Exercise 24-17A (20 minutes)
Project A Project B
A
B
C
D
1
Initial investment
-160000
-105000
2
Annual cash flows,
end of period
3
1
40000
32000
4
2
56000
50000
5
3
80295
66000
6
4
90400
72000
7
5
65000
24000
8
Formula for IRR
Using Excel, Project A’s IRR is 26.96% and Project B’s IRR is 35%.
Exercise 24-18 (15 minutes)
Recovery time computation
PROBLEM SET A
Problem 24-1A (50 minutes)
Part 1
Annual straight-line depreciation = = $115,000
Part 2
Net
Net Cash
Income
Flow
$1,840,000
$1,840,000
(480,000)
(480,000)
(672,000)
(672,000)
(336,000)
(336,000)
(115,000)
(160,000)
(160,000)
$480,000 – $20,000
4 years
Problem 24-1A (Continued)
Part 4
Accounting rate of return = = 21.56%
* Average investment
Asset cost ……………………………………………………………………….
$480,000
Final year’s book value …………………………………………………….
20,000
Sum ………………………………………………………………………………..
$500,000
Average (Sum /2) ……………………………………………………….
$250,000
Part 5
Present Value of Net Cash Flows
Present
Present
Net Cash
Value of
Value of Net
Flows
1 at 7%
Cash Flows
Year 1 ………………………………………………….
$168,900
0.9346
$ 157,854
Year 2 ………………………………………………….
168,900
0.8734
147,517
Year 3 ………………………………………………….
168,900
0.8163
137,873
Year 4* …………………………………………………
0.7629
$53,900
$250,000*
Problem 24-2A (55 minutes)
Part 1
PROJECT Y
Net income ………………………………………………………………………………
$ 56,000
Depreciation expense* …………………………………………………………….
87,500
Net cash flow …………………………………………………………………………..
$143,500
*Annual depreciation = = $87,500
PROJECT Z
Net income ………………………………………………………………………………
$ 36,400
Depreciation expense* …………………………………………………………….
116,667
Net cash flow …………………………………………………………………………..
$153,067
$350,000 – $0
3 years
Part 2
PROJECT Y
PROJECT Z
$350,000 – $0
4 years
Problem 24–2A (Continued)
Part 3
PROJECT Y
*Average investment
Average (Cost/2) …………………………..
$175,000
PROJECT Z
Accounting rate of return = = 20.8%
*Average investment
Asset cost …………………………………………
$350,000
Average (Cost/2) …………………………..
$175,000
$36,400
$175,000*
Problem 24–2A (Continued)
Part 4
PROJECT Y
Present Value of Net Cash Flows
Present
Present
Value of
Value of
Net Cash
Flows
1 at 8%
Annuity
Net Cash
Flows
Years 1-4 ………………………………………………
$143,500
3.3121
$475,286
Amount invested …………………………………..
(350,000)
Net present value ………………………………….
$125,286
PROJECT Z
Present Value of Net Cash Flows
Present
Present
Value of
Value of
Net Cash
Flows
1 at 8%
Annuity
Net Cash
Flows
Years 1-3 ………………………………………………
$394,469
Amount invested …………………………………..
(350,000)
Net present value ………………………………….
$ 44,469
Problem 24-3A (60 minutes)
Part 1
RESULTS USING STRAIGHT-LINE DEPRECIATION
(a)
Income
Before
Deprec.
(b)
Straight–
Line
Deprec.
(c)
Taxable
Income
(a) – (b)
(d)
40%
Income
Taxes
(e)
Net Cash
Flows
(a) – (d)
Year 1 ……………………….
$66,000
$ 9,000
$57,000
$22,800
$43,200
Year 2 ……………………….
66,000
18,000
48,000
19,200
46,800
Year 3 ……………………….
66,000
18,000
48,000
19,200
46,800
Year 4 ……………………….
66,000
18,000
48,000
19,200
46,800
Year 5 ……………………….
66,000
18,000
48,000
19,200
46,800
Year 6 ……………………….
66,000
9,000
57,000
22,800
43,200
Part 2
RESULTS USING MACRS DEPRECIATION
(a)
Income
Before
Deprec.
Deprec.
(a) – (b)
Taxes
(a) – (d)
(b)
MACRS
(c)
Taxable
Income
(d)
40%
Income
(e)
Net Cash
Flows
Problem 24–3A (Continued)
Part 3
NET PRESENT VALUE OF ASSET USING STRAIGHT-LINE DEPRECIATION
Present
Present
Value of
Net Cash
Flows
Value of
1 at 10%
Net Cash
Flows
Year 1 ………………………………………………….
$ 43,200
0.9091
$ 39,273
Year 2 ………………………………………………….
46,800
0.8264
38,676
Year 3 ………………………………………………….
46,800
0.7513
35,161
Year 4 ………………………………………………….
46,800
0.6830
31,964
Year 5 ………………………………………………….
46,800
0.6209
29,058
Year 6 ………………………………………………….
43,200
0.5645
24,386
Totals ………………………………………………….
$273,600
198,518
Amount invested ………………………………….
(90,000)
Net present value …………………………………
$108,518
Part 4
NET PRESENT VALUE OF ASSET USING MACRS DEPRECIATION
Present
Present
Value of
Net Cash
Flows
1 at 10%
Flows
Year 1 ………………………………………………….
$ 46,800
Year 2 ………………………………………………….
