Question

Use Both the Replacement Chain Method and the Equivalent Annual Annuity Method to decide which projects are the best:

Bob the builder is deciding between two mutually exclusive projects. The first project is 3 years long with an initial cash outflow of $13000 and expected annual inflows of $5000. The second project is 6 years long with an initial cash outflow of $15000 and annual cash inflows of $3500. The cost of capital is 10%.

Answer 1

A) In the first case, using Replacement Chain method, we need to repeat the project with the lower time scale in order to bring it similar to that of the project with larger time scale. In this case, the first project has to be repeated to twice. Thus the Cash flows and the NPV of the projects is as given below

Project A:

Year	0	1	2	3	4	5	6
CF	-13000	5000	5000	-8000	5000	5000	5000
Discount rate	1	0.909091	0.826446	0.751315	0.683013	0.6209213	0.564474
DCF	-13000	4545.455	4132.231	-6010.52	3415.067	3104.6066	2822.37
NPV	-990.789

Project B:

Year	0	1	2	3	4	5	6
CF	-15000	3000	3000	3000	3000	3000	3000
Discount rate	1	0.909091	0.826446	0.751315	0.683013	0.6209213	0.564474
DCF	-15000	2727.273	2479.339	2253.944	2049.04	1862.764	1693.422
NPV	-1934.22

From the above NPVs, we can deduce that both the projects are loss making and we should not choose either of them. However, for comparison, Project A is better than Project B.

B) Using Equivalent Annual Annuity Method:

The formulae for calculating the Annual Annuity is

Equivalent Annuity cash flow = (Cost of capital x NPV) / (1 - (1 + Cost of capital)-t )

For Project A, Annuity cash flow = (0.1 x -990)/(1-(1+0.1)^-3) = -398.411

For Project B, Annuity cash flow = (0.1 x -1934.22)/(1-(1+0.1)^-6) = -444.111

Therefore, both the projects should be avoided. However, Project A is comparitively better than Project B.