Chapter 9
Capital Budgeting - Key
I
TRUE OR FALSE
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
II
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
TRUE
FALSE
TRUE
FALSE
TRUE
TRUE
TRUE
FALSE
FALSE
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
TRUE
TRUE
TRUE
TRUE
FALSE
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
TRUE
FALSE
FALSE
FALSE
TRUE
TRUE
FALSE
TRUE
TRUE
FALSE
FALSE
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
FALSE
MULTIPLE CHOICE QUESTIONS
A
16
B
B
17
D
D
18
C
C
19
D
B
20
D
A
21
B
C
22
D
A
23
D
C
24
C
B
25
B
D
26
D
D
27
D
C
28
A
C
29
D
B
30
B
41
42
43
44
45
46
47
48
49
50
51
52
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
TRUE
TRUE
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
FALSE
FALSE
TRUE
FALSE
B
C
D
C
C
C
A
D
B
A
B
A
D
C
C
MULTIPLE CHOICE PROBLEMS
1
C
13
2
B
14
3
B
15
4
D
16
5
C
17
6
B
18
7
B
19
8
D
20
9
D
21
10
B
22
11
B
23
12
C
24
C
B
C
B
C
C
B
C
D
B
C
A
25
26
27
28
29
30
31
32
33
34
35
36
C
D
B
C
B
C
B
A
B
C
B
A
SOLUTIONS TO MULTIPLE CHOICE PROBLEMS
#1
investment
recovered
year
at y-0
unrecovered
105,000.00
50,000.00
55,000.00
45,000.00
10,000.00
10,000.00
-
1
2
3
years
recovered
1
1
0.25 (P10,000 / P40,000) = .25
2.25 payback
or
2 years
#2
#3
#4
+
(P105,000 - P95,000)
P 40,000
= 2.25 years
Average Net income = P95,000 / 5 years = P19,000
ARR = P19,000 / P105,000 =
Total present values of cash inflows
year PV
CASH
FACTOR
FLOWS
1
0.81
50,000.00
2
0.65
45,000.00
3
0.52
40,000.00
4
0.42
35,000.00
5
0.34
30,000.00
Total present values of cash inflows
Initial investment cost
Net present value
Present value = P56,000 x 2.531 =
Initial investment cost
Net present value
18.095 or 18.10%
PRESENT
VALUES
40,500.00
29,250.00
20,800.00
14,700.00
10,200.00
115,450.00
105,000.00
10,450.00
141,736.00
140,000.00
1,736.00
#5
Present value
Initial investment
Profitability index
20,000.00
x 2.531
50,620.00
50,000.00
1.01
P50,620 / P50,000
#6
PV Factor = Investment / Annual cash flows = P68,337 / P27,000 = 2.531
2.531 is at 9%
#7
Present value = P30,000 x 2.487 =
#8
Payback period = P400,000 / P100,000 =
#9
Present values =
Initial investment =
Net present value
#10
Accounting Rate of Return (ARR) = P20,000 / (410,000 / 2) =
#11
PV Factor = P600,000 / P142,000 =
74,610.00
4 years
P142,000 x 4.355 =
618,410.00
600,000.00
18,410.00
0.42254
approximately 11%
between 4.1111 and 4.3555
#12
#13
P20000 / P200,000 =
Revenues
Operating costs
38,000.00
Depreciation
P320,000 / 8 years
40,000.00
Annual net income
ARR =
P12,000 / (P320,000 / 2) =
78,000.00
12,000.00
0.0750
Net income
Depreciation expense
Annual cash flows
12,000.00
40,000.00
52,000.00
Payback
90,000.00
P320,000 / P52,000 =
0.6154
or 6.2 years
#14
ARR = Net income / Average investments =
= 30%
P60,000
(P300,000 + P100,000) / 2
#15
#16
#17
#18
Average investment =
42,000.00
(P80,000 + P4,000 ) / 2 =
year PV Factor at 15%
1
0.8700
2
0.7560
Total PV of cash inflows
x
x
Cash Flows
100,000.00
160,000.00
year PV Factor at 14%
1
0.8800
2
0.7700
3
0.6700
Total PV of cash inflows
x
x
x
Cash Flows
15,000.00
15,000.00
10,000.00
Payback = P200,000 / P40,000 =
=
=
Present Values
87,000.00
120,960.00
207,960.00
Present Values
13,200.00
11,550.00
6,700.00
31,450.00
5.00 years
10%
88,683.00
#19
PV of P1 at 12% = P24,600 x 3.605 =
#20
Payback = P600,000 / P225,000 =
#21
Present value factor = P30,000 / P7,300 = 4.1095
4.231 and 4.111 in between is 4.1095 is at 12%
2.6667 years
4.2310
0.12150
4.1095 in between
4.1110
(0.0015)
#22
#23
Present value =
Initial investment
Net present value
P7,300 x 4.355 at 10%
Profitability index =
P31,792 / P30,000 =
#25
Savings on labor
less, increased in power costs
net savings
PV of 12% for 10yrs
PV of savings
Less ,Investment costs
Net present value
#26
Investment / annual cash flow = Factor of Time Adjusted Rate Of Return
#24
1,792.00
1.0597
1.06
x
=
=
8,000.00
(1,000.00)
7,000.00
5.65
39,550.00
30,000.00
9,550.00
14%
P84,900 / P15,000 = 5.660 this is in Table 4 14% 12 years
#27
31,791.50
30,000.00
1,791.50
Return in five (5) years
factor for 12% for 5 yrs at Table 3
10,000.00
0.5670
5,670.00
PV and the maximum amount that the company would be willing to invest.