51,120
Year 3 ………………………………………………….
46,512
Year 4 ………………………………………………….
43,747
Year 5 ………………………………………………….
43,747
Year 6 ………………………………………………….
41,674
Totals ………………………………………………….
$273,600
Value of
Net Cash
Part 5
Analysis: The net present value using MACRS depreciation is greater than the
net present value using straight-line depreciation because the cash flows are
larger in the earlier years of the asset’s life under MACRS depreciation. They
are larger because the depreciation deductions are larger, resulting in less
income taxes paid in the earlier years.
Problem 24-4A (45 minutes)
Part 1
Alternative 1: Keep the old machine and have it overhauled
Item
Period
Cash
Flow
Present
Value Factor
at 10%
Present
Value of
Cash Flows
Revenues …………………………..
1 – 5
$95,000
3.7908
$360,126
Operating costs ………………….
1 – 5
(42,000)
3.7908
(159,214)
Salvage value ……………………..
5
15,000
0.6209
9,314
Total …………………………………..
210,226
(150,000)
Net present value ……………….
$ 60,226
Part 2
Alternative 2: Sell the old machine and buy a new one
Item
Period
Cash
Flow
Present
Value Factor
at 10%
Present
Value of
Cash Flows
Revenues …………………………..
1 – 5
$100,000
3.7908
$379,080
Operating costs ………………….
1 – 5
(32,000)
3.7908
(121,306)
Salvage value of new
Salvage value of old
29,000
29,000
Total …………………………………..
Net present value ……………….
5
20,000
0.6209
12,418
Problem 24-5A (35 minutes)
Part 1: Payback period
Period
Cash flow
Cumulative cash flow
0 …………………………………………………………………..
$(250,000)
$(250,000)
1 …………………………………………………………………..
47,000
(203,000)
2 …………………………………………………………………..
52,000
(151,000)
3 …………………………………………………………………..
75,000
(76,000)
4 …………………………………………………………………..
94,000
18,000
5 …………………………………………………………………..
125,000
143,000
$76,000 / $94,000 = 0.8 (rounded)
The payback period is about 3.8 years.
Part 2: Break-even time
Period
Cash Flow
0 ……………….
1 ……………….
2 ……………….
3 ……………….
4 ……………….
5 ……………….
Present Value
Present Value
Cumulative
Present Value
$43,749 / $77,613 = 0.6 (rounded)
The break-even time is about 4.6 years.
Part 3: Net present value
From the chart in part 2, we can see that the net present value of the
investment is $33,864.
Problem 24-6A (30 minutes)
Part 1: Payback period
Period
Cash flow
Cumulative cash flow
0 …………………………………………………………………..
1 …………………………………………………………………..
2 …………………………………………………………………..
3 …………………………………………………………………..
4 …………………………………………………………………..
5 …………………………………………………………………..
$31,000 / $75,000 = 0.4 (rounded)
The payback period is about 2.4 years.
Part 2: Break-even time
Period
Cash Flow
Present Value
of 1 at 10%
Present Value
of Cash Flows
Cumulative
Present Value
of Cash Flows
0 ……………….
$(250,000)
1.0000
$(250,000)
$(250,000)
1 ……………….
125,000
0.9091
113,638
(136,362)
2 ……………….
94,000
0.8264
77,682
(58,680)
3 ……………….
75,000
0.7513
56,348
(2,332)
4 ……………….
52,000
0.6830
35,516
33,184
5 ……………….
47,000
0.6209
29,182
62,366
Problem 24-1B (50 minutes)
Part 1
Annual straight-line depreciation = = $70,000
Part 2
Net
Net Cash
Income
Flow
Expected annual sales of new product …………………..
$1,150,000
$1,150,000
Expected annual costs of new product
Direct materials …………………………………………………..
300,000
300,000
Direct labor ……………………………………………………….
420,000
420,000
Overhead excluding depr. on new asset ………………
210,000
210,000
Depreciation on new asset ………………………………….
70,000
Selling and administrative expenses ……………………
100,000
$300,000 – $20,000
4 years
Problem 24-1B (Continued)
Part 3
Payback Period = = 2.86 years
Part 4
Accounting rate of return = = 21.88%
*Average investment
Asset cost ……………………………………………………
$300,000
Final year’s book value …………………………………
20,000
Sum ……………………………………………………………..
$320,000
Average (Sum /2) ………………………………………….
$160,000
Part 5
Present Value of Net Cash Flows
Present
Present
Value of
Net Cash
Value of
Net Cash
$35,000
$160,000*
$300,000
$105,000
Problem 24-2B (55 minutes)
Part 1
PROJECT A
Net income …………………………………………………………………………………..
$39,900
Depreciation expense* …………………………………………………………………
60,000
Net cash flow ……………………………………………………………………………….
$99,900
*Annual depreciation = = $60,000
PROJECT B
Net income …………………………………………………………………………………..
Depreciation expense* …………………………………………………………………
Net cash flow ……………………………………………………………………………….
$240,000 – $0
3 years
Part 2
PROJECT A
PROJECT B
$240,000 – $0
4 years
Problem 24–2B (Continued)
Part 3
PROJECT A
Asset cost ………………………………………….
$240,000
PROJECT B
Accounting rate of return = = 21.6%
*Average investment
Asset cost ………………………………………….
$240,000
Average (Cost/2) …………………………………
$120,000
$25,900
$120,000*