F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
Chapter 9
Capital investment techniques
9.1
(a)
(b)
Average Investment
50 0000 + 10 000
2
=
30 000
Accounting rate of return (average investment)
9 000
X 100
30 000
1
=
30.0%
Accounting rate of return (total investment)
9 000 X 100
50 000
1
18.0%
=
9.2
Proposal 1:
Average Investment
100 000
2
=
50 000
100
1
=
14.0%
150 000 + 20 000
2
=
85 000
=
12 750
=
15.0%
Accounting rate of return
7 000 X
50 000
Proposal 2:
Average Investment
Average Profits (after tax)
-2 000 + 5 000 + 20 000 + 25 500 + 15 250
5
Accounting rate of return
12 750
85 000
X
100
1
Decision - choose Project 2.
9.3
Theory – refer to the text.
9.4
(a)
(b)
Payback period
75 000
18 750
=
Yes
88
4.0 yrs
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
9.5
(a)
Net Profit after Tax
add Depreciation
16 000
5 000
21 000
78 750
21 000
Payback Period
(b)
Average Investment
78 750 + 11 250
2
16 000
100
45 000 X 1
Accounting Rate of Return
=
3.75 years
=
45 000
=
35.6%
=
15 000
=
24%
9.6
(a)
Average profit after tax
Average investment
3 600
30 000 + 0
2
3 600
100
Accounting rate of return
15 000 X 1
Decision: purchase plant as the return > 20.0%
(b)
Average profit after tax
add Depreciation per annum
Average after tax cash flows
Payback period
3 600
3 750
7 350
30 000
7 350
=
4.1 years
Decision - do not purchase as payback period > 4.0 yrs.
9.7
Accounting Rate of Return
Average Net Profit after tax
Accounting Rate of Return
70 000
5
14 000
60 000
X
100
1
=
14 000
=
23.3%
Decision - as the accounting rate of return > 20% you would accept the project
Payback Period
Years
1
Net Profit after tax
5 000
add Depreciation
8 000
After Tax cash flows 13 000
Cumulative cash flows13 000
2
10 000
8 000
18 000
31 000
89
3
15 000
8 000
23 000
54 000
4
20 000
8 000
28 000
82 000
5
20 000
8 000
28 000
110 000
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
6 000
3 years + 28 000
Payback Per iod
=
3.2 years
Dec is ion - as the paybac k per iod > 3 years you would reject the project.
9.8
Proposal 1
Annual Net Prof it after Ta x
add Depreciat ion
After Tax Cash Flows
7 000
20 000
27 000
100 000
27 000
Payback Period
=
3.7 years
Proposal 2
Years
Net Profit after tax
add Depreciation
After Tax cash Flows
1
(2 000)
26 000
24 000
2
5 000
26 000
31 000
Cu mulative cash flows
24 000
55 000 101 000 152 500 193 750
Payback Per iod
3 years +
3
20 000
26 000
46 000
49 000
51 500
4
25 500
26 000
51 500
=
5
15 250
26 000
41 250
3.95 years
9.9
(a)
Sales
Expenses
Depreciation
390 000
232 500
37 500
270 000
120 000
36 000
84 000
Tax (30%)
Net Profit after tax
(b)
Average investment
Accounting rate of return
(c)
(d)
9.10
300 000
2
84 000
300 000
=
X
100
1 =
Profit after tax
add Depreciation
After tax cash flows
Payback period
150 000
28%
84 000
37 500
121 500
300 000
121 500
Theory – refer text.
