Question

Home Ltd. has the option of investing in the following two projects of equal risk; they are mutually exclusive alternatives for expanding the firm’s capacity. The firm’s cost of capital is 12%. The cash flows for each project are given in the following table. PROJECT A PROJECT B Initial investment 545,000 300,000 Year Net cash inflows Net cash inflows 1 135,000 200,000 2 185,000 120,000 3 220,000 92,000 4 280,000 Home Ltd. has incurred a research and development expenditure of $35,000 initially for project A and $25,000 for project B, both of which are considered sunk costs for the business. Due to seasonal demand, business believes for project A only, they will have to incur additional electricity charge of $1,000 each year till year 4. At the end of year 4, the business believes that they could sell project A for $60,000 and at the end of year 3, project B for $50,000. The finance manager has also suggested that any investment that takes more than 4 years to pay back the initial investment should be rejected.

1)Calculate the net present value for each project.  Using the net present value criterion, which project is preferable and why? Show workings   

2) Calculate the payback period of each project. Using the payback period criterion which project is preferable and why? Show workings

3) Calculate the profitability index for each project.  Using the profitability index criterion which project is acceptable and why? Show workings

4) Calculate equivalent annual value for each project. Using the equivalent annual value method which project is acceptable and why? Show workings   

Answer 1

Solution (1)

Year	DF @ 12%	Project A	Project B
Cash Flows	Present Value of Cash Flows	Cash Flows	Present Value of Cash Flows
1	0.893	$ 134,000.00	$       119,642.86	$ 200,000.00	$       178,571.43
2	0.797	$ 184,000.00	$       146,683.67	$ 120,000.00	$         95,663.27
3	0.712	$ 219,000.00	$       155,879.87	$ 142,000.00	$       101,072.80
4	0.636	$ 339,000.00	$       215,440.63	$                   -	$                         -
Present Value of Cash Inflows		$ 876,000.00	$       637,647.03	$ 462,000.00	$       375,307.49
Less: Initial Cash Outflow			$       580,000.00		$       325,000.00
Net Present Value			$         57,647.03		$         50,307.49

By comparing above Calculation, NPV of Project A is more that Project B, Hence Project A should be accepted

Solution (2)

Year	Project A	Project B
Cash Flows	Cumulative Cash Flows	Cash Flows	Cumulative Cash Flows
1	$ 134,000.00	$ 134,000.00	$                200,000.00	$       200,000.00
2	$ 184,000.00	$ 318,000.00	$                120,000.00	$       320,000.00
3	$ 219,000.00	$ 537,000.00	$                142,000.00	$       462,000.00
4	$ 339,000.00	$ 876,000.00	$                                  -	$       462,000.00

Payback Period =	Year before Full Recovery	+	Unrecovered Cost at the start of the year
cash flow during the year

Payback Period of Project A = 3 + ($ 580,000-$ 537,000)/$ 339,000

= 3.13 Years

Payback Period of Project B = 2 + ($ 325,000-$ 320,000)/ $ 142,000

= 2.04 Years

Decision on the basis of Payback Period = Project B has less payback period hence Project B should be selected

Solution (3)

Profitability Index	=	Discounted Cash Inflows
Initial Cash Outflows

PI of Project A = $ 637,647.03 / $ 580,000

= 1.10

PI of Project B = $ 375,307.49 / $ 325,000

= 1.15

Decision on the basis of Profitability Index = PI of Project B is better than Project A, Hence Project B should be selected

Solution (4)

Equivalent Annual Value	=	Net Present Value
Annuity for the duration of the project

EAV of Project A = $ 57,647.03 / 3.037

= $ 18,979.39

EAV of Project B = $ 50,507.49 / 2.402

= $ 20,945.47

Decision on the basis of EAV = Project B has better EAV than Project A, Hence Project B should be selected