Question

A company is considering installing a sprinkler system within its factory in order to
reduce losses to material. Two systems are being considered, the first (system A) will
cost HK$ 250,000 and the other (system B) HK$ 350,000. Each has a working life of 5
years with no residual value at the end of that time.
The projected annual savings in losses to material are:
System A System B
Year 1 80,000 90,000
Year 2 80,000 100,000
Year 3 70,000 110,000
Year 4 60,000 130,000
Year 5 60,000 130,000
The company expects projects of this type to payback in 3½ years, has a cost of capital
of 11%.
Evaluate each scheme using payback, discounted payback and net present value.
In each case advise whether or not the scheme meets the decision–making criterion
and which scheme is preferred.

Answer 1

A company is considering installing a sprinkler system within its factory in order to
reduce losses to material. Two systems are being considered, the first (system A) will
cost HK$ 250,000 and the other (system B) HK$ 350,000. Each has a working life of 5
years with no residual value at the end of that time.
The projected annual savings in losses to material are:
System A System B
Year 1 80,000 90,000
Year 2 80,000 100,000
Year 3 70,000 110,000
Year 4 60,000 130,000
Year 5 60,000 130,000
The company expects projects of this type to payback in 3½ years, has a cost of capital of 11%.
Evaluate each scheme using payback, discounted payback and net present value. In each case advise whether or not the scheme meets the decision–making criterion and which scheme is preferred.

.

System A

.

Payback period

Years	0	1	2	3	4	5
Cash flow	-250000	80000	80000	70000	60000	60000
Cumulative cash flow	-250000	-170000	-90000	-20000	40000	100000

Here take full 3 years and a portion of 4^th year

portion of 4^th year = 20000 / 60000 = 0.3333 year

Payback period = 3.33 years

.

Discounted payback

Years	0	1	2	3	4	5
Cash flow	-250000	80000	80000	70000	60000	60000
PVIF,11%	1	0.9009	0.811622	0.73119	0.65873	0.59345
PV of cash flow	-250000.00	72072.00	64929.76	51183.30	39523.80	35607.00
Cumulative cash flow	-250000	-177928	-112998.24	-61814.94	-22291.14	13315.86

Here take full 4 years and a portion of 5^th year

portion of 5^th year = 22291.14 / 35607 = 0.63 year

Discounted Payback period = 4.63 years

.

Net Present Value (NPV)

NPV = PV of cash flow - initial investment

PV of cash flow =

72072.00

64929.76

51183.30

39523.80

35607.00

=

263315.86

initial investment = 250000

.

NPV = 263315.86 - 250000 = 13315.86

.

System B

Years	0	1	2	3	4	5
Cash flow	-350000	90000	100000	110000	130000	130000
Cumulative cash flow	-350000	-260000	-160000	-50000	80000	210000

Here take full 3 years and a portion of 4^th year

portion of 4^th year = 50000 / 130000 = 0.38 year

Payback period = 3.38 years

.

Discounted payback

Years	0	1	2	3	4	5
Cash flow	-350000	90000	100000	110000	130000	130000
PVIF,11%	1	0.9009	0.811622	0.73119	0.65873	0.59345
PV of cash flow	-350000.00	81081.00	81162.20	80430.90	85634.90	77148.50
Cumulative cash flow	-350000	-268919.00	-187756.80	-107325.90	-21691.00	55457.50

Here take full 4 years and a portion of 5^th year

portion of 5^th year = 21691.00 / 77148.50 = 0.28 year

Discounted Payback period = 4.28 years

.

Net Present Value (NPV)

NPV = PV of cash flow - initial investment

PV of cash flow =

81081.00

81162.20

80430.90

85634.90

77148.50

=

405457.50

initial investment = 350000

.

NPV = 263315.86 - 350000 = 55457.50

.

.

*In each case advise whether or not the scheme meets the decision–making criterion and which scheme is preferred.

.

*We assume that it is mutually exclusive, so selection of one project be consider other not select.

.

Based on Payback period

.

The company expects projects of this type to payback in 3½ years.

And both are with in this criteria.

>So consider short length, which is System A, payback period of 3.33 years.

.

>Based on Discounted payback period. Both are not acceptable, because each payback period is beyond the condition.

.

Based on NPV

>we consider it is mutually exclusive project, so Project with highest NPV should be selected.

Which is system B with NPV of 55457.50