1-3 . (11-A1- P2)(15-25 Min.) Answers Are Printed in the Text at the End of the Assignment

CMA-1I

CAPITAL BUDGETING - CHAPTER 11

1-3 . (11-A1- p2)(15-25 min.) Answers are printed in the text at the end of the assignment material.

1. a. PVA = 2000 (4.3295) = $ 8659

b. PVA = 2000 (3.7908) = $ 7581.60

c. PVA = 2000 (2.9906) = $ 5981.20

2. a. PV = annual withdrawal x PVA (5, 5%)

100,000 = annual withdrawal x 4.3295

annual withdrawal = 100,000 / 4.3295 = $23,097.36

b. annual withdrawal = 100,000 / 3.7908 = $26,379.66

3.

4. (11-A2) (20-30 min.) This is a straightforward exercise.

1.The model indicates that the computers should be acquired because the net present value is positive.

Sketch of Cash Flows

14%Total (in thousands)

DiscountPV 0 1 2 3

Factor@ 14% –––––––––––––Cash effects of operations,

$150,000 2.3216 $348,240 150 150 150

Investment (330,000) (330)

Net present value $ 18,240

11-A3(20-30 min.) This is a straightforward exercise.

1.The model indicates that the computers should not be acquired.

Sketch of Cash Flows

12%Total (in thousands)

DiscountPV 0 1 2 3

Factor@ 12% ––––––––––––––––

Cash effects of operations,

$150,000(1-.40) 2.4018 $216,162 90 90 90

Cash effect of depreciation,

savings of income taxes:

$110,000 x .40 = $44,000 2.4018 105,679 44 44 44

Total after-tax effect on cash 321,841

Investment (330,000) (330)

Net present value $ (8,159)

2.The computers should be acquired. The net present value rises, and now it is positive:

After-tax impact of disposal on cash: .60($45,000 - 0) = $27,000

PV is $27,000 x .7118 = $19,219

Net present value as above (8,159)

New net present value $11,060

3.This requirement demonstrates that the choice of a discount rate often is critical to a decision.

Applying 8% discount factor:

$150,000(1 - .40) x 2.5771 = $231,939

$110,000 x .40 x 2.5771 = 113,392

$345,331

Investment (330,000)

NPV is positive, so acquire. $ 15,331

5. (11-29)(10-15 min.)

1.$100,000 = Future amount x .3506

Future amount= $100,000 ÷ .3506

= $285,225

2.$100,000 = Future annual amount x 4.6389

Future annual amount= $100,000 ÷ 4.6389

= $21,557

6. (11-30)(10 min.)

The deferral cost O’Neal $405,600 in present value, computed as follows:

Present value of $2,000,000 in 2 years $1,594,400

Present value of $2,000,000 today 2,000,000

Sacrifice in present value $ 405,600

A more detailed analysis follows:

Present ValuePresent ValuePresent Value

@ 12%of Originalof Revised

Yearfrom Table 1Contract Contract

20X1 1.0000 $6,000,000 $4,000,000

20X2 .8929 6,250,300 6,250,300

20X3 .7972 6,377,600 7,972,000

Total $18,627,900 $18,222,300

Difference ($18,627,900 - $18,222,300) = $405,600

7. (11-44)(30-35 min.)

1.Annual Operating Cash Flows

CannonKodakDifference

Salaries $49,920(a) $41,600(b) $ 8,320

Overtime 1,728(c) -- 1,728

Repairs and maintenance 1,800 1,050 750

Toner, supplies, etc. 3,600 3,300 300

Total annual cash outflows $57,048 $45,950 $11,098

(a)($ 8 x 40 hrs.) x 52 weeks x 3 employees = $320 x 52 x 3 = $49,920

(b)($10 x 40 hrs.) x 52 weeks x 2 employees = $400 x 52 x 2 = $41,600

(c)($12 x 4 hrs.) x 12 months x 3 machines = $ 48 x 12 x 3 = $ 1,728

Initial Cash Flows

Cannon Kodak Difference

Purchase of Kodak machines $ -- $49,000 $49,000

Sale of Cannon machines -- -3,000 -3,000

Training and remodeling -- 4,000 4,000

Total $ -- $50,000 $50,000

PV Present

of $1.00 Value of

Discounted Cash Flows Annual Cash Flows

at 12% 0 1 2 3 4 5

Total Project Approach:

Kodak:

Initial cash outflow 1.0000 $( 50,000)

Operating cash flows 3.6048 (165,641) (45,950) (45,950) (45,950) (45,950) (45,950)

Total $(215,641)

Cannon:

Operating cash flows 3.6048 $(205,647) (57,048) (57,048) (57,048) (57,048) (57,048)

Difference in favor of

retaining Cannon $( 9,994)

Incremental Approach

Initial investment 1.0000 $(50,000)

Annual operating

cash savings 3.6048 40,006 11,098 11,098 11,098 11,098 11,098

Net present value

of purchase $( 9,994)

2.The Cannon machines should not be replaced by the Kodak equipment.