#28
years
a
Working capital
cash inflow
working capital released
net present value
#29
P100,000 / P25,000
amount
b
now
1 - 6 years
6
(30,000.00)
10,000.00
30,000.00
factor at
18%
c
1.00
3.50
0.37
present
value
d
(b x c)
(30,000.00)
34,980.00
11,100.00
16,080.00
4 years
=
#30
investment
year
payback is 5 years or at year 5
1
2
3
4
5
outflow
inflows
(50,000.00)
20,000.00
20,000.00
(50,000.00) 20,000.00
20,000.00
balance
(50,000.00)
(30,000.00)
(10,000.00)
(20,000.00)
-
#31
Net income
AROR
#32
=
(P30,000 - {P100,000 - P10,000}) =
=
5 years
P12,000 / { (P100,000 + P10,000)/ 2 } =
P50,000 x 30% =
#33
Profitability Index (PI)
=
P30,000 - P18,000 =
#35
Payback
=
21.81% or 22%
P15,000
PV of cash inflow
P30,000 / P6,000
P40,000
5 years
=
Cash flows
Less, depreciation (P30,000 / 5 years)
6,000.00
2,000.00
Net savings
4,000.00 P4,000 / P30,000
#36
= 1.25
P50,000
Investment
#34
12,000.00
13.30%
=
Working capital is an investment not an expense, so no tax adjustment is needed
PROBLEMS
9.1
Cost
Delivery and set up costs
475,000.00
12,500.00
Total investment costs
Average income per year
5 days x 52 weeks x P400 =
Less, Average operating costs per year
Cash net income
5 days x 52 weeks x P25
6,500.00
97,500.00
Less, Depreciation costs
Net income
(P487,500 - P27,500) / 10 years =
46,000.00
51,500.00
a
Cash payback
b
Present values of annual inflows
Present values of salvage value
c
487,500.00
104,000.00
5.00
P487,500 / P97,500 =
P97,500 x 6.418
P27,500 x .422
10years at 9%
625,755.00
11,605.00
Total Present values
Initial cost of investment
637,360.00
487,500.00
Net present value
149,860.00
Annual Rate of Return
P51,500 / [ (487,500 + P27,500 ) / 2 ] =
P51,500 / P257,500 =
20%
years
9.2
Annual net income
Annual cash flows
a
b
Cost of investment
Payback
Total Present values
Initial cost of investment
30,000.00
78,000.00
240,000.00
3.08
P240,000 / P78,000 =
P78,000 x 3.791
295,698.00
240,000.00
55,698.00
Net present value
c
Annual Rate of Return
P30,000 / [ (240,000 + P0 ) / 2 ] =
P30,000 / P120,000 =
25%
9.3
Red
Annual net income
Add, back depreciation
Payback, in years
Blue
30,000.00
Red: P400,000 / 8 yrs = P50,000
Blue : P560,000 / 8 yrs = P70,000
50,000.00
50,000.00
70,000.00
Annual cash flows
a
80,000.00
120,000.00
5
Red: P400,000 / P80,000
4.67
Blue : P560,000 / P120,000
b
Total present values
Red
P80,000 x 5.747
Blue
P120,000 x 5.747
459,760.00
Initial investment cost
Net present values
c
Annual rate of return
Net income
Average investments(Cost / 2)
ARR
(1 /2)
9.4
1
2
400,000.00
689,640.00
560,000.00
59,760.00
129,640.00
30,000.00
50,000.00
200,000.00
0.15
280,000.00
0.18
Net income
64,000.00
Depreciation
Net cash inflows per year
52,500.00
116,500.00
Present value factor at 13% for 12 years
Total present values
5.9176
689,400.40
a
Initial cost of investment
Net present values
630,000.00
59,400.40
c
Payback
b
Internal rate of return
PV Factor =
5.408
P630,000 / P116,500 =
P630,000 / P116,500 = 5.4077
Scanning at 12 year line , 5.4077 is approximately 15%
True rate or exact rate using interpolation is computed as follows
At 14%
PV Factor =
5.660
at 16%
5.197
0.463
0.252
0.15089
15.089%
Exact rate =
years
14% + [{.2523 / .463} x 2% ] =
14% + .01089 =
5.660
5.408
years
9.5
Cash flows
year
a
PVF at 12%
Cool
1
0.893
2
3
0.797
0.712
Hot
Cash flows
38,000.00
PV of cash flows
33,934.00
42,000.00
48,000.00
128,000.00
33,474.00
34,176.00
101,584.00
Cost of investments
Net present values
Cash flows
PV of cash flows
42,000.00
37,506.0
42,000.00
42,000.00
126,000.00
33,474.0
29,904.0
100,884.0
90,000.00
11,584.00
90,000.00
10,884.00
1.13
1.1
PV of Hot can be computed at P42,000 x 2.402 = P100,884 also
b
Profitability index = PV / Cost
c
Both are acceptable, however, Cool is preferred as it has higher NPV ang PI
a
Machine 1
9.6
Present values
(P50,000 - P15,000) x 4.486 =
157,010.00
Cost
Net present values
152,000.00
5,010.00
Machine 2
Present values
(P60,000 - P20,000) x 4.486 =
179,440.00
Cost
Net present values
b
c
d
Machine 1
P157,010 / P152,000 =
1.03
Machine 2
P179,440 / P170,000 =
1.06
IRR
Machine 1 PV Factor = P152,000 / P35,000 =
4.34
PV Factor at 6 years of 4.355 is at
Machine 2 PV Factor = P170,000 / P40,000 =
4.25
PV Factor at 6 years of 4.231 is at
Both machines are acceptable
NPV
both are positive
PI
both are more than 1
IRR
9.7 a
170,000.00
9,440.00
