15 0)

4 0) 3 0) 40) 0) 0)

= -$594.40) + $997.10) = $40) 2.7

c Using straight-line depreciation, net cash flow at time 0) remains -$4,0) 0) 0) , but the net cash flow at times 1 through 6 becomes $1,30) 0) , which is calculated as follows:

Earnings before depreciation $1,50) 0)

NPV = -4,0) 0) 0) + 1,30) 0) x annuity factor (15%, 6 years) = $919.83

IRR = 23.21%

19 If the firm uses straight-line depreciation, the present value of the cost of buying, net of the annual depreciation tax shield (which equals 40)  10) 0) 0) = 40) 0) ), is:

60) 0) 0) – 40) 0)  annuity factor(15%, 6 years) = 4486.21

The equivalent annual cost, EAC, is therefore determined by:

EAC  6-year annuity factor = 4486.21

EAC  3.7845 = 4486.21

EAC = $1185.42

Note: this is the equivalent annual cost of the new washer, and does not include any

of the washer’s benefits

20) a The year-wise CCA for the new grill, over its expected life, is as follows:

1 $20) ,0) 0) 0) $3,0) 0) 0) $17,0) 0) 0)

Operating cash flow contribution, excluding tax shields, for year 1 through 3

= Saving in energy expenses x (1 - 35) = $10) ,0) 0) 0) x (1 - 35) = $6,50) 0) Now,

we must consider the effect of the CCA tax shield on the project’s yearly cashflows

Contribution from saving in

At time 0) , the CF from the investment is -$20) ,0) 0) 0) At the end of year 3, the grill is sold for $5,0) 0) 0)

Therefore, total cash flows are:

0) -20) ,0) 0) 0)

PV = -20) ,0) 0) 0) + 6,50) 0) x annuity factor(12%, 3 years) + 5,0) 0) 0) x discount factor (12%, 3 years) = -$829.3

We next calculate the present value of the CCA tax shield:

PV of CCA tax shield:

=

c c

r r

d

SdT r

r d

5.0) 1

=

12 0) 1

1 12

0) 3 0)

35 0) 3 0) 50) 0) 0) 12

0) 1

12 0) 5 0) 1 3

0) 12 0)

35 0) 3 0) 20) 0) 0) 0)

b CCA for the first 5 years of the plant and equipment’s life is as follows:

(In thousands of dollars)

= Operating Cash Flow

For calculating project cash flows for each year, we will need to calculate the

tax savings generated from the CCA tax shield We do this by multiplying

each year’s CCA by the firm’s tax rate (40) % in this case)

(in thousands of dollars)

Initial investment in working

Decrease in working capital

Operating Cash Flow

Total Cash Flow

c The project NPV is calculated in two phases First, we calculate the present

value from cash flows excluding the CCA tax shield:

Total Cash Flow (excluding

x Discount Factor (10) %) 1.0) 0) 0) 0) 90) 9 0) 826 0) 751 0) 683

PV of total cash flow (excl

Total PV (excl CCA tax

* Notice, you could also calculate this as follows, keeping in mind that there could be some difference of result due to rounding errors.

4 3

2 ( 1 1 )

6 5 ) 1 1 (

2 9 )

1 1 (

8 12 1 1

4 16



We next calculate the present value of the CCA tax shield:

PV of CCA tax shield =

 t

c c

r r

d

SdT r

r d

5.0) 1

, where S = 0)

=

10) 0) 1

10) 0) 5 0) 1 25 0) 10) 0)

4 0) 25 0) 50) 0) 0) 0)

L  annuity factor(10) %, 5 years) = $21,895

The project saves $20) ,0) 0) 0) in annual labour costs, so its net operating cash flow

including the depreciation tax shield is:

24

Sales revenue 33,0) 0) 0) 38,50) 0) 44,0) 0) 0) 55,0) 0) 0) 55,0) 0) 0) Less: cost 19,50) 0) 22,750) 26,0) 0) 0) 32,50) 0) 32,50) 0) Profit before tax 13,50) 0) 15,750) 18,0) 0) 0) 22,50) 0) 22,50) 0) Tax (35 percent) 4,725 5,513 6,30) 0) 7,875 7,875 Cash flow from

operations

(excluding CCA) (A)

8,775 10) ,237 11,70) 0) 14,625 14,625 Net working capital

requirement 6,60) 0) 7,70) 0) 8,80) 0) 11,0) 0) 0) 11,0) 0) 0) 0) Investment in net

working capital 6,60) 0) 1,10) 0) 1,10) 0) 2,20) 0) 0) -11,0) 0) 0) Investment in plant and

equipment 25,0) 0) 0)

Investment cash flow (B) 31,60) 0) 1,10) 0) 1,10) 0) 2,20) 0) 0) -11,0) 0) 0) Total cash flow

(excluding CCA)(A – B) -31,60) 0) 7,675 9,137 9,50) 0) 14,625 25,625Present value of total

cash flow (excluding

CCA) -31,60) 0) (1.15)

675 , 7

2 ) 15 1 (

137 , 9

3 ) 15 1 (

50) 0) , 9

4 ) 15 1 (

625 , 14

5 ) 15 1 (

625 , 25

Present value (excluding

CCA) -31,60) 0) 6,674 6,90) 9 6,246 8,362 12,740)

= 9,331

Present value of CCA Tax Shield (PVTS), given a zero salvage value:

)15.0) 5.0) (115

.0) 15.0)

35.0) 15.0) 0) 0) 0) ,25

= $4,0) 90) NPV = $9,331 + $4,0) 90) = $13,421

25 Find the equivalent annual cost of each alternative

EAC of Net Capital

)12.0) 5.0) (13.0) 12.0)

