Question

"A manufacturing firm is considering two mutually exclusive alternatives given below. The net cash flows in dollars for years 0 through 2 for Project A is:
-4,200
2,500
2,100
The net cash flow in dollars for years 0 through 2 for Project B is:
-7,400
4,900
5,700
Determine which project is a better choice if MARR = 11%. Enter the IRR as a percentage between 0 and 100 for the project that is a better choice. If neither project should be chosen, enter 0."

Answer 1

For project A:

Let, IRR = K

Then,

4200 = 2500/(1+K) + 2100/(1+K)^2

At K = 6%

P.V. of cash inflows = $4227.48

At K = 7%

P.V. of cash inflows = $4170.67

With the method of interpolation,

K = 6% + ((PV of cash inflows at 6% - 4200)/( PV of cash inflows at 6%- PV of cash inflows at 7%))*(7%-6%)

K = 6% + ((4227.48-4200)/( 4227.48-4170.67))*(7%-6%)

K = 6.48%

For project B:

Let, IRR = R

Then,

7400 = 4900/(1+R) + 5700/(1+R)^2

At R = 27%

P.V. of cash inflows = $7392.27

At R = 26%

P.V. of cash inflows = $7479.21

As per the method of interpolation,

R = 26% + ((7479.21-7400)/( 7479.21-7392.27))*(27%-26%)

R = 26.91%

Since, IRR of project B is 26.91% and it is higher than the IRR of project A as well as higher than the MARR of 11%. So, Project B will be selected.

So, IRR of project B = 26.91 (%)