both are greater than the minimum required rate of return of 9%
1 Cash payback =
P320,000 / P62,000 =
2 Present values
P62.000 x 5.535
Cost of investment
343,170.00
320,000.00
23,170.00
Net Present value
3 Profitability index = P343,170 / P320,000 =
4 Internal rate of return (IRR) =
5 Annual rate of return (ARR) =
5.16
P320,000 / 62,000 = 5.16
5.16 for 8 years is at
1.07
11%
P22,000 / [(P320,000 + 0) / 2] = 13.75%
years
9.8 a
Based on estimates:
Present values
P70,000 x 4.355 =
304,850.00
Initial costs
Net present value
300,000.00
4,850.00
accept
b
Based on actual:
Present values
P58,000 x 5.759 =
334,022.00
Initial costs
Net present value
340,000.00
(5,978.00)
reject
9.9 a
Present value of annual cash flows = P4,300 x 5.335
Present value of salvage value =
P3,000 x .467
Total present values
Cost
Present value of annual cash flows =
Present value of salvage value =
(658.50)
(P4,300 + P500) x 5.335
P3,000 x .467
Total present values
Cost
Net present value
c
9.10 a
b
c
1,401.00
24,341.50
25,000.00
Net present value negative - reject
b
22,940.50
25,608.00
1,401.00
27,009.00
25,000.00
positive - accept
2,009.00
Additional benefits would need to have a total present value of at least P658 in order for the van to be purchased
Present value of net cash flows
(P2,520,000 - P2,250,000) = P270,000 x 8.514 =
2,298,780.00
Present value of salvage value = P3,900,000 x .149 =
Total present values
581,100.00
2,879,880.00
Investment costs
Net present value
2,700,000.00
179,880.00
Present value of net cash flows
(P2,085,000 - P1,875,000) = P210,000 x 8.514 =
1,787,940.00
Present value of salvage value = P3,900,000 x .149 =
Total present values
581,100.00
2,369,040.00
Investment costs
Net present value
2,700,000.00
(330,960.00)
Present value of net cash flows
(P2,520,000 - P2,250,000) = P270,000 x 7.469 =
2,016,630.00
Present value of salvage value = P3,900,000 x .104 =
Total present values
405,600.00
2,422,230.00
Investment costs
Net present value
2,700,000.00
(277,770.00)
If # of campers attending each week is only 80, NPV decreases by P510,840, that is from positive P179,880 to a
negative P330,960. Investment should not be made unless attedees is closer to 100.
9.11 a
Old loss
(2,000.00)
New Net income (loss)
Receipts
P20,000 x 5% =
1,000.00
Depreciation
P12,000 / 10 years =
1,200.00
Net income (Loss)
(200.00)
Net difference
b
(1,800.00)
Payback on the vending machine only
P12,000. / P 1,000 =
12 years
relevant payback:
Payback
Change in cash flow is P3,000 = salary of employee terminated
P12,000 / P3,000 =
4.00
c
1 Present value of inflows
P3,000 x 4.195 =
12,577.50
Cost of investment
12,000.00
Net present value
577.50
2 IRR is approximately 23%
d
Present value P3,000 - (P14,000 x 5%) =
Cost
11,319.75
12,000.00
Net present value
e
Cost
P12,000 / 4.1925 = P2,862.25
Receipts =
9.12 a
(680.25)
(P2,862.25 - P2,000) / 5% =
17,245.00
Revenue
100,000.00
Cash expense
Annual cash inflow
b
Present value
60,000.00
40,000.00
P40,000 x 4.4941
179,764.00
Cost
160,000.00
Net present value
19,764.00
c
IRR factor
P160,000 / P40,000 = 4.00
d
Payback =
P160,000 / P40,000 = 4 years
e
Profitability index
f
IRR > than required
P179,764 / P160,000 =
PB < than required
depends on which one will be given more weight.
approximately
23%
4 years
1.1235
9.13 a
Cash payback
P262,000 / P42,400 =
b
IRR
at 12 years 6.1793 is approximately 12%
c
Present value
P42,400 x 6.8137 =
6.1792
12%
288,900.88
Cost
262,000.00
Net present value
d
26,900.88
yes, acceptable
9.14
1
Use table PV of Ordinary Annuity of P1
P200,000 = Annual Payments x the factor at interest rate at 30 years
a
AP = P200,000 / 11.2578
17,765.46
b
AP = P200,000 / 9.4269
21,215.88
c
AP = P200,000 / 8.0552
24,828.68
2
P200,000 = Annual Payments x the factor at interest rate at 15 years
a
AP = P200,000 / 8.5595
23,365.85
b
AP = P200,000 / 7.6061
26,294.68
c
AP = P200,000 / 6.8109
29,364.69
3 a
Total payments = 30 x P21,216 =
636,480.00
Total interest paid P636,480-200,000
b
436,480.00
Total payments = 15 x P26295 =
394,425.00
Total interest paid P394,425 - 200,000
9.15 a
Use table PV of P1
PV of P1 at 12% for 5 years is .5674
194,425.00
The P500 million is the future amount
PV = P500,000,000 x .5674 =
b
283,700,000.00
Use table PV of Ordinary annuity of P1. The P100 million is a uniform periodic payment at the
end of series of years. Therefore it is an annuity.