90
=
2.5 years
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
9.11
Year
Cash Flow
0
- 30 000
1
5 500
2
6 000
3
11 000
4
11 000
5
13 000
Net Present Value
PVIF(14%)
1.0000
.8772
.7695
.6750
.5921
.5194
P/Value
- 30 000
4 825
4 617
7 425
6 513
6 752
+ 132
Decision - buy machine as NPV > 0
Using a Sharp EL – 738/735S calculator
Clear the calculator: CFi , 2nd F , CA , ON/C
30 000 +/- ENT , 5 500 ENT , 6 000 ENT , 11 000 ENT , ENT , 13 000 ENT , 14 I/Y ,
2ndF , CASH, ▼ , COMP
the answer is: +131
9.12
(a)
NPV
At 18%
Project P
Cost
(- 85 000 X 1.0000)
Cash Flows (30 000 X PVIFA,5,18%)
Net Present Value
Project Q
Cost
(- 118 000 X 1.0000)
Cash Flows (40 000 X 3.1272)
Net Present value
- 85 000
93 816
+8 816
- 118 000
125 088
+ 7 088
Decision - choose Project P
(b)
At 12%
Project P
Cost
(- 85 000 X 1.0000)
Cash Flows (30 000 X PVIFA,5,12%)
Net Present Value
- 85 000
108 144
+23 144
Project Q
Cost (-118 000 X 1.0000)
Cash Flows (40 000 X 3.6048)
Net Present Value
-118 000
144 192
+26 192
Decision - choose Project Q
91
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
Using a Sharp EL-735/735S calculator
Clear calculator: CFi , 2nd F , CA , ON/C
Project P
85 000 +/- ENT , 30 000 (x,y) , 5 ENT , 18 I/Y , 2ndF , CASH , ▼ , CO MP
the answer is: +8 815
then enter: ▲, 12 ENT , ▼ , COMP
the answer is: + 23 143
Clear calculator: CFi , 2nd F , CA , ON/C
Project Q
118 000 +/- ENT , 40 000 (x,y) , 5 ENT , 18 I/Y , 2ndF , CASH , ▼ , COMP
the answer is +7 087
then enter: ▲, 12 ENT , ▼ , COMP
the answer is + 26 191
9.13
(a)
16 900 X PVIFA,6,i%
therefore:
PVIFA,6,i% =
64 000
16 900
=
64 000
=
3.7870
=
3.7870
This corresponds to an interest rate of approximately 15%
(b)
Using the same method as (a) the answer is 20%
(c)
Using the same method as (a) the answer is 24 %
Using a Sharp EL-738/735S calculator
Clear calculator: CFi , 2nd F , CA , ON/C
(a) 64 000 +/- ENT , 16 900 (x,y) , 6 ENT , 2ndF , CASH , CO MP
the answer is: 14.98%
(b) using the same method as (a) the answer is 20%
(c) using the same method as (a) the answer is 24%
92
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
9.14
(a)
Year
s
PVIF
0
1.0000
- 115 200
- 72 000
- 115 200
- 72 000
1
0.8929
25 000
15 000
22 323
13 394
2
0.7972
30 000
20 000
23 916
15 944
3
0.7118
30 000
20 000
21 354
14 236
4
0.6355
35 000
25 000
22 243
15 888
5
0.5674
30 000
20 000
17 022
11 348
6
0.5066
30 000
15 000
15 198
7 599
+6 856
+ 6 409
12%
Cash Flows
Machine 1
Net Present Value
Machine 2
Machine 1
Total Net Present value
Machine 2
(b)
Internal Rate of Return
Machine 1
14%
Machine 2
15%
(c)
Method
NPV
IRR
Ranking
1
Machine 1
Machine 2
2
Machine 2
Machine 1
Using a Sharp EL – 738/735S calculator
Machine 1
Clear the calculator: CFi , 2nd F , CA , ON/C
115 200 +/- ENT , 25 000 ENT , 30 000 ENT , ENT , 35 000 ENT ,
30 000 ENT , ENT ,12 I/Y , 2ndF, CASH, ▼ , COMP ; the answer is: +6 856
then enter: ▲, COMP ; the answer is 14.01%
Machine 2
Clear the calculator: CFi , 2nd F , CA , ON/C
72 000 +/- ENT , 15 000 ENT , 20 000 ENT , ENT , 25 000 ENT ,