Net savings= (Present value of expenditures to retain Cannon machines) less (Present value of expenditures to convert to Kodak machines)

= $205,647 - $215,641 = $(9,994)

3.a.How flexible is the new machinery? Will it be useful only for the presently intended functions, or can it be easily adapted for other tasks that may arise over the next 5 years?

b.What psychological effects will it have on various interested parties?

8. (11-33)(10-15 min.)

1.The quickest solution is to "net" the flows for each year:

1.$200,000 - $150,000 =$ 50,000┐

2. 250,000 - 200,000 = 50,000 ├ an annuity of 3 payments (a)

3. 300,000 - 250,000 = 50,000 ┘

4. 400,000 - 300,000 = 100,000┐ an annuity of 2 payments

5. 450,000 - 350,000 = 100,000┘ deferred three years (b)

(a) $50,000 x 2.3216 $116,080

(b) $100,000 x 1.6467 x .6750 111,152

Total $227,232

Less initial investment 220,000

Net Present Value (NPV) $ 7,232

Various other approaches would reach the same answer, but they would involve more computations.

2.The NPV is positive because at a 12% rate, the present value of the net inflows will be higher than at 14%, so NPV will increase.

9. (11-34)(30-45 min.)

This problem deals essentially with sensitivity analysis, which asks how the basic forecasted results will be affected by changes in the critical factors (useful life, cash flows) that influence rate of return.

1.$25,000 ÷ $5,000 = 5 years

2.NPV= ($5,000 x 6.8137) - $25,000 = $9,069

3.a) NPV = ($5,000 x 3.7908) - $25,000 = ($6,046)

b) NPV = ($5,000 x 8.5136) - $25,000 = $17,568

4.NPV = ($3,000 x 6.8137) - $25,000 = ($4,559)

5.NPV = ($4,000 x 5.3349) - $25,000 = ($3,660)

10. (11-A3) (20-30 min.) This is a straightforward exercise.

1.The model indicates that the computers should not be acquired.

Sketch of Cash Flows

12%Total (in thousands)

DiscountPV 0 1 2 3

Factor@ 12% ––––––––––––––––

Cash effects of operations,

$150,000(1-.40) 2.4018 $216,162 90 90 90

Cash effect of depreciation,

savings of income taxes:

$110,000 x .40 = $44,000 2.4018 105,679 44 44 44

Total after-tax effect on cash 321,841

Investment (330,000) (330)

Net present value $ (8,159)

2.The computers should be acquired. The net present value rises, and now it is positive:

After-tax impact of disposal on cash: .60($45,000 - 0) = $27,000

PV is $27,000 x .7118 = $19,219

Net present value as above (8,159)

New net present value $11,060

3.This requirement demonstrates that the choice of a discount rate often is critical to a decision.

Applying 8% discount factor:

$150,000(1 - .40) x 2.5771 = $231,939

$110,000 x .40 x 2.5771 = 113,392

$345,331

Investment (330,000)

NPV is positive, so acquire. $ 15,331

11. (11-A4)(25-30 min.)

1.Cash effects of operations:

Before tax annual cash inflow $ 350,000

Taxes @ 40%: 350,000 x .4 140,000

After-tax cash inflow $ 210,000

Present value @ 16%: $210,000 x 4.8332 $1,014,972

Cash effects of depreciation*:

Year Tax Savings** PV factor Present Value

1 .1429 x $1,500,000 x .4 = $ 85,740 .8621 $73,916

2 .2449 x 1,500,000 x .4 = 146,940 .7432 109,206

3 .1749 x 1,500,000 x .4 = 104,940 .6407 67,235

4 .1249 x 1,500,000 x .4 = 74,940 .5523 41,389

5 .0893 x 1,500,000 x .4 = 53,580 .4761 25,509

6 .0892 x 1,500,000 x .4 = 53,520 .4104 21,965

7 .0893 x 1,500,000 x .4 = 53,580 .3538 18,957

8 .0446 x 1,500,000 x .4 = 26,760 .3050 8,162

Total present value $366,339

*Short-cut using Exhibit 11-7: .6106 x .40 x $1,500,000 = $366,360, which differs from the $366,339 computed above only because of a rounding error.

**Factors .1429, .2449, etc. are from Exhibit 11-6.

Summary:

Present value of cash effects of operations $1,014,972

Present value of cash effects of depreciation 366,339

Total after-tax effect on cash $1,381,311

Investment (1,500,000)

Net present value is negative, so don't acquire. $ (118,689)

2.The 7-year MACRS analysis will apply regardless of the economic life of the equipment. The only change from requirement 1 will be the added five years of cash effects from operations:

PV of $210,000 per year for 5 years at 16%

= 3.2743 x $210,000 = $687,603

To account for the delay of 10 years before

savings begin: $687,603 x .2267 $155,880*

NPV as above (118,689)

NPV is positive, so acquire. $ 37,191

*Or, $210,000(5.5755 - 4.8332) = $210,000 x .7423 = $155,883, which differs from $155,880 only because of a rounding error.