35.0) 3.0) 10)

37 2 12 1

0) 6 1 42 0)

0) 5 1

)12.0) 5.0) (13.0) 12.0)

35.0) 3.0) 12

84 2 12 1

0) 6 1 42 0)

26 1

EAC for Quick and Dirty:

$7.63m = Annuity (3.60) 5)

60) 5 3

63 7

16 9

$1.84m

Since the operating costs are the same, the project with the lower EAC is cheaper This is Do-It-Right

* Investment – PV of CCA tax shield

** Annuity discounted at 12%; number of years = project life

investment activity (A)

All figures in thousands of dollars 0) 1 2 3 4

Cost 550) 750) 350) 125 Pretax profit (excluding CCA) 330) 0) 0) 450) 0) 0) 210) 0) 0) 75.0) 0)

(excluding CCA tax shield) (B)

(excluding CCA tax shield) (A+B)

Present Value of CCA Tax Shield (PVTS):

)20) 0) 5.0) (125.0) 20) 0)

35.0) 25.0) 20) 0)

65 35

$ 2 1

1 1 45

NPV (in thousands of dollars):

= PVTS + PV TOTAL CF (excluding CCA tax shield)

75 98 ) 2 1 (

5 226 )

2 1 (

5 452 2

1

5 134 420) 65

PV of CCA tax shield (PVTS):

1 10)

0) 25 0)

35 0) 25 0) 0) 0) 0) , 10) 0) 10)

0) 1

) 10) 0) 5 0) ( 1 25

0) 10)

.

0)

35 0) 25 0)

750) , 8 10) 1

0) 5 1 35

28

You can access information on CCA asset classes and rates on commonly used assets by

going to the following link on Revenue Canada’s website:

http://www.cra-arc.gc.ca/tax/business/topics/solepartner/reporting/capital/classes-e.html

As of May 29, 20) 0) 8 this site had a table with 17 listed asset classes The minimum

eligible CCA rate is 4 percent and the maximum eligible rate is 10) 0) percent Fifteen of

the 17 asset classes have declining balance CCA rates These include asset Class 13

(leasehold interest) and asset Class 14 (patents, franchises, concessions or licenses for a

limited period) Notice that these classes include assets for which the cost to a business

may not be a onetime initial outlay but rather a fixed recurring periodic cost over their

economic life (such as, on leasehold interests) The CCA on such items is also computed

as a fixed charge on a straight line basis

Net capital expenditure 3,40) 4.788 2,143.0) 0) 0) 1,486.170) 848.0) 0) 0) 1,829.70) 8 (114.0) 0) 0) )

Sales & net cap-expd to total

Note: Calculations were done as follows:

 Capital expenditure = change in gross Physical Plant &Equipment (PP&E) from year to

year For example, capital expenditure for 20) 0) 7 = PP&E for 20) 0) 7 minus PP&E for 20) 0) 6.

 Net capital expenditure (net Cap.Expd.) = capital expenditure – after tax sales of fixed

assets

Differences in ratios between the two companies may be explained as follows:

Given the nature of the businesses of the two companies, the extent of capital

intensity for Rogers Communication is much more than Microsoft Rogers invests

more in tangible physical assets to generate a certain dollar amount of sales than

does Microsoft On the other hand Microsoft invests a lot on intangibles such as

Research and Development and skilled human resources Also, during the period

under consideration, Microsoft has a commanding market presence with a large and

growing sales revenue and is much more cash rich company than Rogers

Communications From the website, we also note that working capital investments

for Microsoft have been increasing, reflecting growth and prosperity Relevant

information on working capital for Rogers Communication was not available

30) If the savings are permanent, it is worth $250) ,0) 0) 0) to the firm It can take $250) ,0) 0) 0)

out of the project now without ever having to replace it So the most the firm

should be willing to pay is $250) ,0) 0) 0)

31 Project Evaluation

Assumptions

Plant and Equipment 10) 0) ,0) 0) 0) 0) 0)

Start up cost before tax 25,0) 0) 0) 0) 0)

Start up cost after tax 16,50) 0) 0) 0)

Operating cash flow (after tax) 33,000.00 34,650.00 36,382.50 38,201.63 36,291.54

Depreciation tax shield 6,80) 0) 0) 0) 6,80) 0) 0) 0) 6,80) 0) 0) 0) 6,80) 0) 0) 0) 6,80) 0) 0) 0) Salvage value

Total Cash Flow 39,800.00 41,450.00 43,182.50 45,001.63 43,091.55

(a)

i) Note: Cash flow at year 0) includes initial investment after tax [10) 0) ,0) 0) 0) + (25,0) 0) 0) *(1-.34)]

0) 0) 250) , 35 2

 Discounted Payback period = 

0) 1 177 , 17 3

93 876 , 35

b) Using NPV and IRR decision rule the project should accepted It has a positive

NPV of $35,876.93 and an IRR of 23.57 % which is higher that the cost of capital rate

(c) i)

PV tax shield with zero salvage value =

 t

c c

r r

d

SdT r

r d

5.0) 1

)12.0) 5.0) (125

.0) 12.0)

34.0) 25.0) 0) 0) 0) ,10) 0)

28 742 , 21

$ 12 1

0) 6 1 37 0)

50) 0) , 8

Operating cash flow (after

Depreciation tax shield 6,80) 0) 0) 0) 6,80) 0) 0) 0) 6,80) 0) 0) 0) 6,80) 0) 0) 0) 6,80) 0) 0) 0)

Total Cash Flow 39,800.00 41,450.00 43,182.50 45,001.63 53,091.55

Year Cash flow Discount Factor (12%) PV of cash flow 12 % Cumulative cash flow