Question

You are considering two mutually exclusive projects, A and B.

Project A costs $70,000 and generates cash flows of $10,000 for 10 years.

Project B costs $80,000 and generates cash flows of $2,000 for six years and then cash flows of $28,000 for four years.

Report rates in percentage form to two decimal places i.e. 10.03% not 10%

At what discount rate would make you indifferent between choosing one project or another?
What is the highest discount rate in which you can still produce a non-negative NPV for at least one project?

Answer 1

For you to be indifferent between the two projects, their Net Present Value (NPV) must be equal. To the discount rate where the NPV of both projects are equal, we calculate the Internal Rate of Return (IRR) of cash flows of Project A subtracted from Project B (i.e. B-A)

Year	Cash Flows
	Project A	Project B	B-A
0	-70,000	-80,000	-10,000
1	10,000	2,000	-8,000
2	10,000	2,000	-8,000
3	10,000	2,000	-8,000
4	10,000	2,000	-8,000
5	10,000	2,000	-8,000
6	10,000	2,000	-8,000
7	10,000	28,000	18,000
8	10,000	28,000	18,000
9	10,000	28,000	18,000
10	10,000	28,000	18,000

The IRR of these Cash flows of B-A is 3.8948%. At this discount rate, you will be indifferent between the two projects.

To calculate the highest discount rate where atleast one project produces a non-negative NPV, we will find the IRR for both Project A and Project B.

IRR (for Project A) = 7.07%

IRR (for Project B) = 5.6964%

Therefore, the highest discount rate is 5.6964%. Below this discount rate, the NPV of Project B will be negative.