Internal Rate of Return IRR
Trying to find the interest rate i* for which Net Present Worth NPW = 0.
We know that the rate is between 7% and 8%.
i | (NPW) |
---|---|
7 | 891.0 |
i* | 0 |
8 | -272.8 |
Using interpolation to find the actual value, we get the interpolation equation:
(891.0 - 0.0) / (i* - 7)
= {891.0 - (-272.8)} / (8-7)
From this, we get i* = 7.76%
Please explain this for me, how it arrives at 7.76?
My algebra is not good. All I come up with is 1163.80 / (-1163.80) = -1
At i = 7 %, NPW = 891
At i = 8%, NPW = -272.8
Using interpolation, (simple representation)
i = 7 + [(891-0)/(891-(-272.8)]*(8-7)
= 7 + [891/(891+272.8)]*1
= 7 + 891/1163.8
= 7 + 0.765595
= 7.76%
Equation given in question will reduece to the value given above,
Solving equation given in ques
(891.0 - 0.0) / (i - 7) = {891.0 - (-272.8)} / (8-7)
891 / (i - 7) = {891.0 + 272.8)} / (8-7)
891 / (i - 7) = 1163.8 / 1
891 / (i - 7) = 1163.8
(i - 7) = 891/1163.8
(i - 7) = 0.765595
i = 7+0.765595
i = 7.76%
Pls comment if you require further explanation
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