20 000 ENT , 15 000 ENT , 12 I/Y , 2ndF, CASH, ▼ , COMP ; the answer is: +6 408
then enter: ▲, COMP ; the answer is 15.02%
93
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
9.15
(a) Profit before depreciation and tax
less Depreciation
Net Profit before tax
Tax (30%)
Net Profit after tax
53 720
25 000
28 720
8 616
20 104
150 000 + 0
2
Average Investment
Accounting rate of Return
20 104
75 000
X
100
1
=
75 000
=
26.8%
(b) Net Profit after tax
add Depreciation
After tax cash flows
20 104
25 000
45 104
150 000
45 104
(c) Payback Period
=
3.3 years
(d) Present Value
45 104 X PVIFA,6,12%
=
185 441
(e) IRR
45 104 X PVIFA,6, i%
=
150 000
150 000
45 104
=
3.3256
PVIFA, 6 , i%
Therefore the internal rate of return will be
20%
Using a Sharp EL-738/735S calculator
Clear calculator: CFi , 2nd F , CA , ON/C
150 000 +/- ENT , 45 104 (x,y) , 6 ENT , 2n dF , CASH , CO MP
the answer is: 20%
9.16
(a)
A
4 000
2 808
1 192
Average cash flows
less Depreciation
Profit after Tax
B
8 000
5 162
2 838
Accounting rate of return
Project A
Project B
1 192
8 424
2 838
15 486
100
X 1
100
X 1
Decision - choose Project A
94
=
14.2%
=
18.3%
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
(b) Payback period
Project A
8 424
4 000
=
2.11 years
Project B
7 486
+16 000
=
2.47 years
2 years
Decision - choose Project A
(c) Net Present Value
Project A
4 000 X PVIFA,3,12% - 8 424
Project B
Years
0
1
2
3
NPV
+1 183
Cash Flows
- 15 486
nil
8 000
16 000
PVIF
1.0000
0.8920
0.7972
0.7118
NPV
- 15 486
nil
6 378
11 389
+2 281
4 000 X PVIFA,3,i%
=
8 424
8 424
PVIFA, 3,i% = 4 000
=
2.106
=
20%
PVIF
1.0000
0.8475
0.7182
0.6086
NPV
- 15 486
nil
5 746
9 738
-2
Decision - choose Project B
(d) Internal rate of return
Project A
Internal Rate of Return
Project B (at 18 %)
Years
Cash Flows
0
- 15 486
1
nil
2
8 000
3
16 000
Therefore the IRR for Project B is 18%
Decision - choose Project A
95
i
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
Using a Sharp EL – 738/735S calculator
Project A
Clear the calculator: CFi , 2nd F , CA , ON/C
8 424 +/- ENT , 4 000 (x,y) ,3 ENT, 12 I/Y , 2ndF , CASH , ▼ , CO MP ;
the answer is: + 1 183
then enter: ▲, COMP ; the answer is 20%
Project B
Clear the calculator: CFi , 2nd F , CA , ON/C
15 486 +/- ENT, 0 ENT, 8 000 ENT , 16 000 ENT , 12 I/Y , 2ndF, CASH,
▼ , COMP ; the answer is: +2 280
then enter: ▲, CO MP ; the answer is 18%
9.17
(a) Accounting rate of return
Machine A
1 054
5 000
X
100
1
= 21.08%
Machine B
1 916
8 000
100
X 1
= 23.95%
Decision - choose B
(b) Payback period
Machine
Net profit after tax
add Depreciation
Annual cash flows
A
1 054
2 000
3 054
B
1 916
3 200
5 116
=
3.27 years
=
3.13 years
Payback period
Machine A
Mac hine B
10 000
3 054
16 000
5 116
Decision - choose B
(c) Net present value
Machine A -10 000 + 3 054 X PVIFA,5,10%
=
+1 577
Machine B
=
+3 394
-16 000 + 5 116 X PVIFA, 5,10%
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F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
Decision - choose B
(d) Internal rate of return
Machine A
PVIFA,5,i%
=
10 000
3 054
=
3.2744
i
=
16%
16 000
5 116
=
3.1274
i
=
18%
Machine B
