436 Chapter 15
c. Time
Cash Flow
PV Factor for 8%
Present Value
0
$(190,000)
1.0000
$(190,000)
1
0.9259
37,036
2
0.8573
28,291
3
0.7938
26,195
4
0.7350
24,255
5
0.6806
20,418
6
0.6302
18,906
7
0.5835
17,505
8
0.5403
14,588
NPV
$ (2,806)
46. a. Time:
t0
t1
t2
t3
t4
t5
t6
t7
Amount:
($41,000)
$5,900
$8,100
$8,300
$8,000
$8,000
$8,300
$9,200
b. Year
Cash Flow
Cumulative
1
$5,900
$ 5,900
2
8,100
14,000
3
8,300
22,300
4
8,000
30,300
5
8,000
38,300
6
8,300
46,600
Payback = 5 years + [($41,000 – $38,300) ÷ $8,300] = 5.3 years
c.
Cash Flow
Discount
Present
Description
Time
Amount
Factor
Value
Purchase the truck
t0
$(41,000)
1.0000
$(41,000)
Cost savings
t1
5,900
0.9259
5,463
Cost savings
t2
8,100
0.8573
6,944
Cost savings
t3
8,300
0.7938
6,589
Cost savings
t4
8,000
0.7350
5,880
Cost savings
t5
8,000
0.6806
5,445
Cost savings
t6
8,300
0.6302
5,231
Cost savings
t7
9,200
0.5835
5,368
NPV
$ (80)
47. a. Year
PV Factor
PV
0
$(5,000,000)
1.0000
$(5,000,000)
1–7
838,000
5.5824
4,678,051
7
400,000
0.6651
266,040
NPV
$ (55,909)
Chapter 15 437
d. PV of annual cash flows = $5,000,000 – $266,040
PV of annual cash flows = $4,733,960
PV of annual cash flows = Annual cash flow 5.5824
ing 14 workers.
48. a. Payback period = $140,000 ÷ ($47,500 – $8,500) = 3.6 years
b. Discount factor = Investment ÷ Annual cash flow
employees.
49. a. The incremental cost of the replacement equipment: $580,000 – $12,000 =
$568,000
Cash Flow
Discount
Present
Description
Time
Amount
Factor
Value
Incremental cost
t0
$(568,000)
1.0000
$(568,000)
Cost savings
t1 – t8
120,000
5.3349
640,188
NPV
$ 72,188
PI = $640,188 ÷ $568,000 = 1.1
Yes, the replacement equipment should be purchased because the NPV > 0 and
the PI > 1.
c. Net investment ÷ Annual annuity = Discount factor of IRR
438 Chapter 15
50. a. Computation of net annual cash flow:
Increase in revenues
$ 46,000
Increase in cash expenses
(21,000)
Increase in pre-tax cash flow
$ 25,000
Less depreciation
(9,750)
Income before tax
$ 15,250
Income taxes (30 percent)
(4,575)
Net income
$ 10,675
Add depreciation
9,750
After-tax cash flow
$ 20,425
Cash Flow
Discount
Present
Description
Time
Amount
Factor
Value
Initial cost
t0
$(195,000)
1.0000
$(195,000)
Annual cash flow
t1 – t20
20,425
9.1286
186,452
NPV
$ (8,548)
b. This is not an acceptable investment because the NPV is less than $0.
c. Minimum annual after tax cash flow Discount factor = $195,000
$21,361 = (Minimum cash revenues – $21,000 – $9,750)(1 – Tax rate) + $9,750
Proof: Computation of net annual cash flow:
Increase in revenues
$ 47,337
Increase in cash expenses
(21,000)
Increase in pre-tax cash flow
$ 26,337
Less depreciation
(9,750)
Income before tax
$ 16,587
Income taxes (30 percent)
(4,976)
Net income
$ 11,611
Add depreciation
9,750
After-tax cash flow
$ 21,361
51. a. Cash flow after tax (CFAT):
Year
Pre-Tax CF
Depreciation
Tax
CFAT
1
$104,000
$ 64,000
$14,000
$ 90,000
2
118,000
102,400
5,460
112,540
3
118,000
60,800
20,020
97,980
4
102,000
48,000
18,900
83,100
5
86,000
44,800
14,420
71,580
Timeline:
t0
t1
t2
t3
t4
t5
$(320,000)
$90,000
$112,540
$97,980
$83,100
$71,580
Chapter 15 439
accessible website, in whole or in part.
