Question

Your company has tasked you with the evaluation of two projects for investments, Project X and Project Y. Each project has a cost of capital of R10,000 and the required return of 12 percent.
The projects’ expected cash flows (in Rands) are listed below:

Year	Project X	Project Y
0	(10,000.00)	(10,000.00)
1	6,500.00	4,000.00
2	3,000.00	4,000.00
3	3,000.00	4,000.00
4	2,000.00	4,000.00

Required:
11.1. Calculate each project’s payback period, net present value (NPV and profitability index (PI).
11.2. Which project should be accepted if they are independent?
11.3. Which project should be accepted if they are mutually exclusive?

Answer 1

11.1

Project X
Year	Cash flow stream
0	-10000
1	6500
2	3000
3	3000
4	2000

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

this is happening between year 2 and 3

therefore by interpolation payback period = 2 + (0-(-500))/(2500-(-500))

2.17 Years

Project X
Discount rate	12.000%
Year	0	1	2	3	4
Cash flow stream	-10000	6500	3000	3000	2000
Discounting factor	1.000	1.120	1.254	1.405	1.574
Discounted cash flows project	-10000.000	5803.571	2391.582	2135.341	1271.036
NPV = Sum of discounted cash flows
NPV Project X =	1601.53
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
PI= (NPV+initial inv.)/initial inv.
=(1601.53+10000)/10000
1.16

Project Y
Year	Cash flow stream	Cumulative cash flow
0	-10000	-10000
1	4000	-6000
2	4000	-2000
3	4000	2000
4	4000	6000

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

this is happening between year 2 and 3

therefore by interpolation payback period = 2 + (0-(-2000))/(2000-(-2000))

2.5 Years

Project Y
Discount rate	12.000%
Year	0	1	2	3	4
Cash flow stream	-10000	4000	4000	4000	4000
Discounting factor	1.000	1.120	1.254	1.405	1.574
Discounted cash flows project	-10000.000	3571.429	3188.776	2847.121	2542.072
NPV = Sum of discounted cash flows
NPV Project Y =	2149.40
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
PI= (NPV+initial inv.)/initial inv.
=(2149.4+10000)/10000
1.21

11.2

Both project X and Y have positive NPV and can be selected

11.3

Project Y has higher NPV and should be selected