PV of Annuity = P100,000,000 x 3.6048 =
360,480,000.00
In particular, note that Prudential is willing to lend more than in No. 1 even though the interest rate
is the same. Because the company will get its money back more quickly.
9.16 a
PV = P30,000 x .6302
18,906.00
b
PV = P30,000 x ..4104
12,312.00
c
Halves the rates and double the number of periods. Present values decline:
PV = P30,000 x .6246
18,738.00
9.17
a
P80,000 = Future amount x .3050
FA = P80,000 / .30
262,295.08
b
P80,000 = Future annual amount x 4.3436
FAA = P80,000 / 4
18,417.90
9.18
List price
42,000.00
Less, Trade in allowance
Initial cash outlay
(9,000.00)
33,000.00
Present value of cash operating savings, from 12 year,
PV of ordinary annuity at 12% = P5,000 x 6.1944
30,972.00
Net present value - NPV is negative, do not buy
(2,028.00)
The trade-allowance really consists of a P3,000 adjustment of the selling price and a bonafide
P6,000 cash allowance for the old equipment. The relevant amount is the incremental cash outlay
of P33,000. The book value is irrelevant.
9.19
The quickest solution is to get the "net" inflows for each year:
1 End of year
Inflows
1
2
Outflows
200,000.00
250,000.00
net flows
150,000.00
200,000.00
50,000.00
50,000.00
3
300,000.00
250,000.00
50,000.00
4
400,000.00
300,000.00
100,000.00
5
450,000.00
350,000.00
100,000.00
3 payments
2 payments
P50,000 x 2.3216
P100,000 x 1.6467 x .6750
116,080.00
111,152.25
Total present values
227,232.25
less, initial investment
210,000.00
Net present value
17,232.25
2 The IRR is more than 14%, because the NPV is positive.
9.20 a
initial
year
investments
0
net cash inflows
each year
60,000.00
cumulative
-
(60,000.00
1
28,000.00
(32,000.00)
2
26,000.00
(6,000.00)
3
24,000.00
18,000.00
Payback period =
2
+ ( P6,000 / P 24,000) = 2 + .25
= 2.25 years
b
Net present value
net cash inflows
year
0
PV Factor
each year
at 12%
-
-
Present value
(60,000.00)
1
28,000.00
0.8929
25,001.20
2
3
26,000.00
24,000.00
0.7972
0.7118
20,727.20
17,083.20
net present value
c
2,811.60
at a 12% rate, NPV is positive, Therefore, to get an exact IRR, try a higher rate then interpolate.
inflow
14% factor
PV
at 16% factor
PV
28,000.00
26,000.00
0.8772
0.7695
24,561.60
20,007.00
0.8621
0.7432
24,138.80
19,323.20
24,000.00
0.6750
16,200.00
60,768.60
0.6407
15,376.80
58,838.80
initial investment
net present value
60,000.00
768.60
60,000.00
(1,161.20)
at 14%
true rate
60,769.00
at 16%
58,839.00
1,930.00
60,769.00
60,000.00
769.00
True rate = 14% + (769 / 1,930) x 2% = 14% + .8% = 14.8%
d
Depreciation per year P60,000 / 3 years =
P20,000
Expected Savings in annual operating costs (average)
(P28,000 + P26,000 + P24,000) / 3 = P26,000
(a)
ARR on initial investment =
(b)
ARR on average investment =
(P26,000 - P20,000 ) / P60,000 =
10.00%
(P26,000 - P20,000 ) / P30,000 =
20.00%
9.21
Old machine:
Operating cash outflows
Investment in inventories - outflows
P50,000 x 3.00
P200,000 x 1
(150,000.00)
(200,000.00)
Liquidation value of inventories at terminal date
Disposal value of machine *
P200,000 x .40
P4,000 x .40
80,000.00
1,600.00
(268,400.00)
New machine
Net cash outlay (P62,000-P15,000)
Operating cash outflows
P47,000 x 1.00
P40,000 x 3
(47,000.00
(120,000.00)
Investment in inventories - outflows
Liquidation value of inventories at terminal date
P160,000 x 1
P160,000 x .40
(160,000.00)
64,000.00
Disposal value of machine *
P4,000 x .40
PV in favor of new machine - minimizes the PV of future costs
1,600.00
(261,400.00)
7,000.00
* could be excluded from both alternatives as they have the same amounts - irrelevant cost
Using the incremental cost analysis approach:
Net cash outlay (P62,000 - P15,000)
P47,000 x 1
(47,000.00)
Liquidation value of inventory at time zero
P40,000 x 1
40,000.00
Difference in recovery of cash from inventory
liquidation value at terminal date
Operating savings
(P50,000 - P40,000)
P40,000 x .40
P10,000 x 3
(16,000.00)
30,000.00
Net present value in favor of new machine
7,000.00
9.22
Alternative 1
1 Amount invested
10,000.00
Alternative 2
10,000.00
Total increase in cash flows:
Year 0 - 5
P2,000 x 5; P1,500 x 5
10,000.00
7,500.00
Years 6 - 10
totals
P1,000 x 5; P1,500 x 5
5,000.00
15,000.00
7,500.00
15,000.00
Average annual cash flow
1,500.00
1,500.00
Less, Depreciation or amortizations P10,000 / 10 years
1,000.00
1,000.00
500.00
500.00
0.05
0.05
Average annual net income
ARR on original investments
2 IRR
Alternative 1 could also be interpreted at cash inflows received at P1,000 for the next 10 years
plus P1,000 for the first 5 years.
