Question

The management team of U. Dunnit Limited have four projects for consideration. In the past, they have evaluated projects against simple payback. The following information is available:

   Project A Project B Project C Project D

   £ £ £ £

Capital outlay 65,000 140,000 30,000 160,000 respectively to the years

Net cash inflows:

Year 1 30,000 45,000 20,000 35,000

Year 2 20,000 45,000 10,000 35,000

Year 3 15,000 45,000 10,000 55,000

Year 4 10,000 45,000 55,000

Year 5 10,000 45,000 65,000

REQUIRED

Evaluate the projects using each of the following methods:

(a) Payback.

(b) Accounting rate of return using full capital outlay (investment).

(c) Net present value and profitability index. Assuming a cost of capital of 6%.

Answer 1

1)

project A

Project A
Year	Cash flow stream	Cumulative cash flow
0	-65000	-65000
1	30000	-35000
2	20000	-15000
3	15000	0
4	10000	10000
5	10000	20000

Payback period is the time by which undiscounted cashflow cover the intial investment outlay

this is happening at end of year 3

therefore pay back period is 3

Accounting rate of return = cash inflow/intial investment

= (30000+20000+15000+10000+10000)/65000 =130.769%

Discount rate	6.000%
Year	0	1	2	3	4	5
Cash flow stream	-65000	30000	20000	15000	10000	10000
Discounting factor	1.000	1.060	1.124	1.191	1.262	1.338
Discounted cash flows project	-65000.000	28301.887	17799.929	12594.289	7920.937	7472.582
NPV = Sum of discounted cash flows
NPV Project A =	9089.62
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
PI= (NPV+initial inv.)/initial inv.
=(9089.62+65000)/65000
1.14

Project B
Year	Cash flow stream	Cumulative cash flow
0	-140000	-140000
1	45000	-95000
2	45000	-50000
3	45000	-5000
4	45000	40000
5	45000	85000

Payback period is the time by which undiscounted cashflow cover the intial investment outlay

this is happening between year 3 and 4

therefore by interpolation payback period = 3 + (0-(-5000))/(40000-(-5000))

3.11 Years

Accounting rate of return = cash inflow/intial investment

= (45000+45000+45000+45000+45000)/140000=160.71%

Discount rate	6.000%
Year	0	1	2	3	4	5
Cash flow stream	-140000	45000	45000	45000	45000	45000
Discounting factor	1.000	1.060	1.124	1.191	1.262	1.338
Discounted cash flows project	-140000.000	42452.830	40049.840	37782.868	35644.215	33626.618
NPV = Sum of discounted cash flows
NPV Project B =	49556.37
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
PI= (NPV+initial inv.)/initial inv.
=(49556.37+140000)/140000
1.35

Project C
Year	Cash flow stream	Cumulative cash flow
0	-30000	-30000
1	20000	-10000
2	10000	0
3	10000	10000
4	55000	65000
5	65000	130000

Payback period is the time by which undiscounted cashflow cover the intial investment outlay

this is happening at end of year

therefore pay back period is 2

Accounting rate of return = cash inflow/intial investment

= (20000+10000+10000+55000+65000)/30000=533.33%

Discount rate	6.000%
Year	0	1	2	3	4	5
Cash flow stream	-30000	20000	10000	10000	55000	65000
Discounting factor	1.000	1.060	1.124	1.191	1.262	1.338
Discounted cash flows project	-30000.000	18867.925	8899.964	8396.193	43565.151	48571.781
NPV = Sum of discounted cash flows
NPV Project C =	98301.01
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
PI= (NPV+initial inv.)/initial inv.
=(98301.01+30000)/30000
4.28

Project D
Year	Cash flow stream	Cumulative cash flow
0	-160000	-160000
1	35000	-125000
2	35000	-90000
3	55000	-35000

cumulative cash flow is not turning positive in any period so payback cannot be calculated

Accounting rate of return = cash inflow/intial investment

= (35000+35000+55000)/160000=78.125%

Discount rate	6.000%
Year	0	1	2	3
Cash flow stream	-160000	35000	35000	55000
Discounting factor	1.000	1.060	1.124	1.191
Discounted cash flows project	-160000.000	33018.868	31149.875	46179.061
NPV = Sum of discounted cash flows
NPV Project D =	-49652.20
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
PI= (NPV+initial inv.)/initial inv.
=(-49652.2+160000)/160000
0.69