atrill sol pc ch07

8/12/2019 Atrill Sol Pc Ch07

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Copyright 2009 Pearson Education Canada 1

Chapter 7

Making Capital Investment Decis ions: Further Issues

Solutions to Even-Numbered Problems and Cases

7.2 James Bay Geological Engineering Company

Discount rate, 8%Project Cash Flows

($ thousands)

Year Machine 1 Machine 2 Machine 30 (200) (400) (600)

1 150 150 140

2 125 140 130

3 130 120

4 120 120

5 110

6 100

7 90

8 70NPV 46.06 50.32 52.76


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(a)Common-period-of-time approach:

Year Machine 1 Machine 2 Machine 3

0 46.06 50.32 52.76

1 0 0

2 46.06 0

3 0 0

4 46.06 50.32

5 0

6 46.06

7

8

NPV $148.42 $87.30 $52.76

Buy Machine 1, as it provides the highest net present value over the eight-year period.

(b) Equivalent-annual-annuity approach using Table 5 in Appendix A:

Machine 1: NPV = $46.06 0.5606

= Equivalent annuity payment of $25.82

Machine 2: NPV = $50.32 0.3019; Payment = $15.19

Machine 3: NPV = $52.76 0.1740; Payment = $9.18

Buy Machine 1, as it provides the highest equivalent annual annuity over the eight yearperiod.

(c) Yes, both methods selected Machine 1 as the best option.


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7.4 Wu and Chu Chocolates Emporium

(a)

For each year, sum the probability multiplied by cash flow for each growth scenario. For

example, for Year 1, the expected cash inflow is 40% 200 + 30% 150 + 30% 100 =155.

The complete expected cash flow schedule for each year is as follows:

Discount rate 14%

Expected Cash Flows

Year ($ thousands)

0 (600.00)

1 155.00

2 217.50

3 275.00

4 198.00

Expected NPV 6.17

(b) Based on the expected cash flows in part (a) and a 14% cost of capital, WCCEshould buy the new machine because the net present value is positive.


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7.6 Lee Caterers Ltd

Approach 1

Step 1:Calculate the NPV for each project:

Cook/Chill Project

Cash Flows Discount Rate Present Value

($000) 10% ($000)

Initial outlay (200) 1.00 (200)

1 years time 85 0.91 77.4

2 years time 94 0.83 78.0

3 years time 86 0.75 64.5

4 years time 62 0.68 42.2

NPV 62.1

Cook/Freeze Project

Cash Flows Discount Rate Present Value

($000) 10% ($000)

Initial outlay (390) 1.00 (390)

1 years time 88 0.91 80.1

2 years time 102 0.83 84.7

3 years time 110 0.75 82.5

4 years time 110 0.68 74.85 years time 110 0.62 68.2

6 years time 90 0.56 50.4

7 years time 85 0.51 43.4

8 years time 60 0.47 28.2

NPV 122.3

Step 2: Calculate the NPV for the eight-year period.

Eight years is the minimum period over which the two projects can be compared. The

cook/chill project will provide the following NPV over this period:

NPV = $62.1 + $62.1 0.683 = $104.5

This NPV of $104,500 is lower than the NPV for the cook/freeze project of $122,300(see above). Hence, the cook/freeze project should be accepted.


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Approach 2

Using the equivalent-annual-annuity approach we derive the following:

Cook/chill: $62.1 0.3155 = $19.59

Cook/freeze: $122.3 0.1874 = $22.92

This approach leads to the same conclusion as the earlier approach: the cook/freezeproject should be accepted because it has a higher equivalent annual annuity.

7.8 Simonson Engineers Limited

(a) Step 1:Determine the expected cash flow for each year.

(a) (b) (a) (b)

Estimated Cash Flows Probability Of Occurrence Expected Value

($ millions) ($ millions)

Year 2 2.0 0.2 0.4

3.5 0.6 2.1

4.0 0.2 0.8

3.3

Year 3 2.5 0.2 0.5

3.0 0.4 1.25.0 0.4 2.0

3.7

Year 4 3.0 0.2 0.6

4.0 0.7 2.8

5.0 0.1 0.5

3.9

Year 5 2.5 0.2 0.5

3.0 0.5 1.5

6.0 0.3 1.8

3.8


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Step 2:Calculate the expected net present value, ENPV.