P10,000 = PV pf P1,000 at X% for 10 years + PV of P1,000 at X% for the first 5 years.
Let F1 = be the value of X% for 10 years and F2 be the value of X% for 5 years
P10,000 = P1,000 (F1) + P1,000(F2)
P10,000 = P1,000 ( F1 + F2)
F1 + F2 = P10,000 / P1,000 = 10
F1 at 8% for 10 years = 6.7101
F2 at 8% for 5 years = 3.9927
F1 at 10% for 10 years = 6.1446
F2 at 10% for 5 years = 3.7908
at 8% (P1,000 x 6.7101) + (P1,000 x 3.9927) = P10,703
at 10% (P1,000 x 6.1446) + (P1,000 x 3.7908) = P9,935
at 8%
in rate (F1 + F2)
10.7028
true rate
at 10%
-
in pesos
10,703.00
-
9.9354
9,935.00
0.7674
768.00
Exact rate = 8% + (.7028 /.7674) x 2% = 8% +1.83% = 9.83%
Alternative 2
P10,000 = PV pf P1,500 at X% for 10 years
P10,000 = P1,500 (F)
F = P10,000 / P1,500 = 6.6667
in rate (F1 + F2)
10.7028
10.0000
in peso
10,703.00
10,000.00
-
-
0.7028
703.00
At 8% F = 6.7101
6.7101
6.7101
true rate
6.6667
At 10%, F = 6.1446
6.1446
0.5655
0.0434
True rate = 8% + (.0434 / .5655) x 2% = 8% + .15% = 8.15%
3 The difference between the 9.83% return on Alternative 1 and the 8.15% return on alternative 2 is from the
fact that under Alt. 1, there are greater cash inflows during the first 5 years than under Alt. 2. Under the
Discounted Cash Flow (DCF) method, early cash inflows are weighted more heavily than inflows of later
years since this method considers the time value of money.
9.23
1 PV of annual cash inflows
PV of salvage value of machine at end of 6 years
PV of salvage value of parts at end of 6 years
P50,000 x 3.8887
194,435.00
P22,000 x .4556
P15,000 x .4556
10,023.20
6,834.00
Total present values
211,292.20
Initial investments
202,000.00
Net present value
9,292.20
2 IRR
IRR will be greater than 14% because the net present value is positive, try 16%
PV of annual cash inflows
P50,000 x 3.6847
PV of salvage value of machine at end of 6 years
P22,000 x .4104
PV of salvage value of parts at end of 6 years
P15,000 x .4104
184,235.00
9,028.80
6,156.00
Total present values
199,419.80
Initial investments
202,000.00
Net present value negative
(2,580.20)
Therefore, the IRR is just below 16%
3 ARR
a
Average annual income
50,000.00
Less, Depreciation (P187,000 - P22,000) / 6 years
27,500.00
Net annual income
Initial investment
ARR on initial investment
b
22,500.00
(P187,000 + P15,000)
Average annual income
50,000.00
Less, Depreciation (P187,000 - P22,000) / 6 years
27,500.00
Net annual income
Average investment (P202,000 + P22,000 +P15,000) / 2 = P119,500
ARR on average investment
4 The models in requirements 1 and 2 would give a positive decision.
However, the 11.14% ARR based on initial investment might give a negative decision because it is less
than 14%.
202,000.00
11.14%
22,500.00
119,500.00
18.83%
9.24
1
Total PV
Cash effects of operation (P150,000 x .60% net of tax)
P90,000 x 2.2459
Savings on income taxes on deprn. (P100,000 x .40)
P40,000 x 2.2459
202,131.00
89,836.00
Total after tax effect on cash
291,967.00
Investments
Net present value, negative
(300,000.00)
(8,033.00)
The computers should not be acquired.
2 After tax impact of disposal on cash P.60 (P40,000 - 0) = P24,000
PV is P24,000 x .6407
15,376.80
Net present value in (1)
(8,033.00)
New net present value , positive
7,343.80
The computers should be acquired.
3 Applying a 12% discount factor
P150,000 (1 -.40) x 2.4018 =
P90,000 x 2.4018
P100,000 x .40 x 2.4018
P40,000 x 2.4018
216,162.00
96,072.00
Total present values
312,234.00
Investments
(300,000.00)
Net present value, positive, therefore acquire
12,234.00
9.25
Sales
520.00
less, expenses excluding depreciation
350.00
Depreciation
100.00
Total expenses
450.00
Income before income taxes
Income taxes at 40%
70.00
28.00
Net income
42.00
Cash effects of operations:
Cash inflows from operations less cash expenses
Less, Income tax outflow without depreciation ( P170 x .40)
P520 -350
170.00
68.00
102.00
Effect on deprection as savings on income tax
Depreciation P100 x .40%
Total after tax effect on cash
40.00
142.00
Total after tax effect on cash is
Cash inflows from sales
520.00
Cash outflows for expenses
(350.00)
Cash outflows for tax
Total after tax cash received.