PVIFA,5,i%
=
Decision - choose B
Using a Sharp EL – 738/735S calculator
Machine A
Clear the calculator: CFi , 2nd F , CA , ON/C
10 000 +/- ENT , 3 054 (x,y) ,5 ENT, 10 I/Y , 2ndF , CASH , ▼ , CO MP ;
the answer is: + 1 577
then enter: ▲, COMP ; the answer is 16%
Machine B
Clear the calculator: CFi , 2nd F , CA , ON/C
16 000 +/- ENT , 5 116 (x,y) ,5 ENT, 10 I/Y , 2ndF , CASH , ▼ , CO MP ;
the answer is: + 3 394
then enter: ▲, COMP ; the answer is 18%
9.18
(a) Payback period
X
2 years +
12 000
20 000
Y
2 years +
20 700
30 000
=
2.69 years
Z
3 years +
3 600
49 000
=
3.07 years
Decision - choose X
97
=
2.60 years
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
(b) Net present value
Project X
Years
0
1
2
3
4
Total NPV
Project Y
NPV
=
Cash flow
- 82 000
40 000
30 000
20 000
20 000
Factor
1.0000
.9091
.8264
.7513
.6830
NPV
- 82 000
36 364
24 792
15 026
13 660
+ 7 842
- 80 700 + 30 000 X PVIFA,4,10%
= +14 397
Project Z
Years
0
1
2
3
4
Total NPV
Cash flow
-83 600
10 000
30 000
40 000
49 000
Factor
1.0000
.9091
.8264
.7513
.6830
NPV
-83 600
9 091
24 792
30 052
33 467
+13 802
=
15 %
80 700
30 000
=
2.6900
i
=
18%
=
16%
Decision - choose Y
(c) Internal rate of return
Project X
Project Y
PVIFA, 4,i%
=
Project Z
Decision - choose Y
98
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
Using a Sharp EL – 738/735S calculator
Project X
Clear the calculator: CFi , 2nd F , CA , ON/C
82 000 +/- ENT, 40 000 ENT, 30 000 ENT, 20 000 ENT, ENT, 10 I/Y,
2ndF, CASH, ▼ , COMP ; the answer is: +7 844
then enter: ▲, COMP ; the answer is 15%
Project Y
Clear the calculator: CFi , 2nd F , CA , ON/C
80 700 +/- ENT , 30 000 (x,y) , 4 ENT, 10 I/Y , 2ndF , CASH , ▼ , CO MP ;
the answer is: + 14 396
then enter: ▲, CO MP ; the answer is 18%
Project Z
Clear the calculator: CFi , 2nd F , CA , ON/C
83 600 +/- ENT, 10 000 ENT, 30 000 ENT, 40 000 ENT, 49 000 ENT, 10 I/Y ,
2ndF, CASH, ▼ , COMP ; the answer is: +13 805
then enter: ▲, COMP ; the answer is 16%
9.19
Theory – refer text.
9.20
(a) Net present value (8%)
Machine A
Machine B
-37 920 + PVIFA,5,8% X 14 400
-58 440 + PVIFA,5,8% X 20 400
=
=
+19 575
+23 011
(b) Internal rate of return
Machine A
PVIFA, 5,i%
=
37 920
14 400
=
2.6333
i
=
26%
58 440
20 400
i
=
=
2.8647
22%
Machine B
PVIFA,5,I%
=
(c) Recommend - Machine B – based upon NPV.
99
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
(d) Net present value (15%)
Machine A
Machine B
-37 920 + PVIFA,5,15% X 14 400
-58 440 + PVIFA,5,15% X 20 400
=
=
+10352
+9 945
(e) Recommend - Machine A
Using a Sharp EL – 738/735S calculator
Machine A
Clear the calculator: CFi , 2nd F , CA , ON/C
37920 +/- ENT, 14 400 (x,y) , 5 ENT, 8 I/Y , 2ndF , CASH , ▼ , COMP ;
the answer is: + 19 575
then enter: ▲, COMP ; the answer is 26%
then enter: 15 ENT, ▼ , COMP ; the answer is +10 351
Machine B
Clear the calculator: CFi , 2nd F , CA , ON/C
58 440 +/- ENT, 20 400 (x,y) , 5 ENT, 8 I/Y , 2ndF , CASH , ▼ , CO MP ;
the answer is: + 23 011
then enter: ▲, COMP ; the answer is 22%
then enter: 15 ENT, ▼ , COMP ; the answer is +9 944
9.21
Theory – refer text.