b. Year
Cumulative Cash Flow
1
$ 90,000
$ 90,000
2
112,540
202,540
3
97,980
300,520
4
83,100
383,620
Net present value:
Time
Amount
Discount Factor
Present Value
0
$(320,000)
1.0000
$(320,000)
1
90,000
0.9259
83,331
2
112,540
0.8573
96,481
3
97,980
0.7938
77,777
4
83,100
0.7350
61,079
5
71,580
0.6806
48,717
NPV
$ 47,385
IRR is 14 percent.
52. a. Maple Commercial Plaza:
t0
t1 – t10
t10
$(800,000)
$210,000
$400,000
High Tower:
t0
t1 – t10
t10
$(3,400,000)
$830,000
$1,500,000
b. Maple Commercial Plaza:
Calculation of annual cash flow:
Pre-tax cost savings
$210,000
Depreciation ($800,000 ÷ 25)
(32,000)
Pre-tax income
$178,000
Taxes (40 percent)
(71,200)
After-tax income
$106,800
Depreciation
32,000
After-tax cash flow
$138,800
t0
t1 – t10
t10
$(800,000)
$138,800
$432,000*
*Includes $32,000 from tax loss on sale [0.40 × ($400,000 – $480,000)]
440 Chapter 15
High Tower:
Calculation of annual cash flow:
Pre-tax cost savings
$ 830,000
Depreciation ($3,400,000 ÷ 25)
(136,000)
Pre-tax income
$ 694,000
Taxes
(277,600)
After-tax income
$ 416,400
Depreciation
136,000
After-tax cash flow
$ 552,400
t0
t1 – t10
t10
$(3,400,000)
$552,400
$1,716,000*
*Includes $216,000 from tax loss on sale [0.40 × ($1,500,000 – $2,040,000)]
c. After-tax NPV, Maple Commercial Plaza:
Year
Amount
Discount Factor
Present Value
0
$(800,000)
1.0000
$(800,000)
1–10
138,800
5.8892
817,421
10
432,000
0.3522
152,150
NPV
$ 169,571
After-tax NPV, Hightower:
Year
Amount
Discount Factor
Present Value
0
$(3,400,000)
1.0000
$(3,400,000)
1–10
552,400
5.8892
10
1,716,000
0.3522
NPV
d. After-tax NPV, Hightower:
Year
Amount
Discount Factor
Present Value
0
$(3,400,000)
1.0000
$(3,400,000)
1–10
180,400
5.8892
1,062,412
1–10
372,000*
4.1925
1,559,610
10
1,716,000
0.3522
604,375
NPV
$ (173,603)
*Rental portion of cash flow = $620,000 × (1 – Tax rate)
53. a. Depreciation per year = $1,500,000 ÷ 14 = $107,143
Chapter 15 441
Before-tax CF
$ 350,000
Less depreciation
(107,143)
Income before tax
$ 242,857
Less tax (25%)
(60,714)
Net income
$ 182,143
Add depreciation
107,143
After-tax cash flow
$ 289,286
PV of 14 yr. annuity of $289,286 @ 10%
$ 2,131,083
Less cost
(1,500,000)
NPV
$ 631,083
b. Discount factor = $1,500,000 ÷ $289,286 = 5.1852
c. Cash flow Discount factor = $1,500,000
d. $1,500,000 ÷ $289,286 = 5.1852
54. a. Incremental annual after-tax cash flows:
Year 0
Purchase of new equipment
$(300,000)
One-time transfer expense, net of tax ($80,000 0.6)
(48,000)
Sale of old equipment, net of tax ($5,000 0.6)
3,000
Total initial cash outflow
$(345,000)
ANNUAL OPERATIONS
Year 1
Year 2
Year 3
Year 4
Cash operating
savings
$ 90,000
$150,000
$150,000
$150,000
Less tax effect (40%)
(36,000)
(60,000)
(60,000)
(60,000)
Cash savings after tax
$ 54,000
$ 90,000
$ 90,000
$ 90,000
Depr. tax shield
(see sched. below)
48,000
36,000
24,000
12,000
After-tax operating
cash flows
$102,000
$126,000
$114,000
$102,000
Depreciation Schedule
Depreciable Base: $300,000
Year
Rate
Depreciation
Depr. Shield
1
4/10
$120,000
2
3/10
90,000
3
2/10
60,000
4
1/10
30,000
442 Chapter 15
b. The company should reject the proposal since the NPV is negative.