12. (11-B3)(20-30 min.) This is a straightforward exercise.

1. The model indicates that the equipment should not be acquired.

Sketch of Cash Flows

14%Total (in thousands)

DiscountPV 0 1 2 3 4 5

Factor@ 14%

Cash effects of operations,

$140,000(1-.40) 3.4331 $ 288,380 84 84 84 84 84

Cash effect of depreciation,

savings of income taxes*: 3.4331 109,859 32 32 32 32 32

Total after-tax effect on cash $ 398,239

Investment (400,000) (400)

Net present value $ (1,761)

*Depreciation is $400,000 ÷ 5 = $80,000 per year;

annual tax savings is $80,000 x .40 = $32,000.

2.The equipment should be acquired. The net present value is positive.

After-tax impact of disposal on cash:

.60($30,000 - 0) = $18,000

PV is $18,000 x .5194 = $ 9,349

Net present value as above (1,761)

New net present value $ 7,588

3.Applying 10% discount factors:

$140,000(1 - .40)(3.7908) = $ 318,427

$80,000(.40)(3.7908) = 121,306

$ 439,733

Investment (400,000)

NPV is positive, so acquire. $ 39,733

13. (11-B4)(25-30 min.)

1.See Exhibit 11-B4 on the following page for requirement 1.

2.The major reason for this requirement is to underscore the fact that the present value of the depreciation tax savings is unchanged regardless of the length of the economic life of the asset.

PV of the $53,300 to be received in the 6th year,

$53,300 x .4104 factor = $21,873

NPV as above (16,385)

NPV is positive, so acquire. $ 5,488

EXHIBIT 11-B4

Total

1.16%PV Sketch of Cash Flows (in dollars)

Discount@ 16%0 1 2 3 45 6

Factor(in dollars) –––––––––––––––––––––––––––––––––––––––

Cash effects on operations,

$82,000(1 - .35) 3.2743 174,502 <–––53,300 53,300 53,300 53,300 53,300 53,300

Cash effects of depreciation:

Rate x Cost= Savings

Year Income Tax Deduction @ 35%

1 .20 x $250,000 = $50,000 $17,500 .862115,087 <–––17,500

2 .32 x $250,000 = $80,000 28,000 .743220,810 <––––––––––28,000

3 .192 x $250,000 = $48,000 16,800 .640710,764 <––––––––––––––––16,800

4 .1152 x $250,000 = $28,800 10,080 .55235,567 <–––––––––––––––––––––––10,080

5 .1152 x $250,000 = $28,800 10,080 .4761 4,799 <–––––––––––––––––––––––––––––10,080

.6 .0576 x $250,000 = $14,400 5,040 .4104 2,068 <––––––––––––––––––––––––––––––––––––5,040

PV of tax shield 59,095

Total after-tax effect on cash 233,615

Investment (250,000) (250,000)

NPV is negative, so don't acquire. (16,385)

Note: The cash effects of MACRS depreciation can be computed more easily using Exhibit 11-7. Present value of tax savings = Original cost x Tax rate x Factor from 11-7 = $250,000 x .35 x .6753 = $59,089. This differs slightly from the $59,095 calculated above because of rounding error.

14. (11-B5)(5-10 min.)

1.Book value $20,000

Sale price 9,000 $ 9,000

Net loss $11,000

Tax savings x .30 3,300

Net immediate cash inflow,

including tax savings $12,300

2.Sales price $35,000 $35,000

Book value 20,000

Net gain $15,000

Income tax x .30 (4,500)

Net immediate cash inflow, after taxes $30,500

15. (11-36)(5-10 min.) In thousands of dollars.

(S)Sales 540

(E)Expenses excluding depreciation 350

(D)Depreciation 100

Total expenses 450

Income before income taxes 90

(T)Income taxes at 40% 36

(I)Net income 54

Cash effects of operations:

(S - E)Cash inflow from operations, 540 - 350 = 190

Income tax outflow at 40% 76

After-tax inflow from operations 114

Effect of depreciation:

(D)Depreciation, $100

Income tax savings at 40% 40

Total after-tax effect on cash 154

Total after-tax effect on cash is

either S - E - T = 540 - 350 - 36 = 154 or I + D = 54 + 100 = 154

16. (11-37) (5-10 min.)

Cash effects of operations:

Cash inflow from operations: $1,200,000 - $600,000 $600,000

Income tax outflow @ 40% 240,000

After-tax inflow from operations (excluding depreciation) $360,000

Effects of depreciation:

Depreciation, $400,000

Income tax savings @ 40% 160,000

Total after-tax effect on cash $520,000

17. (11-38)(10 min.)

The month and day on which an asset is acquired does not affect its tax depreciation. The half-year convention is applied to all assets.

2001 2002

1.3-year property: 33.33% and 44.45% of $40,000 $13,332 $17,780

2.5-year property: 20% and 32% of $7,000 1,400 2,240

3.5-year property: 20% and 32% of $5,000 1,000 1,600

4.7-year property: 14.29% and 24.49% of $4,000 572 980

END

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