www.studyguide.pk
INVESTMENT APPRAISAL
Methods
1.
Payback period
2.
3.
4.
ARR (Average rate of return / Accounting rate of return)
NPV (Net Present Value) → Discounted Cash flow The discounting method
IRR (Internal rate of return)
NET PRESENT VALUE
Years
0
1
2
3
4
5
Cash outflow /
Discount Factor
Cash inflow
(1000 000)
1
500000
0.8929
500000
0.7972
500000
0.7118
500000
0.6355
500000
0.5674
Net Present Value
Present Value
(1000 000)
446450
398600
355900
317750
283700
802400
* interest rate = i = 12%
PV =
A
(1 + i ) n
where i = interest rate
n = number of years
A = amount
PV = Present Value
Exercise Pg. 367
Q.1.
Years
0
1
2
3
4
5
Residual
Value
£
Cash outflow /
Cash inflow
(20 000)
6000
6000
6000
6000
6000
5000
Discount Factor
Present Value
1
0.91
0.82
0.74
0.67
0.61
0.61
(20 000)
5460
4920
4440
4020
3660
3050
Net Present Value
£ 5550
Q.2.
Project A
£ (000)
£
(000)
Years
0
Cash outflow /
Cash inflow
(100)
Discount Rate
Present Value
1
(100)
www.studyguide.pk
1
2
3
4
5
100
100
0
0
0
Net Present Value
Project B
0.92
0.86
0.79
0.73
0.68
£ (000)
92
86
0
0
0
£ 78
£
(000)
Years
0
1
2
3
4
5
Cash outflow /
Cash inflow
(100)
10
10
100
100
0
Net Present Value
Discount Rate
Present Value
1
0.92
0.86
0.79
0.73
0.68
(100)
9.2
8.6
79
73
0
£ 69.8
Project C
£ (000)
£
(000)
Years
0
1
2
3
4
5
Cash outflow /
Cash inflow
(100)
0
10
100
100
150
Net Present Value
Discount Rate
Present Value
0.92
0.86
0.79
0.73
0.68
(100)
0
8.6
79
73
102
£ 162.6
Option C is the best choice since it gives the highest net present value as
compared to other two.
Q.3.
(i)
Payback period
Year: 3
Months:-
50
×12 = 3
200
Period: 3 years 3 months
(ii)
Accounting rate of return
Profit = 1100 – 750
=
350
= £ 70 000 (Average profit)
5
www.studyguide.pk
ARR
=
70 000
×100
750000
= 9.3%
Q.3.(b) @ 8%
£ (000)
£
(000)
Years
0
1
2
3
4
5
R.V.
Cash outflow
(750)
200
250
250
200
150
50
Net Present Value
Discount Rate
0.9259
0.8573
0.7938
0.7350
0.6806
0.6806
Present Value
(750)
185.18
214.325
198.45
147.00
102.09
34.03
£ 131.075
@ 10%
£ (000)
£
(000)
Years
0
1
2
3
4
5
R.V.
Cash outflow
(750)
200
250
250
200
150
50
Net Present Value
Discount Rate
1
0.9091
0.8264
0.7513
0.6830
0.6209
0.6209
Present Value
(750)
181.82
206.6
187.825
136.6
93.135
31.045
£ 87.025
@ 12%
£ (000)
£
(000)
Years
0
1
2
3
4
5
Cash outflow
(750)
200
250
250
200
150
Discount Rate
0.8929
0.7972
0.7118
0.6355
0.5674
Present Value
(750)
178.58
199.3
177.95
127.1
85.11
www.studyguide.pk
R.V.
Q.4.
50
Net Present Value
0.5674
28.37
£ 46.41
According to 3 year payback rule Project B can be discarded as it takes
3 years and ½ × 12 =- 0.6 months.
So net present values of Project A & Project C have to be compared now.
Years
0
1
2
3
4
5
R.V.
Discount Factor
1
0.91
0.83
0.75
0.68
0.62
0.62
Net Present Value
PV–A (£m)
(10)
3.64
3.32
6.00
5.44
4.96
1.24
£ 14.6
PV–C (£m)
(10)
7.28
4.98
3.00
2.72
2.48
0.31
£ 10.77
Project A should be chosen as the net present value from this is higher than that
of Project C while Project B was already discarded at the screening stage.