(28.00)
142.00
9.26
Investment
(45,000.00)
Cash operating savings
Annual savings
Income taxes at 40%
13,500.00
P13,500 x 40%
After tax effect on cash
5,400.00
8,100.00
Present value (P8,100 x 4.5638)
PV of tax savings from depreciation:
Investment x PV Factor x tax rate
36,966.78
P45,000 x .7809 x .40
14,056.20
Overhaul requirement:
Total cost
5,000.00
Less, income tax savings at 40%
2,000.00
Total after tax effect
3,000.00
Present value (P3,000 x .6355)
(1,906.50)
Residual value
Cash received
4,000.00
Book value
-
Gain
4,000.00
Income tax effect on gain at 40%
1,600.00
Total after tax effect
2,400.00
Present value (P2,400 x .4523)
Net present value of all cash flows
1,085.52
5,202.00
The investment is desirable
9.27
1
2
New machine
Disposal value of old machine
Incremental tax on gain on disposal
Net cost of investment
120,000.00
(20,000.00)
1,400.00
101,400.00
(P20,000 - P16,000) x 35%
Savings before taxes
Less, Income tax
40,000.00
Net cash flow before tax
40,000.00
Less depreciation expense
(P120,000 - 16,000)/10 years
Net income subject to tax
(10,400.00)
29,600.00
tax rate
0.35
Net cash flows after tax
9.28
1
2
Net income before depreciation
Less Depreciation expense
Net income after depreciation
Less Income tax
Net income after tax
Accounting Rate of Return (ARR)
(10,360.00)
29,640.00
(P60,000 / 10 years)
(P6,000 x .35)
(P3,900 / 60,000)
12,000.00
(6,000.00)
6,000.00
(2,100.00)
3,900.00
6.5%
3
Cash flow before taxes
Less income tax
Net cash flow after taxes
12,000.00
(2,100.00)
9,900.00
(P6,000 x .35)
4
Payback period
P60,000 / 9,900
in years
5
Payback reciprocal
P9,900 /60,000
in percentage
or it can be computed by dividing 1 with the payback period
6.06
16.50%
1 / 6.06
16.50%
9.29
Purchase price
100,000.00
Start up costs
Trade in value of fold machine
3,000.00
(15,000.00)
Salvage values of other assets
(6,000.00)
Tax savings on loss on retirement
Repair cost saved
(800.00)
(8,000.00)
Additional working capital
24,000.00
Net initial cost of investment
97,200.00
tax computation
9.30
1 Sales
Variable costs
Contribution margin
Fixed operating costs
cash flows
(10,000 x P15)
(10,000 x P8)
150,000.00
(80,000.00)
150,000.00
(80,000.00)
(10,000 x P7)
70,000.00
(25,000.00)
70,000.00
(25,000.00)
45,000.00
45,000.00
Depreciation expense
(P100,000 / 5 years)
Incremental net income before taxes
Cash flows before taxes
(20,000.00)
25,000.00
45,000.00
Income tax at 32%
Increase in net income
(8,000.00)
17,000.00
Add back, depreciation expense
20,000.00
NET CASH INFLOW PER YEAR
37,000.00
2 Net cash inflow per year
(8,000.00)
37,000.00
37,000.00
Present value factor, 5 years annuity at 14% (Table II)
Present value of future net cash flows
3.433
127,021.00
Less Investment
Net present value
100,000.00
27,021.00
3 Payback period
Net investment cost
Net annual cash inflows
a
100,000.00
b
37,000.00
Payback period (a / b)
4 Internal rate of return
2.7027
IRR
Them IRR is over 24.75%.
The factor is to be determined using the payback period which2.703
Because 2.7027, the closest factor in the five-year row of Table II is 2.745 at 24% and 2.689 at 25%.
(Remember, the higher the rate, the lower the factor.)
Get interest rates where the factor is in between.
To determine the exact or true rate:
At 24%
Present value of P1 in annuity
2.745
Payback factor
At 25%
Difference
Exact rate [24% + (.042/.056) x 1%]
2.745
2.703
2.689
0.056
0.042
0.2475
5 The book rate or accounting rate of return
Net income after tax
Average investment
P100,000 / 2
a
17,000.00
b
50,000.00
Rate of return (a / b)
0.34
6 The only change required is the determination of the present value of the salvage value
less the tax on the gain.
Salvage value
Tax rate at 32%
5,000.00
1,600.00
(P5,000 x 32%)
net cash inflow, end of year 5
Present value factor for single payment 5 years at 14%
in table I
3,400.00
0.519
Present value of salvage value
Add, net present value from number 2
1,764.60
27,021.00
NET PRESENT VALUE
28,785.60
NOTE:
We did not have to recompute annual net cash flows. The company still used P20,000 for
Depreciation expense, therefore at end of year 5, the book value is zero and there will be
a gain equal to the salvage value.
9.31
Cases
A
B
CASE A
annual net
cash inflows
cost of
capital
internal rate
of return
503,040.00
808,938.00
14%
12%
20%
18%
investments
120,000.00
180,000.00
Net present
value
122,892.00
208,062.00
C
124,141.00
600,000.00
10%
16%
162,880.00
D
200,000.00
900,000.00
12%
18%
230,000.00
1 Internal rate of return (IRR)
Investment
Annual net cash inflows
Payback factor ( at 10 periods interest of 20%)
a
b
503,040.00
120,000.00
(a / b)
4.1920
2 Net present value
CASE B
PV of cash inflows (14% for 10 years) (P120,000 x 5.2162)
PV of investments
625,932.00
(503,040.00)
Net present value
122,892.00
1 Investment
Annual net cash inflows
PV factor at 18% for 10 years
Present value of net cash inflows
a
b
180,000.00
4.4941
( a x b)
808,938.00
2 Net present value
Net present value of cash inflows at 12% for 10 years
(P180,000 x 5.65 )
Present value of investments
Net present value
1,017,000.00
(808,938.00)
208,062.00
CASE C
1 Annual net cash inflow
Investment
a
PV factor (16% for 10 years)
b
4.8332
(a / b)
124,141.36
Annual net cash inflow
600,000.00
2 Cost of capital
Investment
Net present value
600,000.00
162,880.00
Total PV of cash inflows
a
762,880.00
Annual net cah inflow
Present value factor (which at 10% for 10 years)
b
124,141.36
(a /b)
6.14525
nearest is 6.1446
CASE D
1 Annual net cash inflow
Investment
900,000.00
Net present value
230,000.00
Total PV of cash inflows
a
1,130,000.00
PV factor at 12% for 10 years
b
5.65
(a / b )
200,000.00
Annual net cash inflow
9.32
1 Annual profit net of tax
Process 1
Process 2
Sales ( 100,000 @ P50)
Less, Variable costs at P20 and at P10
5,000,000.00
(2,000,000.00)
5,000,000.00
(1,000,000.00)
Contribution margin
3,000,000.00
4,000,000.00
Less, Varia Fixes costs:
Cash fixed costs
* Depreciation expense on the investment for 4 yrs.
