COMPUTATION OF NET INVESTMENT
Case 1
Kendra Enterprises plans to add a new machine to increase
production capacity. The machine cost P180,000 plus P20,000
for installation and transportation costs and requires P40,000
additional working capital.
Purchase price of new machine
Installation and transportation costs
Additional net working capital
Net Investment
₱
₱
₱
₱
180,000
20,000
40,000
240,000
₱
₱
₱
180,000
20,000
200,000
The depreciable basis of the machine is:
Purchase price of new machine
Installation and transportation
Depreciable basis
General format for computing the net investment:
Purchase price of new asset
Add: Installation and transportation costs
Add: Additional net working capital
Less: Proceeds from sale of old asset
Add/Less: Tax effects on disposal of old asset
And/or the purchase of new one
Net Investment
NET OPERATING CAS
Case 2
The management of Maingat Company plans to replace a sorting
machine that was acquired several years ago at a cost of P60,000.
The machine has been depreciated to its residual value of P10,000.
A new sorter can be purchased for P96,000. The dealer will grant a
trade-in allowance of P16,000 on the old machine. If a new machine is
not purchased, Maingat Company will spend P10,000 to repair the old
machine. Gains and losses on trade-in transactions are not subject to
income taxes. The cost to repair the old machine can be deducted in
computing income taxes. Income taxes are estimated at 40% of the
income subject to tax. Additional working capital required is P50,000.
Required: Compute the net initial investment in this project.
Solution:
Purchase price of new sorter
Add: Additional working capital
Total
Less: Trade-in allowance on old sorter
Avoidable repairs cost on old sorter
(net of increase in income taxes)
Net Investment
₱
₱
₱
₱
₱
96,000
50,000
146,000
6,000 ₱
₱
22,000
124,000
16,000
Determination of Ann
The Visayan Division o
considering a new prod
materials costs by an e
The new method is als
of labor and overhead
the estimated depreci
over a period of ten ye
of income before incom
(or savings) expected f
Solution:
Annual savings in direc
Annual savings in direc
Total savings before de
Less:
Savings after depreciat
Less:
Net increase in income
Add:
Net cash returns (savin
NET OPERATING CASH FLOWS OR RETURNS
Determination of Annual Cash Savings
The Visayan Division of Marlow Supply Company has been
considering a new production method that can reduce
materials costs by an estimated amount of P52,000 a year.
The new method is also expected to result in an annual savings
of labor and overhead method amounting to P64,000 and
the estimated depreciation at P60,000 a year
over a period of ten years. Income taxes are estimated at 30%
of income before income taxes. What are the annual net returns
(or savings) expected from the new production method?
Solution:
Annual savings in direct materials costs
Annual savings in direct labor and overhead costs
Total savings before depreciation
Depreciation
Savings after depreciation
Incremental income taxes (30%)
Net increase in income
Depreciation
Net cash returns (savings)
₱
₱
₱
₱
₱
₱
₱
₱
₱
52,000
64,000
116,000
60,000
56,000
16,800
39,200
60,000
99,200
CONCEPT OF NET INVESTMENT COSTS
CAPITAL BUDGETING
INVESTMENT PROPO
THOSE THAT DO NOT
A company is considering to replace Machine A with Machine B.
Machine B will cost P150,000 and will result in annual savings of P40,000
before tax because of expected increase in operating efficiency. Machine B
has an estimated useful life of 10 years and salvage value of P10,000.
Machine A has a book value of P16,000 and a disposal value of P20,000 now.
Straight line depreciation is used and the company has an average income tax
rate of 35%.
Required: Determine the Net Investment
Solution:
Net Investment:
Cost of Machine B
Adjustment:
Proceeds from disposal of Machine A
Tax on gain
Net investment cost
₱
₱
₱
₱
Assume that Great Com
which will be depreciate
The machine will gener
Great will not incur add
tax rate is 35%.