Year 1 Year 2 Year 3 Year 4 Year 5

($ millions) ($ millions) ($ millions) ($ millions) ($ millions)

Expected cash flows (9.0) 3.3 3.7 3.9 3.8

Discount factor 0.909 0.826 0.751 0.683 0.621

Expected present values (8.18) 2.73 2.78 2.66 2.36

ENPV 2.35

The expected net present value is $2.35 million.

(b) To find the NPV of the worst possible outcome and the probability of itsoccurrence, use the worst cash flow for each year.

Year 1 Year 2 Year 3 Year 4 Year 5

($millions)

($millions)

($millions)

($millions)

($millions)

Cash flows (worst) (9.0) 2.0 2.5 3.0 2.5

Discount factor 0.909 0.826 0.751 0.683 0.621

Present values (8.18) 1.65 1.88 2.05 1.55

NPV (1.05)

Probability ofoccurrence

0.2 0.2 0.2 0.2 = 0.0016

(c) The ENPV of the project is positive, and so its acceptance will increase the wealthof shareholders.


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7.10 Devonia Laboratories Ltd.

(a) Expected sales volume per year

(11,000 0.3) + (14,000 0.6) + (16,000 0.1)

= 13,300 units

Expected annual sales revenue = 13,300 $20= $266,000

Annual labour costs = 13,300 $8

= $106,400

Annual ingredient costs = 13,300 $6

= $79,800

Incremental cash flowsYears

0 1 2 3 4

$000 $000 $000 $000 $000

Sale of patent rights (125.0)

Sale of equipment (85.0) 35.0

Sales 266.0 266.0 266.0 266.0

Cost of ingredients (79.8) (79.8) (79.8) (79.8)

Labour costs (106.4) (106.4) (106.4) (106.4)

Termination Costs (10.0)

Additional overhead (15.0) (15.0) (15.0) (15.0)

(210.0) 64.8 64.8 64.8 89.8

Discount factor (at 12%) 1.0 0.893 0.797 0.712 0.636

(210.0) 57.9 51.6 46.1 57.1

ENPV 2.7

(b) As the ENPV of the project is positive, the wealth of shareholders would beincreased by accepting the project. However, the ENPV is low in relation to the size

of the project and careful checking of the key estimates and assumptions would beadvisable. A relatively small downward revision of sales or upward revision of costscould make the project ENPV negative.

(c) Refer to the chapter material for a discussion of the strengths and weaknesses of theexpected net present value method.


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7.12 Plato Pharmaceuticals Ltd.

(a) The annual operating cash flows must first be calculated:

Sales (150 $5) Variable costs (150 $3) Fixed costs $160 = $140

The net present value can now be calculated as follows:

Discount rate 12% $000

Annual cash flows (140 3.6048*) 505

Residual value of machinery (Yr 5) (100 0.5674) 57

562

Lessinitial cost (Yr 0) (520)

NPV 42

* This is the sum of the discount factors over the five-year period. This approach canbe used as a short cut when cash flows are constant.

(b) (i) If the discount rate was 20%, the NPV of the project would be:

$000

Annual cash flows (140 2.9906) 419

Residual value of machinery and equipment (100 0.4019) 40

459

LessInitial cost (520)

NPV (61)

An 8% change in the discount rate leads to a $103 change in the NPV of the project.Thus, for every 1% change in the discount rate there is a $13 ($103/8) change in theNPV. To achieve a NPV of zero, the discount rate must increase by 42/13 = 3.2%. Hencethe IRR is 12% + 3.2% = 15.2%.

This is an increase of nearly 27% [(15.2% 12%)/12%] on the cost of capital figureprovided.

(ii) The initial cost would have to increase by $42,000 for the project to becomeunprofitable. This represents an increase of 8.0% (42/520).


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(iii) The required reduction in the net cash flows from operations before the projectbecame unprofitable is calculated as follows:

Let F = the annual operating cash flows(F annuity factor for a five year period) NPV = 0

This can be rearranged:

(F annuity factor for a five year period) = NPV

F 3.6048 = $42,000

= $42,000/3.6048

= $11,651

This is a reduction of just over 8.0% ($11.651/140) on the cash flow figuresprovided.

(iv) The decrease necessary in the residual value is calculated as follows:

Let V = the required residual value:

(V discount factor at end of five years) NPV of project = 0

Which can be rearranged:

(V discount factor at end of five years) = NPV of projectV 0.5674 = $42,000

= $42,000/0.5674

= $74,022

This is a decrease of over 74.0% (74,022/100,000) on the figure provided.

atrill sol pc ch07

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