Question

How do you isolate for i* with (P/A,i*,12) since the equation for this is very long [((1+i)^6-1)/(i(1+i)^6)]

Machine X PW (Cash outflows) = PW (Cash inflows) 200 = 75 (P/A, 1*,6)+ 50 (P/F,i*,6). Solving: i* = 31.9% Project Parameters Machine X Machine Y First Cost ($) 200 400 75 120 Net annual cash inflow (AOR - AOC) Salvage Value (SV) 50 150 Machine Y PW (Cash outflows) = PW (Cash inflows) 400 = 120(P/A,1*,12) + 150 (P/F,i*,12) Solving: i* = 29.1%. Life (years) 12 MARR = 10% Decision: Machines X and Y are acceptable.

is there an easier equation for (P/A, i*, 12)?

Answer 1

We use the interpolation technique to solve for i%.

Solving for Machine X with interpolation technique

200 = 75*(P/A, i%,6) + 50 * (P/F, i%,6)

Dividing whole equation by 25

8 = 3*(P/A, i%,6) + 2 * (P/F, i%,6)

Using trail and error method

When i = 30%, value of 3*(P/A, i%,6) + 2 * (P/F, i%,6) = 3 * 2.642746 + 2 * 0.207176 = 8.342590

When i = 31%, value of 3*(P/A, i%,6) + 2 * (P/F, i%,6) = 3 * 2.587527 + 2 * 0.197866 = 8.158315

When i = 32%, value of 3*(P/A, i%,6) + 2 * (P/F, i%,6) = 3 * 2.534246 + 2 * 0.189041 = 7.980821

using interpolation

i = 31% + (8.158315 - 8) / (8.158315 - 7.980821) *(32%-31%)

i = 31% + 0.891%

i = 31.9%

Same value as given above in your solution

Same way we can solve for machine Y too.

Pls comment if you require further explationation