Year
Cash Flow
11% PV Factor
Present Value
0
$(345,000)
1.0000
$(345,000)
1
0.9009
91,892
2
0.8116
102,262
3
0.7312
83,357
4
0.6587
67,187
NPV
$ (302)
(CMA adapted)
clude:
Comparison of actual and projected results to validate that a project is meet-
ing expected performance, to take any necessary corrective action, or to
terminate a project not achieving expected performance.
investment audit will be done.
b. Practical difficulties that would be encountered in collecting and accumulating
information include:
vironment.
Identifying the impact of inflation on all costs in the capital project justifica-
tion.
Updating the original proposal for approval of changes that may have oc-
curred after the initial approval.
audit.
(CMA adapted)
56. a.
Year
Revenue
VC
FC
1–4
$115,000
$ 69,000
$20,000
$26,000
5–8
175,000
105,000
20,000
50,000
9–10
100,000
60,000
20,000
20,000
Chapter 15 443
Year
Cash Flow
PV Factor
PV
0
$(140,000)
1.0000
$(140,000)
1–4
3.1699
82,417
5–8
2.1651
108,255
9–10
0.8096
16,192
10
0.3855
3,855
NPV
$ 70,719
b. Year
Revenue
VC
FC
Net Cash Flow
1–4
$ 78,000
$15,000
$27,000
5–8
130,000
17,500
52,500
9–10
66,950
25,000
11,050
Year
Cash Flow
PV Factor
PV
0
$(127,500)
1.0000
$(127,500)
1–4
3.1699
85,587
5–8
2.1651
113,668
9–10
0.8096
8,946
10
0.3855
9,059
NPV
$ 89,760
57. a.
Cash
Cash
Net
Cumulative
Year
Receipts
Expenses
Inflows
Cash Flows
1
$3,000,000
$2,530,000
$ 470,000
$ 470,000
2
3,200,000
2,400,000
800,000
1,270,000
3
3,720,000
2,582,000
1,138,000
2,408,000
4
5,120,000
3,232,000
1,888,000
4,296,000
5
6,400,000
3,520,000
2,880,000
7,176,000
Payback = 4 + [($6,400,000 – $4,296,000) ÷ $2,880,000] = 4.7 years
b.
Year
Cash Flow
PV Factor
PV
0
1.0000
$(6,400,000)
1
470,000
0.9259
435,173
2
800,000
0.8573
685,840
3
1,138,000
0.7938
903,344
4
1,888,000
0.7350
1,387,680
5
2,880,000
0.6806
1,960,128
6
2,880,000
0.6302
1,814,976
7
1,632,000
0.5835
952,272
8
648,000
0.5403
350,114
NPV
$ 2,089,527
444 Chapter 15
c.
Year
Net Income
1
$ (330,000)
2
0
3
338,000
4
1,088,000
5
2,080,000
6
2,080,000
7
832,000
8
(152,000)
$ 5,936,000
Average annual income = $5,936,000 ÷ 8 = $742,000
Average investment = (Cost + Salvage) ÷ 2
product line should be added.
58. a. Initial cost: t0 = $(1,460,000) + $340,000 = $(1,120,000)
Annual cash flow:
Additional revenue ($1.20 220,000)
$264,000
Labor savings ($160,000 – $100,000)
60,000
Other operating savings ($192,000 – $80,000)
112,000
Total
$436,000
b. Discount factor = $1,120,000 ÷ $436,000 = 2.5688
c. $1,120,000 ÷ $436,000 = 2.6 years
(CMA adapted)