Required:
1
2
3
4
5
150,000
Solution:
1
(20,000)
1,400
131,400
2
𝐴𝑐𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 Rate
𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡)
if the problem is silent:
3
4 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜�=
𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥)
5
CAPITAL BUDGETING TECHNIQUES IN EVALUATING CAPITAL
INVESTMENT PROPOSALS
THOSE THAT DO NOT CONSIDER TIME VALUE OF MONEY
Assume that Great Company is planning to spend P60,000 for a machine
which will be depreciated on a straightline basis over a ten-year period.
The machine will generate additional cash revenues of P12,000 a year.
Great will not incur additional costs except for depreciation. The income
tax rate is 35%.
Required:
Determine the net income after tax
Determine the accounting rate of return (ARR)
Determine the after tax annual cash flow
Determine the payback period and the payback reciprocal
Determine the payback bailout period.
Solution:
Incremental Cash revenues per year
Less: Annual depreciation
Taxable Income
Income tax
Net Income after tax
₱
₱
₱
₱
₱
12,000
6,000
6,000
2,100
3,900
𝐴𝑐𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 Rate of Return=(𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥)/(𝑁𝑒𝑡
𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡)
Accounting Rate of Return
6.50%
𝐴𝑐𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 Rate of Return=(𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥)/(𝐴𝑣𝑒𝑟𝑎𝑔𝑒
𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡)
Accounting Rate of Return
Incremental Cash Revenues per year
Income tax
Annual Cash Flow after tax
13%
₱
₱
₱
12,000
2,100
9,900
𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜�=(𝑁𝑒𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡)/(𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤
𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥)
Payback Period
6.06 years
𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑅𝑒𝑐𝑖𝑝𝑟𝑜𝑐𝑎𝑙=(𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥)/(𝑁𝑒𝑡
𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡)
4.1
𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑅𝑒𝑐𝑖𝑝𝑟𝑜𝑐𝑎𝑙=(𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑎𝑓𝑡𝑒𝑟 𝑡𝑎𝑥)/(𝑁𝑒𝑡
𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡)
Payback Reciprocal
16.5%
16.5%
5.1
In some cases cash inflows are not equal throughout the life of investments.
In such cases the computation of payback period will be different from what
has been presented. Assume the following cash inflow patterns:
Initial investment
Cash flows:
Year 1
Year 2
Year 3
Year 4
₱
60,000
₱
₱
₱
₱
20,000
40,000
20,000
10,000
Payback could be computed as follows:
Year
0
1
2
3
4
Net cash inflows
Initial
Each year
Cumulative
Investment
Unrecovered cost
₱
(60,000)
0 ₱
(60,000)
₱ 20,000 ₱
(40,000)
₱ 40,000 ₱
₱ 20,000 ₱
20,000
₱ 10,000 ₱
30,000
The payback period is exactly two years. But in some cases, the payback
period may not happen at an exact number of years.
Assume that instead of having an investment of P60,000 but P62,000,
payback will be presented as follows:
Year
0
1
2
3
4
Net cash inflows
Initial
Each year
Cumulative
Investment
Unrecovered cost
₱
(62,000)
0 ₱
(62,000)
₱ 20,000 ₱
(42,000)
₱ 40,000 ₱
(2,000)
₱ 20,000 ₱
18,000
₱ 10,000 ₱
28,000
Notice that on the second year, the initial investment was almost
