Can someone please show me how to linear interpolate with the given problem. I\'

Question

Can someone please show me how to linear interpolate with the given problem. I'll just fuss real quick, Every time the instructor or a text material shows the steps, it always ends up saying, use trial and error, or just interpolate; Cool, but they never actually follow through with the interpolation procedure. Im the kinda dummy who needs to see it over and over again. here we are:

A powertool for plastic costs 400, w/4 year UL, no SV, and a 2 yr, pay back period. . Assume uniform EoY benefits.

Question: compute the after tax rate of return, based on MACRS depreciation, and 34% combined coporate ITR.

I have already tabulized everything above. to make is easy for you.

After tax ROR= -400+177.33(p/f,i,1)+192.5(p/f,i,2)+152.14(p/f,i,3)+142.1(p/f,i,4)

So with the ^above^ prob, how should I go about linearly interpolating it? Thanks.

yr btcf macrs dep TI IT atcf 0 -400 - - - -400 1 200 133.3 66.8 -22.6 177 2 200 177.8 22.2 -7.548 192 3 200 59.240 140.78 -47.858 152 4 200 29.640 170 -57.922 142

Explanation / Answer

For Calculation of IRR or actual Rate of Return we have to use trail and error method to find Rate of Return.

For this purpose we have to take two discount rate and calculate NPV so as one NPV is positive and other is negative.

Actual Rate of Return (IRR) =Lower Rate+ (NPV at LR/(NPV at LR-NPV at HR))* Difference in rate

20% +(320.41/326.33)*45 = 64.18%

Year ATCF Depreciation FCF 0 -$400.00 -$400.00 1 $177.00 $133.30 $310.30 2 $192.00 $177.80 $369.80 3 $152.00 $59.24 $211.24 4 $142.00 $29.64 $171.64

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