Total
Net income before income tax
Income tax at the rate of 32%
400,000.00
600,000.00
1,000,000.00
1,400,000.00
1,500,000.00
2,100,000.00
1,600,000.00
1,900,000.00
(512,000.00)
Net income after tax
1,088,000.00
(608,000.00)
1,292,000.00
* Cost of investment / 4 years
2 Accounting rate of return on average investments
Net income after tax
Average investments
(investment / 2)
ARR
a
1,088,000.00
1,292,000.00
b
2,000,000.00
3,000,000.00
0.5440
0.4307
54.40%
43.07%
(a / b)
OR
3 Net income after tax (see solution in no. 1)
Add back, depreciation expense
1,088,000.00
1,292,000.00
1,000,000.00
1,500,000.00
2,792,000.00
Annual cash inflows after tax
a
2,088,000.00
PV factor at 16% for 4 years
b
2.7980
2.7980
=(a x b)
d
5,842,224.00
4,000,000.00
7,812,016.00
6,000,000.00
(c - d)
1,842,224.00
1,812,016.00
Investment
a
4,000,000.00
6,000,000.00
Annual cash inflow
b
2,088,000.00
2,792,000.00
(a / b)
1.92
2.15
Present value of annual cash inflows
PV of investment
c
Net present value
4 Payback period
Payback period
5 Recommendation:
Net income
1,088,000.00
ARR
Net present value
1,292,000.00
0.544
0.431
1,842,224.00
1,812,016.00
1.92
2.15
Payback
Comparing the different measures, it seems that Process I has more advantanges over
Process 2, so most likely it would be Process I. However, the management
must also consider the effects of qualitative issues that could be associated to the
two processes.
9.33
a
b
Cost of new equipment
Cost of removing old equipment
175,000.00
5,000.00
Resale value of old equipment
(40,000.00)
Net cost of investment
140,000.00
Net present value before taxes
Annual operating costs -old equipment
Annual operating costs -new equipment
(P30,000-+ P48,00
(P25,000+ P20,000
Annual operating cost savings before taxes
Present value of Savings
Net initial cost of investment
Net Present value
c
The investment should be made since the NPV has a positive results.
78,000.00
(45,000.00)
33,000.00
(P33,000 x 5.019)
165,627.00
(140,000.00)
25,627.00
9.34
Analysis of Cash Flows
PRESENT
PROPOSED
Revenue
Expenses:
Miscellaneous
Salaries
Net cash flows
Required Investment:
Equipment
Termination pay
200,000.00
15,000.00
100,000.00
110,000.00
13,000.00
210,000.00
(10,000.00)
13,000.00
2,000.00
-
19,000.00
-
28,000.00
47,000.00
DIFFERENCE
*
(12,000.00
**
(47,000.0
* 10% x P150,000 = P15,000 comission
**An acceptable alternative would be to show P3,000 and P22,000 resprectively. The incremental investment
would still be P19,000.
a
Present value of P12,000 per year for 10 years at P12,000 x 6.000
Required investment
Net present value
72,000.00
47,000.00
25,000.00
The requirements of the problem focus on the incremental approach. The total project apporach could
view the problem as choosing the alternative that minimizes the net present value of the future costs:
Present:
Operating cash outflows, P10,000 x 6.00
(60,000.00)
Proposed:
Operating cash inflows, P2,000 x 6.00
Termination pay
Equipment
Total
Difference in favor of proposed investment
b
12,000.00
(28,000.00)
(19,000.00)
(35,000.00)
25,000.00
The minimum amount of annual revenue that the company would have to receive to justify the
investment would be theat amount yielding an incremental net present value of zero. As the initial
investment is constant, any change in the incremental net present value is due solely to a change in the
amount of revenue. Therefore, the maximum drop in the incremental net present value of P25,000 equals
the maximum drop in the present value of the revenue stream. This implies a maximum drop of
P25,000 / 6 = P4,167 in annual revenue and a minimum amount of annual revenue of P15,000 - P4,167 =
P10,833
Let X = Revenue at point of indifference, where net present value is zero
NPV = PV (New annual cash flows - old annual cash flfows) - Required investment
0
0
= 6.00[(X - 13,000) - (-10,000)] - 47,000
= 6.00(X -13,000 + 10,000) - 47,000
0
0
= 6.00(X- 3,000) - 47,000
= 6.00X - 18,000 - 47,000
6.00X = 65,000
X
= 10,833
Part 2 demonstrates sensitivity analysis, where the manager may see the potential impact of the
possible errors in the forecasts of revenue. Such analysis shows how much of a margin of safety is
available. In this case, his "best guess" is revenue of P15,000 ( in part 1). Sensitivity analysis shows
him that a decline of revenue would have to occur from P15,000 to P10,833 before the rate of return on the
project would decline to the minimum acceptable level.