recovered and only a small portion of the next year's cash inflow
is needed to fully recover the initial investment. Thus, the exact
payback can be computed using the following formula:
𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜�=2 𝑦𝑒𝑎𝑟𝑠+ 2,000/20,000
𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜�=2 𝑦𝑒𝑎𝑟𝑠+ 2,000/20,000
Payback Period
Payback Reciprocal
2.10 years
36.29%
Average CF
Divided by Net Investment cost
Payback Reciprocal
₱
₱
22,500
62,000
36.29%
6 Payback bailout period:
End of year
1
2
3
4
5
6
7
8
9
10
Scrap values
₱
40,000
₱
35,000
₱
30,000
₱
25,000
₱
20,000
₱
15,000
₱
10,000
₱
5,000
₱
2,000
₱
-
The completed table would show the following:
Year
Net Annual
Cumulative
Scrap Value Total value
cash flow
net cash inflow
recovered
0
1
₱
9,900 ₱
9,900 ₱
40,000 ₱ 49,900
2
₱
9,900 ₱
19,800 ₱
35,000 ₱ 54,800
3
₱
9,900 ₱
29,700 ₱
30,000 ₱ 59,700
4
₱
9,900 ₱
39,600 ₱
25,000 ₱ 64,600
5
₱
9,900 ₱
49,500 ₱
20,000 ₱ 69,500
6
₱
9,900 ₱
59,400 ₱
15,000 ₱ 74,400
7
₱
9,900 ₱
69,300 ₱
10,000 ₱ 79,300
8
₱
9,900 ₱
79,200 ₱
5,000 ₱ 84,200
9
₱
9,900 ₱
89,100 ₱
2,000 ₱ 91,100
10
₱
9,900 ₱
99,000 ₱
₱ 99,000
Note that at year 3, initial investment is almost recovered. However, an exact Payback bail-out
could be computed similar to uneven returns as follows:
Payback Bail-out Period
3.47 years
3.47 years
3.74 years
No. of years prior to recovery
Add
divided by
Total amount
recoverable
₱
(62,000)
₱
(12,100)
₱
(7,200)
₱
(2,300)
₱
2,600
₱
7,500
₱
12,400
₱
17,300
₱
22,200
₱
29,100
₱
37,000
an exact Payback bail-out
. of years prior to recovery
Unrecovered cost at the beg. Of the period
(Total value recovered on the year of recovery - Total value recovered prior to recovery)
THOSE THAT DO CONSIDER TIME VALUE OF MONEY
DISCOUNTED PAYBACK PERIOD
Assume the following proposals were available to Company A:
PROJECT 1 PROJECT 2
Cost of Capital
10%
10%
Amount of invesment
₱
1,000 ₱
1,000
Yearly Net Cash Inflows
Year 1
₱
500 ₱
100
Year 2
₱
400 ₱
300
Year 3
₱
300 ₱
400
Year 4
₱
100 ₱
600
₱
1,300 ₱
1,400
𝐷𝐶�=𝐶�∗ 〖 (1+𝑖) 〗 ^(−𝑡)
Year
Annual
PV of 1 factor Discounted
cash flows
cash flows
PROJECT 1
0
1
2
3
4
₱
₱
₱
₱
₱
Discounted Payback Period
PROJECT 2
Discounted Payback Period
500
400
300
100
1,300
1.00
0.91
0.83
0.75
0.68
₱
454.55
₱
330.58
₱
225.39
₱
68.30
₱ 1,078.82
2.95 years
0
1
2
3
4
₱
₱
₱
₱
₱
100
300
400
600
1,400
3.88 years
1.00
0.91
0.83
0.75
0.68
₱
90.91
₱
247.93
₱
300.53
₱
409.81
₱ 1,049.18
DISCOUNTED CASH FLOW METHODS
NET PRESENT VALUE
Assume that a certain project will cost P6,075 and will earn cash inflows,
after tax, of P2,000 for four years with a minimum desired rate of return of 10%
Determine whether the project is acceptable or not by using the net present valu
(NPV) method.
PV of cash inflows
PV of cash outflows
Net Present Value
Cumulative
Unrecovered cost
₱
₱
₱
₱
₱
(1,000)
(545.45)
(214.88)
10.52
78.82
₱
₱
₱
₱
₱
(1,000)
(909.09)
(661.16)
(360.63)
49.18
Year
1 to 4
0
0
1
2
3
4
Cash Flow
PV factor
₱
2,000 3.1698654463
₱
(6,075)
1
₱
₱
₱
₱
₱
(6,075)
2,000
2,000
2,000
2,000
₱
₱
₱
₱
₱
(6,075)
1,800
1,800
1,800
1,800
INTERNAL RATE OF RETURN OR TIME ADJUSTED RATE OF RETURN
ll earn cash inflows,
sired rate of return of 10%
y using the net present value
Present Value
₱
6,339.73
₱
(6,075.00)
₱
264.73
Using the same example, the PV factor is determined as follows:
P6,075 = P2,000 x PV Factor
PV Factor
IRR
3.0375
12%
Suppose the expected cash flow is P1,800 instead of P2,000.