9.22
(a) Net present value (10%)
Project A
Year
Cash Flow
0
-10 000
1
8 000
2
2 000
3
2 000
4
1 000
5
115
Total NPV
PVIF,10%
1.0000
.9091
.8264
.7513
.6830
.6209
NPV
-10 000
7 273
1 653
1 503
683
71
+1 183
Project B
-25 000 + 15 000 X PVIFA,3,10 % X PVIF,2,10% = +5 828
Project C
-15 000 + 5 000 X PVIFA,5,10%
= +3 954
100
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
NPV ranking: B,C,A
(b) Net present value (18%)
Project A
Year
Cash Flow
PVIF,18%
0
-10 000
1.000
1
8 000
.8475
2
2 000
.7182
3
2 000
.6086
4
1 000
.5158
5
115
.4371
Total NPV
Project B
-25 000 + 15 000 X PVIFA,3,18% X PVIF,2,18%
Project C
- 15 000 + 5 000 X PVIFA,5,18 %
NPV
-10 000
6 780
1 436
1 217
516
50
-1
=
-1 576
=
+636
NPV ranking: C (positive NPV), A (just beaks even on NPV),
rejec t B (negative NPV)
(c) IRR
Project A
At an interest rate of 18% the NPV is nil. Therefore the IRR is 18%
Project B
At an interest rate of 16% the NPV will be:
-25 000 + 15 000 X PVIFA,3,6% X PVIF,2,16%
=
As the NPV is almost zero the IRR will be approximately:
Project C
5 000 X PVIFA,5,i%
PVIFA,5,i%
i
=
=
=
15 000
3.0000
20%
IRR ranking: C,A,B
(d)
NPV – 10%
A , B, C
Mutually
Exclusive
B
NPV –18%
A, C
C
IRR (10% cost of capital)
A, B, C
C
IRR (18% cost of capital)
A, C
C
Method
Independent
101
+37
16%
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
Using a Sharp EL – 738/735S calculator
Project A
Clear the calculator: CFi , 2nd F , CA , ON/C
10000 +/- ENT, 8 000 ENT, 2 000 ENT, ENT, 1 000 ENT, 115 ENT,10 I/Y ,
2ndF, CASH, ▼ , COMP ; the answer is: +1 182.66
then enter: ▲,18 ENT , ▼ , COMP ; the answer is - 0.65
then enter: ▲, COMP ; the answer is 17.995%
Project B
Clear the calculator: CFi , 2nd F , CA , ON/C
25 000 +/- ENT , 0 ENT, ENT , 15 000 ENT , ENT , ENT , 10 I/Y ,
2ndF , CASH , ▼ , CO MP ; the answer is: + 5 828.74
then enter: ▲,18 ENT , ▼ , COMP ; the answer is - 1 577.07
then enter: ▲, COMP ; the answer is 16.04%
Project C
Clear the calculator: CFi , 2nd F , CA , ON/C
15 000 +/- ENT , 5 000 (x,y) , 5 ENT, 10 I/Y , 2ndF , CASH , ▼ , COMP ;
the answer is: + 3 953.93
then enter: ▲,18 ENT , ▼ , COMP ; the answer is + 635.86
then enter: ▲, COMP ; the answer is 19.86%
9.23
Project
IRR
NPV
Payback
P
18%
+4 373
3.15 years
Q
14%
+1 397
2.32 years
R
16%
+4 539
2.80 years
102
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
Using a Sharp EL – 738/735S calculator
Project P
Clear the calculator: CFi , 2nd F , CA , ON/C
23 000 +/- ENT, 0 ENT, 5 000 ENT, 15 000 ENT, 20 000 ENT, 12 I/Y ,
2ndF, CASH, ▼ , COMP ; the answer is: +4 373
Project Q
Clear the calculator: CFi , 2nd F , CA , ON/C
43 180 +/- ENT, 25 000 ENT, 15 000 ENT, 10 000 ENT, 5 000 ENT,
2ndF, CASH, COMP ; the answer is: 14%
Project R
Clear the calculator: CFi , 2nd F , CA , ON/C
53 170 +/- ENT , 19 000 (x,y) , 4 ENT, 12 I/Y ,