Another approach to solve requirement 2 could be:
If 10% is the minimum acceptable rate of return, the minimum acceptable net present value must
be zero, using the 10% rate:
NPV = PV if future cash flows - initial investment
Let X = Annual cash inflow
Then 0 = 6.00(X) - 47,000
X
= P47,000 / 6.00
X = P7,833
Present value of P7.833 per year for 10 years at 10% P7,833 x 6.00
47,000.00
Required investment
Net present value
47,000.00
(0.00)
Note that the requirement asks for the minimum amount of revenue, as distinguished from the difference
in cash flows.
The following analysis shows that revenue can fall toP10,833. Note also that there can be negative
cash flows under both alternatives; the alternative with the least negative cash flow is preferable
Present
Proposed
Revenues
200,000.00
10,833.00
Expenses
210,000.00
13,000.00
Net cash flow from operations
(10,000.00)
(2,167.00)
Diff. in cash flows
(7,833.00)
9.35
1 Payback period
P200,000 / P40,000
2 Present value of cash inflow at 10% for 8 years
5 years
P40,000 x 5.335
Investment
200,000.00
Net present value
3 Yes
13,400.00
Assuming that the only criteria is the NPV because it has a positive NPV
9.36
a
213,400.00
P1,000 is being compounded for 3 years, so your balance on January 1, 2011 is P1,259.71
longway
a
b
c
d
e
(bxc)
( b + d)
end of
beginning
interest
interest
ending
year
balance
rate
amount
balance
2009
1,000.00
0.08
80.00
1,080.00
2010
1,080.00
0.08
86.40
1,166.40
2011
1,166.40
0.08
93.31
1,259.71
shortcut formula
FV = PV(1 + k )4
P1,000(1 + .08)4 = P1,259.71
b
The effective annual rate for 8 percent, compunded quarterly
longway
a
b
c
end of
year
2009-1st
2nd
3rd
4th
2010- 1st
2nd
3rd
4th
2011-1st
2nd
3rd
4th
beginning
balance
1,000.00
1,020.00
1,040.40
1,061.21
1,082.43
1,104.08
1,126.16
1,148.69
1,171.66
1,195.09
1,218.99
1,243.37
interest
rate
d
(bxc)
interest
amount
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
20.00
20.40
20.81
21.22
21.65
22.08
22.52
22.97
23.43
23.90
24.38
24.87
e
( b + d)
ending
balance
1,020.00
1,040.40
1,061.21
1,082.43
1,104.08
1,126.16
1,148.69
1,171.66
1,195.09
1,218.99
1,243.37
1,268.24
shortcut
use FV for % at 12 periods (4 quarters is x 3 years)
FV =
P1,000(1.2682) = P1,268.20
c
as you solve this problem, keep in mind that the tables assume that payments are made at the end
of each period. Therefore, you may solve this prblem by finding the future value of an annuity of P250
for 4 years at 8 percent.
longway
a
b
c
beginning
beginning
additional
of year
balance
investment
2008
250.00
2009
270.00
250.00
2010
561.60
250.00
2011
876.53
250.00
shortcut
FV = P250(4.5061) = P1,126.53
FV of annuity of P250 for 4 years at 8 percent is 4.5061
d
d
(bxc)
interest
amount
interest
rate
0.08
0.08
0.08
20.00
41.60
64.93
e
( b + d)
ending
balance
270.00
561.60
876.53
1,126.53
An amount is deposited in 4 equal payments in the account at 8% interest rate to obtain balance similar to the amount
equal to requirement letter a (P1,259.71)
longway
a
beginning
of year
2008
2009
2010
2011
b
c
beginning
balance
279.56
301.92
628.00
980.17
shortcut formula
P1,259.71 = Amount(4.5061)
Amount = P1,259.71 / 4.5061
=
279.56
additional
investment
279.56
279.56
279.56
d
(bxc)
interest
amount
interest
rate
0.08
0.08
0.08
22.36
46.52
72.61
e
( b + d)
ending
balance
301.92
628.00
980.17
1,259.73
9.37
a
Alternative a - Investment in the Project
Year
1
2
3 (1+2)
4
5 (3 - 4)
Loan balance
Interest at
Accumulated
Cash for
Loan Balance
beginning of
the year
10% per
year
amount at
End of year
Repayment
of loan
0
at end of
Year
-
1
100,000.00
10,000.00
110,000.00
45,000.00
65,000.00
2
65,000.00
6,500.00
71,500.00
45,000.00
26,500.00
3
26,500.00
2,650.00
29,150.00
45,000.00
(15,850.00)
* Cash of P45,000 is available to pay P29,150 total accumulated loan balance.
b
Alternative b - Keep cash and invest in time deposit
1
Investment
2
Interest at
3 (1+2)
Accumulated
balance at
10% per
amount at
year
End of year
beginning
Year
0
1
of year
11,915.00
at
1,191.50
13,106.50
2
13,106.50
1,310.65
14,417.15
3
14,417.15
1,441.72
15,858.87
* Net present value computation:
PV of annual cash inflows for 3 periods at 10%
Present value of investments
Net present value to be used as the initial investment (see year 1)
(P45,000 x 2.487)
111,915.00
100,000.00
11,915.00