Question

4. You are informed that the effective annual required rate of return is 10%. Cash flows for the projects are indicated in the table below (in thousands of dollars):

   Year 0 1 2 3

   1. A -1,800 600 1,00 1,200

   2. B 12,000 -600   -10,800 -5,000

   For the following problems, show all your work (i.e. express al formulas used with values in place of variables).

   a) Consider Project A and Project B independent projects. Calculate the internal rate of return (IRR) for Project A. Calculate the IRR for the Project B. According to your calculations and the IRR decision criterion, would you recommend Project A, Project B or both?
   

   b) Consider Project A and Project B mutually exclusive projects. Calculate the PI for the incremental Project A over B. Using the PI decision criterion, what would you recommend?

Answer 1

A. Calculation of IRR

IRR refers to the rate of return which is internal to a given project for discounting Cash inflows accuring from a given project in such a way that the time value of cash inflows at the internal rate of return will be equal to the initial investment. You can think of the internal rate of return as the rate of growth a project is expected to generate..

Project A

Total initial outflow = 1800

Total inflows = 3700

Present value factor = (Initial investment / Average annual cash inflows)

Project A   = (1800/3700) = 0.486

IRR = 46.9 % (Using present value annuity factor Table)

Project B

Irrespective of Project A , Project B has initial cash inflow

Total initial cash inflow = 12000

Total cash outflow = 16400

IRR would be calculated as

=> (Total cash outflow / Initial inflow) = (1+IRR)³

(16400/12000) = (1+IRR)³ =>

= 1+IRR

IRR = 10.9%

B. Calculation PI, Through using 10% as discounting rate

Particulars	Project A		Project B
Amount (A)	PVF (B)	Total Amount (A*B)	Amount (A)	PVF (B)	Total Amount (A*B)
Cash flow Year 0	1800	1	1800	-12000	1	12000
Cash flow year 1	600	0.909	545.4	- 600	0.909	-545.4
Cash flow year 2	100	0.826	82.6	-10800	0.826	-8920.8
Cash flow year 3	1200	0.7513	901.5	- 5000	0.7513	-3756
Total Cash flows of 3 years			1529.5			13222.2

PI = PV of Cash inflows / PV of Cash ouflows

Prjoect A = 1529/1800 = 85%

Project B = 12000/13222.2= 90%

Project B is better than Project A.

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We were unable to transcribe this image

V1/0.486

1.36