2ndF , CASH , ▼ , CO MP ; the answer is: + 4 540
then enter: ▲, COMP ; the answer is 16%
9.24
Machine A
-20 000 + 8 500 x PVIFA,4,12% = 5 817
5 817
PVIFA,4,12%
Machine B
= $1 915
-30 000 + 10 000 x PVIFA,5,12% = 6 048
6 048
PVIFA,5,12%
= $1 678
Recommend - Machine A
9.25
Project L
Cash flows:
5 000 X PVIFA,3,20% X PVIF,1,20%
5 000 X 2.1065 X .8333
Outlay costs
NPV
NPV
8 777
-10 000
-1 223
103
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
Using a Sharp EL – 738/735S calculator
Clear the calculator: CFi , 2nd F , CA , ON/C
10 000 +/- ENT , 0 ENT , 5 000 (x,y) , 3 ENT, 20 I/Y , 2ndF , CASH , ▼ , CO MP ;
the NPV answer is: -1 223
Note: Project L will be rejected as NPV < 0
Net Present Value
Project M
Years
0
1
2
3
4
5
Cash Flows
-9 000
3 000
4 000
5 000
6 000
7 000
0.8333
0.6944
0.5787
0.4823
0.4019
2 500
2 778
2 894
2 894
2 813
PVIF 20%
Total present value
13 879
Net present value
4 879
Using a Sharp EL – 738/735S calculator
Clear the calculator: CFi , 2nd F , CA , ON/C
9 000 +/- ENT , 3 000 ENT , 4 000 ENT , 5 000 ENT , 6 000 ENT , 7 000 ENT ,
20 I/Y , 2ndF , CASH , ▼ , COMP ; the answer is +4 878
Project N
Year
0
1
2
3
Cash Flows
-29 000
10 000
15 000
25 000
0.8333
0.6944
0.5787
8 333
10 416
14 468
PVIF 20%
Total present value
Net present val ue
33 217
4 217
Using a Sharp EL – 738/735S calculator
Clear the calculator: CFi , 2nd F , CA , ON/C
29 000 +/- ENT , 10 000 ENT , 15 000 ENT , 25 000 ENT , 20 I/Y ,
2ndF , CASH , ▼ , CO MP ; the answer is +4 218
104
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
Equi vale nt annual cash flows:
Project M
4 879
PVIFA,5,20%
= 1 631
Using a Sharp EL – 738/735S calculator
Clear the calculator: CFi , 2nd F , CA , ON/C
4 878 +/- PV , 20 I/Y , 5 N
, COMP PMT, the answer is:
1 631
Project N
4 217
PVIFA,3,20%
= 2 002
Using a Sharp EL – 738/735S calculator
Clear the calculator: 2nd F , CA , ON/C
4 218 +/- PV , 20 I/Y , 3 N , COMP PMT, the answer is:
2 002
Decision - choose N
9.26
Machine A
1.
Cost
2.
Net cash flows
12 000 X PVIFA,5,14% (3.4331)
3.
4.
5.
NPV
-30 000
(-30 000 X 1.0000)
41 197
Tax on net income
12 000 X .30 X PVIFA,5,14% X PVIF,1,14%
12 000 X .30 X 3.4331 X .8772
-10 841
Tax savings on depreciation
6 000 X .30 X PVIFA,5,14% X PVIF,1,14%
6 000 X .30 X 3.4331 X .8772
5 421
Residual value
4 000 X PVIF,5,14% (.5194)
2 078
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F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
6.
Tax effect on gain on disposal
4 000 X 0.30 X PVIF,5,14% X PVIF,1,14%
4 000 X 0.30 X 0.5194 X 0.8772
Total NPV
- 547
7 308
Equi vale nt annual cash flow:
7 308
PVIFA,5,14%
=
Machine B
NPV
1.
Cost (-45 000 X 1.0000)
2.
3.
2 129
- 45 000
Net cash flows
14 000 X PVIFA,10,14%
14 000 X 5.2161
73 025
Tax on net income
14 000 X .30 X PVIFA,10,14% X PVIF,1,14%
14 000 X .30 X 5.2161 X .8772
-19 217
4.
