Question

Question A [AR1: 5 Marks]

Consider the projects described in the table below:

End of Year	Project A Cash Flow ($)	Project B Cash Flow ($)
0	$–90,000	$–90,000
1	17,000	0
2	17,000	0
3	17,000	0
4	17,000	0
5	17,000	0
6	17,000	34,000
7	17,000	34,000
8	17,000	34,000
9	17,000	34,000
10	17,000	90,000

Both projects have an appropriate risk adjusted discount rate of 7 percent.

Required:

a.	Calculate the NPV and IRR for both projects
b.	If projects A and B are independent, which will you undertake?
c.	If projects A and B are mutually exclusive, which will you undertake?

Answer 1

a

Project A
Discount rate	7.000%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-90000	17000	17000	17000	17000	17000	17000	17000	17000	17000	17000
Discounting factor	1.000	1.070	1.145	1.225	1.311	1.403	1.501	1.606	1.718	1.838	1.967
Discounted cash flows project	-90000.000	15887.850	14848.458	13877.064	12969.219	12120.765	11327.818	10586.746	9894.155	9246.874	8641.938
NPV = Sum of discounted cash flows
NPV Project A =	29400.89
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project A
IRR is the rate at which NPV =0
IRR	13.62%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-90000.000	17000.000	17000.000	17000.000	17000.000	17000.000	17000.000	17000.000	17000.000	17000.000	17000.000
Discounting factor	1.000	1.136	1.291	1.467	1.667	1.894	2.152	2.445	2.778	3.156	3.586
Discounted cash flows project	-90000.000	14961.974	13168.275	11589.612	10200.204	8977.364	7901.123	6953.906	6120.245	5386.526	4740.769
NPV = Sum of discounted cash flows
NPV Project A =	-0.001
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	13.62%

Project B
Discount rate	7.000%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-90000	0	0	0	0	0	34000	34000	34000	34000	90000
Discounting factor	1.000	1.070	1.145	1.225	1.311	1.403	1.501	1.606	1.718	1.838	1.967
Discounted cash flows project	-90000.000	0.000	0.000	0.000	0.000	0.000	22655.636	21173.491	19788.310	18493.747	45751.436
NPV = Sum of discounted cash flows
NPV Project B =	37862.62
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project B
IRR is the rate at which NPV =0
IRR	11.63%
Year	0	1	2	3	4	5	6	7	8	9	10
Cash flow stream	-90000.000	0.000	0.000	0.000	0.000	0.000	34000.000	34000.000	34000.000	34000.000	90000.000
Discounting factor	1.000	1.116	1.246	1.391	1.553	1.733	1.935	2.160	2.411	2.692	3.005
Discounted cash flows project	-90000.000	0.000	0.000	0.000	0.000	0.000	17571.522	15740.957	14101.096	12632.072	29954.353
NPV = Sum of discounted cash flows
NPV Project B =	0.000
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	11.63%

B

Select both as NPV is positive for both

C

Select project B as it has higher NPV