Dec 1998 QT211: Quantitative Analysis For Management (Question 3)

A company is attempting to choose which of two three-year projects to develop. The estimated cash flows occuring at the end of each year of the projects are given below:

Year	Cash flows ($)
	Project 1	Project 2
0	(50,000)	(40,000)
1	(30,000)	10,000
2	60,000	10,000
3	40,000	32,000

(a)

Calculate the payback period of both projects using the payback method. Use your calculation to recommend which of the projects should be selected using the payback method.

[5]

Year	Cash flows ($)		Cumulative Cashflow ($)
Year	Project 1	Project 2	Project 1	Project 2
0	(50,000)	(40,000)	-50,000	-40,000
1	(30,000)	10,000	-80,000	-30,000
2	60,000	10,000	-20,000	-20,000
3	40,000	32,000	20,000	12,000
Marks			(1 mark)	(1 mark)

The payback period of project 1 is 3 + 20000/40000 = 3.5 years (1 mark).
The payback period of project 2 is 3 + 20000/42000 = 3.48 years (1 mark).
So, the payback period of project 2 is slightly less than that of project 1 and using the payback method only we would choose project 2 (1 mark).

(b)

Calculate the net present value of each project assuming a 10% cost of capital. Use your calculation to recommend which of the projects should be selected using this assumption and the NPV method.

[3]

NPV with 10% cost of capital (in 1000s).

Project 1:
NPV = -50 + (-30) x 0.909 + 60 x 0.826 + 40 x 0.751 = $2330 (1 mark)

Project 2:

NPV = -40 + 10 x 0.909 + 10 x 0.826 + 32 x 0.751 = $1382 (1 mark)

So using the NPV method with 10% cost of capital we would choose project 1 since it is more profitable. (1 mark)

(c)

Calculate the net present value of each project assuming a 12% cost of capital. Would this higher cost of capital lead you to make a different recommendation to that made in Part (b)?

[3]

NPV with 12% cost of capital (in 1000s).

Project 1:
NPV = -50 + (-30) x 0.893 + 60 x 0.797 + 40 x 0.712 = -$490 (1 mark)

Project 2:
NPV = -40 + 10 x 0.893 + 10 x 0.797 + 32 x 0.712 = -$316 (1 mark)

So using the NPV method with 12% cost of capital neither of the two projects are profitable over the first four years, so if this were the lifetime of the project we would not recommend either. (1 mark)

(d)

Calculate the internal rate of return estimated from your results in Parts (b) and (c) for both of the projects. Use your calculation which of the projects should be selected using the IRR method.

[4]

Project 1: IRR = 10 + 2 x 2330/(2330 + 490) = 11.652% (1 mark)

Project 2: IRR = 10 + 2 x 1382/(1382 + 316) = 11.628% (1 mark)

So the NPV is zero at a slightly higher rate of interest (and we therefore begin to make a profit at a slightly higher interest rate) for project 1 than for project 2 (1 mark) and we would therefore choose project 1 using the IRR method (1 mark).

(e)

Use your answers to Parts (a), (b), (c), and (d) to discuss carefully the relative merits of the three methods i.e. payback, NPV and IRR.

[5]

There are many ways in which the student might use this example to discuss the relative merits of the three methods. Marks should be awarded for the clarity of the argument and the extent to which the student has demonstrated that they understand the issues involved, with respect to this particular example. A total of 5 marks are available: a maximum of two marks should be awarded if a candidate simple lists advantages and disadvantages of the three methods.