Tax savings on depreciation
4 500 X .30 X PVIFA,10,14% X PVIF,1,14%
4 500 X .30 X 5.2161 X .8772
Total NPV
6 177
14 985
Equi vale nt annual cash flow:
14 985
PVIFA,10,14%
=
2 873
Decision - choose Machine B
Alternative Solution:
Machine A
NPV
Years
1. Outlay cost
0
1
2
3
4
5
-30 000
2. Cash flows
12 000
3. Tax on cash flows
4. Depreciation deduction
12 000
12 000
12 000
12 000
-3 600
-3 600
-3 600
-3 600
- 3 600
1 800
1 800
1 800
1 800
1 800
5. Salvage value
4 000
6. Tax on gain on disposal
Total
6
- 1 200
-30 000
12 000
10 200
106
10 200
10 200
14 200
-3 000
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
Using a Sharp EL – 738/735S calculator
Clear the calculator: CFi , 2nd F , CA , ON/C
30000 +/- ENT , 12 000 ENT , 10 200 (x,y) , 3 ENT, 14 200 ENT, 3 000 +/- ENT, 14 I/Y ,
2ndF , CASH , ▼ , CO MP ; the answer is +7 307
Equivalent annual cash flows
Using a Sharp EL – 738/735S calculator
Clear the calculator: CFi , 2nd F , CA , ON/C
7 307 +/- PV , 14 I/Y , 5 N , COMP PMT, the answer is:
2 128
Machine B
NPV
Years
1. Outlay cost
0
1
2 – 10
-45 000
2. Cash flows
14 000
3. Tax on cash flows
4. Depreciation deduction
Total
11
-45 000
14 000
14 000
-4 200
-4 200
1 350
1 350
11 150
-2 850
Using a Sharp EL – 738/735S calculator
Clear the calculator: CFi , 2nd F , CA , ON/C
45 000 +/- ENT , 14 000 ENT , 11 150 (x,y) , 9 ENT, 2 850 +/- ENT, 14 I/Y ,
2ndF , CASH , ▼ , CO MP ; the answer is +14 985
Equivalent annual cash flows
Using a Sharp EL – 738/735S calculator
Clear the calculator: CFi , 2nd F , CA , ON/C
14 985 +/- PV , 14 I/Y , 10 N , COMP PMT, the answer is:
107
2 873
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
9.27
(i)
Years
0
1. Outlay
1
2
3
4
5
6
7
28 000
34 000
32 000
45 000
35 000
30 000
-8 400
-10
200
-9 600
-13
500
-10
500
-9 000
7 050
7 050
7 050
7 050
7 050
7 050
28 000
32 650
28 850
42 450
28 550
26 550
-1 950
0.8772
0.7695
0.6750
0.5921
0.5194
0.4556
0.3996
24 562
25 124
19 474
25 135
14 829
12 096
-779
-141 000
2. Cash Flows
3. Tax on cash flows
4. Depreciation deduction
Total
-141 000
PVIF 14%
Total present value
120 441
Net present value
-20 559
Using a Sharp EL – 738/735S calculator
Clear the calculator: CFi , 2nd F , CA , ON/C
141 000 +/- ENT , 28 000 ENT , 32 650 ENT , 28 850 ENT , 42 450 ENT , 28 550 ENT ,
26 550 ENT , 1 950 +/- ENT , 14 I/Y , 2ndF , CASH , ▼ , COMP ;
the NPV answer is – 20 564
(ii) Net present value index
Net present value
cash outlay
=
120 441
141 000
=
-14.58%
(b) Decision - do not purchase
9.28
(a) (i) NPV
NPV
-250 000
1.
Cost
2.
Cash flows after tax
72 022 X .70 X PVIFA,8,14% (4.6389)
3.
(-250 000 X 1.0000)
Tax savings on depreciation
31 250 X .30 X 4.6389
233 870
43 490
27 360
NPV
108
F i nanci al Managem ent : Pri nci pl es and Ap pl i cat i ons 5E - Sol ut i on s Manu al
(a) (ii) Net present value index
27 360
250 000
=
(a) (iii) IRR
Cash flows after tax
Depreciation tax savings
Total After Tax Cash Flows
59 790 X PVIFA,8,i%
i%
10.94%
50 415
9 375
59 790
=
=
250 000
17% (approx)
Using a Sharp EL – 738/735S calculator
Clear the calculator: CFi , 2nd F , CA , ON/C
250 000 +/- ENT , 59 790 (x,y) , 8 ENT, 14 I/Y , 2ndF , CASH , ▼ , COMP ;
the NPV answer is: 27 358,
then enter: ▲, CO MP ; the IRR answer is : 17.20%
(b)
Decision - buy the machine
9.29
Budget constraint of $850 000.
Ranking on NPV (5,1,6,7) provides a total NPV of $170 000 with total Capital Expenditure
of $800 000.
Ranking on IRR (1,4,6,2,7) provides a total NPV of $140 000 with total Capital Expenditure
of $700 000.
Ranking using the profitability index (4,5,6,1,2) provides a total NPV of $180 000 with a total
Capital Expenditure of $850 000.
Therefore projects will be chosen which maximise the NPV whilst staying within budget
constraints.
T his is the last question in t his c hapter.
109