Question

Problem # 2

Each of two mutually exclusive projects involves an investment of $ 75,000.  

The cash flows for the projects are as follows:

                                         Year              Project “A”                  Project "B"

                                            1                      29,000                        42,000

                                            2                      29,000                        42,000

                                            3                      29,000                        42,000

                                            4                      29,000

               Note: Project "A" covers 4 years and project "B" covers 3 years.                              

                 

        A.   Calculate each project's payback period.          1 point        

                    B.   Compute the IRR of each project. 1 Point

Answer 1

A. Payback Period = ( Last Year with a Negative Cash Flow ) + [( Absolute Value of negative Cash Flow in that year)/ Total Cash Flow in the following year)]

Project A :

Payback Period = 1 +( 33000 / 42000)

= 1.79 years

Hence, the correct answer is 1.79 years

Project B :

Payback Period = 2 +( 17000/ 29000)

= 2.59 years

Hence, the correct answer is 2.59 years

B.

Project A

Let the IRR be x.

Now , Present Value of Cash Outflows=Present Value of Cash Inflows

75,000 =29000/(1.0x) +29000/ (1.0x)^2 +29000/(1.0x)^3+ 29000/(1.0x)^4      

Or x= 20.052%

Hence the IRR is 20.052%

Project B

Let the IRR be x.

Now , Present Value of Cash Outflows=Present Value of Cash Inflows

75,000 =42000/(1.0x) +42000/ (1.0x)^2 +42000/(1.0x)^3   

Or x= 31.209%

Hence the IRR is 31.209%

Note:

1. Payback Period

Project A:

Year	Investment	Cash Inflow	Net Cash Flow
0	-75,000.00	-	-75,000.00	(Investment + Cash Inflow)
1	-	29,000.00	-46,000.00	(Net Cash Flow + Cash Inflow)
2	-	29,000.00	-17,000.00	(Net Cash Flow + Cash Inflow)
3	-	29,000.00	12,000.00	(Net Cash Flow + Cash Inflow)
4	-	29,000.00	41,000.00	(Net Cash Flow + Cash Inflow)

Project B:

Year	Investment	Cash Inflow	Net Cash Flow
0	-75,000.00	-	-75,000.00	(Investment + Cash Inflow)
1	-	42,000.00	-33,000.00	(Net Cash Flow + Cash Inflow)
2	-	42,000.00	9,000.00	(Net Cash Flow + Cash Inflow)
3	-	42,000.00	51,000.00	(Net Cash Flow + Cash Inflow)