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EXERCISES
E5. Chapter The numbers decrease from left to right in a given row because cash received in the future is worth less the higher your required rate of return. The numbers decrease from top to bottom in a given column because cash received further in the future is less valuable today.
E6.
Cash Flow $800 800
Present Value Factor 3.7908 .6209
Total $ 3,032.64 496.72 $3,529.36
E7.
Plan A Total $100,000 Plan B Cash Flow $ 10,000 100,000 Plan C Cash Flow $20,000 Present Value Factor 6.7101 .4632 Total $ 67,101 46,320 $113,421
Present Value Factor 6.7101
Total $134,202
Plan C should be selected as it has the highest present value. E8. Cash Flow ($50,000) Present Value Factor 1.0000 Total ($50,000.00)
92
22,000
3.4331
75,528.20 $ 25,528.20
The net present value is positive so the project should be undertaken. E9. The investment should not be undertaken because the internal rate of return of 12% is less than the required rate of 18%. Initial outlay Annuity amount $79,100 14,000
Outlay annuity amount = PV of annuity factor 5.6500 Internal rate of return E11. Annual depreciation $50,000 5 years Annual tax savings $10,000 .40 Present value of $4,000 per year for 5 years at 12% $4,000 3.6048 $10,000.00 $4,000.00 12%
$14,419.20
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E12. Year 1 2 3 4 Income (Loss) ($200,000) (75,000) 250,000 400,000
The $200,000 loss in year 1 will offset income in year 3 resulting in a tax savings of $80,000 (i.e., $200,000 40% tax rate) in year 3. With respect to the $75,000 loss in year 2, $50,000 of it can be used to offset income in year 3 (resulting in a tax savings of $20,000 in year 3) and $25,000 of it can be used to offset income in year 4 (resulting in a tax savings of $10,000 in year 4). Cash Flow $80,000 20,000 10,000 Present Value Factor .7118 .7118 .6355 Total $56,944 14,236 6,355 $77,535
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E13. The annual cash inflow is $9,514, calculated as follows: Revenue $24,000 Less: Cost other than depreciation 11,000 Depreciation 4,286 Income before taxes 8,714 Less taxes at 40% 3,486 Net income 5,228 Plus depreciation 4,286 Cash flow $9,514 The net present value is positive, so the smoker should be purchased. Cash Flow $9,514 (30,000) E18. The online business may help the company manage a potentially stodgy image associated with its mall locations. Also, the online business may actually generate a number of large sales for the brick and mortar locations. Some customers will shop the Web site to make price and quality comparisons, but they will be unwilling to make, for example, a $5,000 purchase of a diamond ring over the Internet. Thus, after seeing merchandise on the Web site, they may visit one of Precision's mall stores to make a purchase. These potential benefits would be difficult to quantify. Present Value 4.2883 Factor 1.0000 Total $40,798.89 (30,000.00) $ 10,798.89
PROBLEMS
P1. The original contract was worth $11,209,600 in present value terms while the new offer is worth $10,686,290. When the time value of money is taken into account, it is obvious that the new offer is not better than the old one.
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Time 0 1 2 3 4 5
Cash Flow $4,000,000 2,000,000 2,000,000 2,000,000 2,000,000 2,000,000 Cash Flow 2,000,000 2,100,000 2,200,000 2,300,000 2,400,000 5,000,000
PV Factor 1.0000 0.8929 0.7972 0.7118 0.6355 0.5674 PV Factor 0.8929 0.7972 0.7118 0.6355 0.5674 0.5674
Total $4,000,000 1,785,800 1,594,400 1,423,600 1,271,000 1,134,800 $11,209,600 Total 1,785,800 1,674,120 1,565,960 1,461,650 1,361,760 2,837,000 $10,686,290
Time 1 2 3 4 5 5
P2. Cost of new refrigeration unit Additional annual profit ($8,000 - $4,500) Annual electricity savings Additional annual maintenance costs Amount collected from disposal of unit Net present value PV Cash Flow Factor ($22,000) 1.0000 3,500 1,050 (1,900) 5,000 5.2161 5.2161 5.2161 0.2697 PV Amounts ($22,000) 18,256 5,477 (9,911) 1,349 ($6,829)
Since the net present value is less than zero, the investment should not be undertaken.
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P4. a. Present value of ship in Caribbean/Alaska itinerary at 10% ($68,095,769 7.6061) $517,943,229 Present value of ship in Caribbean/Eastern Canada itinerary at 10% ($53,490,300 7.6061) $406,852,571 Present value of ship in Caribbean/Alaska itinerary at 15% ($68,095,769 5.8474) $398,183,200 Present value of ship in Caribbean/Eastern Canada itinerary at 15% ($53,490,300 5.8474) $312,779,180 The cost of the ship is only $180,325,005. Therefore, the NPV will be positive under all of the alternatives which provides strong evidence that the ship should be purchased at either of the two required rates of return. b. The NPV will be positive (suggesting that the ship should be purchased) whether the required return is 10 percent or 15 percent. c. The difference in present values is $111,090,658 ($517,943,229 $406,852,571). Thus, there is a high opportunity cost if the firm decides to operate the ship in a Caribbean/Eastern Canada itinerary.
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P5. Year 1 Revenue $14,500,000 Less amortization 14,000,000 Income before taxes 500,000 Less taxes 200,000 Net income 300,000 Add amortization 14,000,000 Cash flow $14,300,000 Time 0 1 2 3 4 Cash Flow ($18,000,000) 14,300,000 5,800,000 900,000 300,000 Year 2 $7,000,000 4,000,000 3,000,000 1,200,000 1,800,000 4,000,000 $5,800,000 PV Factor 1.0000 .8929 .7972 .7118 .6355 Year 3 $1,500,000 0 1,500,000 600,000 900,000 0 $900,000 Year 4 $500,000 0 500,000 200,000 300,000 0 $300,000
Total ($18,000,000) 12,768,470 4,623,760 640,620 190,650 $ 223,500
Since the NPV is positive, the company should produce the film.
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