Q.5.
a.(i)
Payback Period
PROJECT A:
4 years
PROJECT B:
4 years
and months =
50
×12 = 6
100
4 years and 6 months
(ii)
Accounting rate of return
PROJECT A
Profit = 300 000 – 200 000
ARR
=
100 000
= £ 20 000 (average profit)
5
=
20 000
×100
200 000
= 10%
PROJECT B
Profit = 350 000 – 250 000
ARR
=
100 000
= £ 20 000 (average profit)
5
=
20 000
×100
250 000
www.studyguide.pk
= 8%
Years
0
1
2
3
4
5
R.V.
(b)
Discount Factor
1
0.91
0.83
0.75
0.68
0.62
0.62
Net Present Value
PV–A (£m)
(200)
45.5
41.5
37.5
34.0
31.0
31.0
£ 20.5
PV–C (£m)
(250)
36.4
33.2
45.0
40.8
62.0
31.0
£ (1.6)
The company should opt for Project A since Project B should be immediately
rejected for because the net present value of B is negative. Also the ARR of 10%
is higher for Project A as compared to B and also its payback period is less than
that of B at 4 years.
Q.6.(a)
Cash
@8%
flow
1
500
.93
2
500
.86
3
500
.79
4
500
.74
5
500
.68
Total Present Value
Years
(b)
Present V
465
430
395
370
340
£ 2000
@10%
Present V
@12%
Present V
.91
.83
.75
.68
.62
455
415
375
340
310
£ 1895
.89
.80
.71
.64
.57
445
400
355
320
285
£ 1805
Cash Outflow = 1890000
Net Present Values
@8%⇒ 2000 000 – 1890 000
= £ 110 000
@10% ⇒ 1895 000 – 1890 000
= £ 5000
@12% ⇒ 1805 000 -= 1890 000
= (£ 85000)
The discount factor of 10% produces present value closest to that of cost of
equipment.
(c)
Q.7.
At the rate of 12%, the business loses its profitability as the net present value is
actually showing a loss of £ 85000. Therefore, if the expected rate is 12%, it
would be better to not invest at all but rather leave the capital in the bank where it
would at least care interest.
ARR
PROJECT X
Total profit = £ 160 000
Average annual profit =
160 000
4
= £ 40 000
www.studyguide.pk
ARR
=
40 000
×100
300 000
= 13.3%
PROJECT Y
Total profit = £ 160 000
Average annual profit =
160 000
4
= £ 40 000
ARR
40 000
=
×100
300 000
= 13.3%
PROJECT Z
Total profit = 200 000
Average annual profit =
200 000
4
= £ 50 000
ARR
50 000
=
×100
300 000
= 16.7%
The company should select project Z. since the accounting rate of return is
highest for it as compared to the other two projects. Also it is higher than the
current rate of 12%.
Q.8.
Payback Period
Years = 4
(370 – (90 ×)) = 70
10
Months =
×12
90
= 1.3
Q.9.
Period = 4 years and 1.3 months
Net Present Value
Years
0
1
2
3
4
5
6
R.V.
Cash flow (£000)
Discount actor
(370)
1
90
0.8772
90
0.7695
90
0.6750
90
0.5921
90
0.5194
90
0.4556
20
0.4556
Net Present Value
Present Value (£)
(370000)
78948
69255
60750
53289
46746
41004
9112
£ (10,896)
www.studyguide.pk
Factors to be considered
1.
Prevailing interest rate in the economy.
2.
Techniques other than that already used in the question.
3.
Economic situation of the company.
boom – risks can be taken
revision – think twice rate
4.
Legal considerations – government policies.
5.
Social Environment,
→ e.g. smuggling, making
6.
Leadership attitude
Q.10.
