Question

1. Table A gives investments, NPVs, IRRs and the first three years’ cash flow for several capital investment projects. Each project’s cash flows continue for several more years, longer for some projects than others. The cost of capital is 12% for all projects.

Table A (figures in millions).

Project	Invest in 2000	C1	C2	C3	NPV	IRR
A	100	20	20	20	57	17.8
B	200	0	20	40	64	14.5
C	50	20	20	20	41	37.8
D	75	-10	10	30	0	12
E	30	-10	5	7	-3	11
F	10	3	4	5	5.5	30.2

Projects A and B are mutually exclusive - your firm can take only one. The projects are discrete - you cannot make partial investments in any project.

1. Which project would you choose, A or B?
2. Suppose that the firm now identifies a new project AA with exactly the same cash flows, NPV and IRR as project A. Does the opportunity to invest in AA change your answer to part c?
3. Suppose the firm has only $200 million to invest - a fixed capital constraint. Which projects would you undertake? (Ignore project AA.)
4. Now the firm negotiates a line of credit that allows it to borrow up to $100 million at 8%. Would access to additional debt capital at a cost of 8% change your answers to questions c, d or e?

Answer 1

Solution to a

Project A has NPV of 57, Project B has 64 which is a greater NPV whereas project A has a greater IRR of 17.8% against project B's 14.5%. Based on NPV, it appears that Project B should be chosen since its NPV is higher, but if we have $200 to invest (assuming that we have sufficient funds to invest in either of project A or B which would be $200), we should choose project A over B for 2 possible reasons:

1. It gives a higher IRR of 17.8% meaning an investment of $100 gives a return of 17.8% over the project's life and

2. The remaining $100 can also be invested into project A to scale up project A 2 times and get the same return of 17.8% assuming that the conditions don't change for any investment over $100 in project A and all cash flows are variable and not one time or the remaining $100 may be invested in any discrete combinaion of projects selected from project C to project F that gives a combined IRR of over 14.5%. It can be easily seen what these combinations could be but since that is not the point of this question part, it is dealt with in part c.

Hence, we would always choose Project A over B.

Solution to b

If a new project AA is identified which is identical to project A, investment of $100 in it would generate IRR of 17.8%. Overall IRR on both A and AA would be 17.8%. We would not invest $100 in AA since there are opportunities to generate higher combined IRR (over 17.8%) by investing $100 in a combination of projects from project C to project F.

Solution to c

If the firm has only $200 million to invest - a fixed capital constraint, the combination of projects from C to F would have to generate a combined IRR of over 17.8% to be selected.

Here we can make 2 assumptions and the combinations we would select would differ based on the assumptions that hold good.

Assumption 1: Each project from C to F can be undertaken only once and we cannot replicate or scale up that project by overinvesting than minimum mentioned investment limit since either it would not result in same cash flows or each project just can't be replicated once undertaken.

In this case the only possible selection we can make with $100 would be:

Projects C, E, F and $10 remains uninvested (giving 0% IRR). Investments would be 50, 30, 10 and uninvested 10 respectively. The combined average IRR would be (summation of the products of investment weights and IRR) { [ (50/100) x 37.8] + [ (30/100) x 11 ] + [ (10/100) x 30.2 ] + [ (10/100) x 0 ] } = 25.22%

Assumption 2: Each project from C to F can be undertaken more than once and we can replicate or scale up that project once we choose it by overinvesting than the minimum mentioned investment limit in discrete muliples assuming it would result in same cash flows or each project can be replicated once undertaken.

In this case, possible selections we can make with $100 are:

Projects C, E and F (project F scaled up to 2 times; lets denote this scale up as 2x) - Investments would be 50, 30 and 20 respectively. The combined average IRR would be (summation of the products of investment weights and IRR) { [ (50/100) x 37.8] + [ (30/100) x 11 ] + [ (20/100) x 30.2 ] } = 28.24%

Project C scaled up 2x - Investment of $100. Average IRR would be 37.8%

Projects E and F in the following scales:

Project E (3x), F (1x) Investments would be 90 and 10 respectively. Combined average IRR would be { [ (90/100) x 11] + [ (10/100) x 30.2 ] } = 12.92%

Project E (2x), F (4x) Investments would be 60 and 40 respectively. Combined average IRR would be { [ (60/100) x 11] + [ (40/100) x 30.2 ] } = 18.68%

Project E (1x), F (7x) Investments would be 30 and 70 respectively. Combined average IRR would be { [ (30/100) x 11] + [ (70/100) x 30.2 ] } = 24.44%

Project F (10x) Investments of $100. Combined average IRR would be 30.2%

Project D (1x), F (2x) and $5 would be uninvested residual funds in hand. Investments would be 75 and 20 respectively. Combined average IRR would be { [ (75/100) x 12] + [ (20/100) x 30.2 ] + [ (5/100) x 0 ] } = 15.04%

If assumption 1 holds good, we should select projects C, E and F and the combined IRR of these projects would be 25.22% or if assumption 2 holds good, we should select only project C and replicate it 2 times to get an IRR of 37.8% or if only project F could be replicated 2 times the next best alternative would be C, E and F with IRR of 28.24%.

Solution to d

Since the cost of capital is 12% for all projects, any combination of projects should generate a combined IRR of over 12% to be profitable.

We see that in a) project A has IRR of 17.8% (greater than 12%) hence we selected it; in part b) projects A and AA have combined IRR of 17.8% (greater than 12%) hence we selected them; in part c) all the combinations that we should possibly select along with project A give a combined IRR greater than 12%.

If $100 has a cost of capital of 12% and the line of credit that allows it to borrow up to $100 million has a cost of 8%, the average cost of capital assuming no taxes is 0.5 x 12% + 0.5 x 8% = 10%. Since this is below 12% and all our combinations are over 12%, the line of credit that allows it to borrow up to $100 million has no impact on the answers given in parts a, b and c.