Exact Rate
7%
8%
PV Factor
3.375 3.3872112565
3.31212684
IRR
7.16%
Looking in the PV factor table for the period Year 4, 3.375 is closest to 7%
which is 3.3872 and 8% which is 3.3121. The two interest rates where the
factor is between will be used as the guide in determining the IRR. So we
could say that the IRR is between 7% and 8%. However, to get an exact rate,
an interpolation of the two rates could be done as follows:
At 7%
PV factor
At 8%
Difference
Exact rate
Present Value Factors
3.3872
3.3872
3.375
3.3121
0.0751
0.0122
7.16%
These computations become more complex if annnual cash inflows and outflows w
not uniform. Assume the following:
Initial investment
Cash inflows from operations for
Year 1
Year 2
Year 3
Year
1
₱
90,000
₱
₱
₱
20,000
40,000
60,000
At trial of 12%
Cash
Present Value Total Present
Inflows
Factor
Values
₱
20,000 0.8928571429 ₱ 17,857.14
2
3
₱
₱
40,000 0.7971938776 ₱ 31,887.76
60,000 0.7117802478 ₱ 42,706.81
₱ 92,451.71
To interpolate:
Total Present Values
At 12%
₱ 92,451.71 ₱ 92,451.71
At true rate
₱
90,000
At 14%
₱ 88,820.85
Difference ₱ 3,630.86 ₱
2,451.71
Exact rate
13.35%
13.34%
USTED RATE OF RETURN
mined as follows:
Cost of Capital
Yearly Net Cash Inflows
Year 0
Year 1
Year 2
Year 3
Year 4
ad of P2,000.
IRR
r 4, 3.375 is closest to 7%
wo interest rates where the
termining the IRR. So we
However, to get an exact rate,
Table 1
Year
1
2
3
4
Table 2
nnnual cash inflows and outflows were
₱
₱
₱
₱
(90,000)
20,000
40,000
60,000
At trial of 14%
Present Value Total Present
Factor
Values
0.8771929825 ₱ 17,543.86
Year
1
2
3
4
Table 3
Year
1
2
3
4
PROJECT 1
10%
₱
₱
₱
₱
₱
₱
(1,000)
500
400
300
100
1,300
14.49%
If the cost of capital is equal to IRR
Loan Balance
₱
₱
₱
₱
1,000
644.89
338.33
87.34
Cash flows
₱
500
₱
400
₱
300
₱
100
₱
1,300
If the cost of capital is less than the IRR
Loan Balance
₱
₱
₱
₱
1,000
630.00
311.90
52.45
Cash flows
₱
500
₱
400
₱
300
₱
100
₱
1,300
If the cost of capital is greater than the IRR
Loan Balance
₱
₱
₱
₱
1,000
660.00
365.60
124.10
Cash flows
₱
500
₱
400
₱
300
₱
100
₱
1,300
0.7694675285 ₱
0.6749715162 ₱
₱
30,778.70
40,498.29
88,820.85
PROJECT 2
10%
₱
₱
₱
₱
₱
₱
(1,000)
100
300
400
600
1,400
11.79%
Rate
14.49%
14.49%
14.49%
14.49%
Payment applied to
Interest
Principal
₱ 144.89 ₱ 355.11
₱
93.44 ₱ 306.56
₱
49.02 ₱ 250.98
₱
12.66 ₱
87.34
Loan Balance
₱
644.89
₱
338.33
₱
87.34
₱
(0.00)
Rate
13.00%
13.00%
13.00%
13.00%
Payment applied to
Interest
Principal
₱ 130.00 ₱ 370.00
₱
81.90 ₱ 318.10
₱
40.55 ₱ 259.45
₱
6.82 ₱
93.18
Loan Balance
₱
630.00
₱
311.90
₱
52.45
₱
(40.73)
Rate
16.00%
16.00%
16.00%
16.00%
Payment applied to
Interest
Principal
₱ 160.00 ₱ 340.00
₱ 105.60 ₱ 294.40
₱
58.50 ₱ 241.50
₱
19.86 ₱
80.14
Loan Balance
₱
660.00
₱
365.60
₱
124.10
₱
43.95
than the IRR