Net Present Value
PROJECT A
Years
0
1
2
3
4
Cash flow (£)
Discount actor
(600000)
1
250000
0.909
250000
0.8260
250000
0.7513
250000
0.6830
Net Present Value
Present Value (£)
(600000)
227275
206600
187825
170750
£ 192450
Net Present Value
PROJECT B
Years
0
1
2
3
4
5
6
Cash flow (£)
Discount actor
(1500000)
1
400000
0.9259
400000
0.8573
400000
0.7938
400000
0.7350
400000
0.6806
400000
0.6302
Net Present Value
Present Value (£)
(1500000)
370360
342920
317520
294000
272240
252080
£ 349120
Q.11.
Net Present Value
PROJECT A
Years
0
1
2
3
4
5
Cash flow (£)
(700000)
200000
200000
200000
200000
200000
Discount actor
1
0.9091
0.8264
0.7513
0.6830
0.6209
Present Value (£)
(700000)
181820
165280
150260
136600
124180
www.studyguide.pk
Net Present Value
Years
0
1
2
3
4
58140
Cash flow (£)
Discount actor
(1500000)
1
500000
0.9259
500000
0.8573
500000
0.7938
500000
0.7350
Net Present Value
Present Value (£)
(1500000)
462950
428650
396900
367500
156000
Q.12. Payback Period
(i)
PROJECT A: 3 years
and months
=
100
×12
150
=8
Period = 3 years 8 months
PROJECT B: 3 years
ARR
PROJECT A:
profit = 560 – 250
(ii)
=
310
= 51.67 (average profit)
6
= 20.7%
ARR =
51.67
×100
250
PROJECT B:
profit = 470 – 200
=
270
= 45 (average profit)
6
= 22.5%
ARR
Years
0
1
2
3
45
=
×100
200
PROJECT A
Discount
Factor
1
0.9091
0.8264
0.7513
Cash Flow
Present V
PROJECT B
Cash Flow
Present V
(250)
150
(250)
112.695
(200)
60
50
90
(200)
54.546
41.32
67.617
www.studyguide.pk
4
5
6
0.6830
0.6209
0.5645
150
160
100
102.45
99.344
120.939
90
90
NPV
61.47
55.881
131.639
Q.13. The factors that should be taken into consideration when deciding to proceed
with the investment are:
1.
The prevailing interest rate in the country. this would show whether it would be
better to leave the capital in the bank to earn interest or to invest it E.g. if the
interest rate was 10% while the ARR or the IRR earned was just 7%, then it
would have been more profitable to leave the capital in bank.
2.
The economic situation of the country. This means whether the country is in a
boom or a recession. If the country is in a boom than risks can be taken i.e.
longer investments spread over several years could be chosen. However, if the
country is going into recession then it would not be good to invest in risky
projects or equipment. E.g. the ones that generate revenue within a span of three
to five years should be selected even if they are apparently less profitable than
that of 10 years project. As in short – term projects the revenue is more
guaranteed and higher chances are there for its earning.
3.
Legal considerations also need to be taken into account. This include
government policies on different industries e.g. a firm may have a choice of
investments including a foreign project. However, if there is a policy preventing
investment in foreign project may have to be rejected despite its greater returns
and favourable terms.
4.
Social, environmental and ethical considerations. Certain projects despite their
profitablility may be unethical or socially unacceptable E.g. a project may involve
smuggling goods such as drugs approached animals and may thus be very
profitable. However, it is socially wrong. Then there
5.
Leadership attitude. If the leadership likes taking risks then it would take risky
investments and invest in projects that give higher returns but after several years.
If the leadership attitude is risk averse then the projects selected would be only
moderately profitable and generating returns in a shorter time period.
Ans.
PAYBACK METHOD
Advantages:
• Very simple and easy to calculate
• Quick screening device
• It places stress on early return, forecasts of which are likely to be more
accurate than something long – term.
• An early return is especially important when liquidity is more critical than
profitability.
Disadvantages:
• It ignores the timing of the return prior to payback.
• It ignores the earnings after payback.
• It discriminates against projects that involve a long payback period.
NET PRESENT VALUE
Advantages:
• It takes with account that interest rates affects the present value of future
income. It shows that the future cash flow is discounted by the rate of
interest.
www.studyguide.pk
•
It takes into account the length of time.
Disadvantage
• More complicated than other methods.
• Cost of capital is often difficult to ascertain.
• Complicate mathematically, but it is based on expectations.