This is the second part of Tutorial: Basic Internal Rate of Return,IRR, Calculation and Explanation. Now, let's see the third example.
Example 3:
Question: Return at the end of period is $455,996.00, Annual saving is $6000.00, Period is 30 years, initial saving is $6000.00 as well.
Solution:
1. First of all, let's see the cash flow below:
Year 0: Initial Saving = PW = $6000.00
Year 1: Annual Saving = AW (Annual Worth) = $6000.00
Year 2: Annual Saving = AW = $6000.00
:
:
:
Year 29: Annual Saving = AW = $6000.00
Year 30: Maturity = FW = $455,996.00
2. After understand this cash flow, the equation represents this cash flow is:
Saving = Return
PW + AW (P|A, IRR, 29) = FW ( P|F, IRR , 30)
3. In this complicated case, we can only use second method which is mentioned at Tutorial: Basic Internal Rate of Return,IRR, Calculation and Explanation, that is, the trial and error plus linear interpolation approach.
$6000.00 + $6000.00*(P|A, IRR, 29) = $455,996.00*(P|F, IRR, 30)
4. Since the equation of (P|A, IRR, N) = ((1 + IRR)^N - 1) / ( IRR*(1 + IRR)^N), then
(P|A, IRR, 29) = ((1 + IRR)^29 - 1) / ( IRR*(1 + IRR)^29)
5. Divide the equation $6000.00 + $6000.00*(P|A, IRR, 29) = $455,996.00*(P|F, IRR, 30) by $455,996.00, so
0.013158 + 0.013158*(P|A, IRR, 29) = (P|F, IRR, 30)
6. Rearrange, again.
0.013158 = (P|F, IRR, 30) - 0.013158*(P|A, IRR, 29)
7. Using previous equations to get the follow value:
(P|F, 4%, 30) = 0.3083
(P|F, 5%, 30) = 0.2314
(P|F, 6%, 30) = 0.1741
(P|A, 4%, 29) = 16.9837
(P|A, 5%, 29) = 15.1411
(P|A, 6%, 29) = 13.5907
(P|F, 4%, 30) - 0.013158*(P|A, 4%, 29) = 0.0848
8. Obviously, the IRR is between 5% and 6%. Now, we can using linear interpolation as we did last time.
(P|F, 5%, 30) - 0.013158*(P|A, 5%, 29) = 0.03217
(P|F, IRR, 30) - 0.013158*(P|A, IRR, 29) = 0.013158
(P|F, 6%, 30) - 0.013158*(P|A, 6%, 29) = - 0.00473
(6% - 5%) / (-0.00473 - 0.03217) = (IRR - 5%) / (0.013158 - 0.03217 )
Therefore, IRR = 5.5%
9. Now, let's check the answer by using IRR = 5.5%.
(P|A, 5.5%, 29) = ((1 + 5.5%)^29 - 1) / ( 5.5%*(1 + 5.5%)^29) = 14.3331
(P|F, 5.5%, 30) = 1/(1 + 5.5%)^30 = 0.2006
PW = $455,996.00*(P|F, IRR, 30) - $6000.00*(P|A, IRR, 29) = 5494.26
Note: Due to the use of linear approximation approximation, a small difference is reasonable.
That's all for today. More fascinating articles and sharing will be updated from time to time in Xaivier Blog. So, you are welcome to subscribe our feed, look at our sitemap or simply visit our Homepage.
Written by: Xaivier Chia
Example 3:
Question: Return at the end of period is $455,996.00, Annual saving is $6000.00, Period is 30 years, initial saving is $6000.00 as well.
Solution:
1. First of all, let's see the cash flow below:
Year 0: Initial Saving = PW = $6000.00
Year 1: Annual Saving = AW (Annual Worth) = $6000.00
Year 2: Annual Saving = AW = $6000.00
:
:
:
Year 29: Annual Saving = AW = $6000.00
Year 30: Maturity = FW = $455,996.00
2. After understand this cash flow, the equation represents this cash flow is:
Saving = Return
PW + AW (P|A, IRR, 29) = FW ( P|F, IRR , 30)
3. In this complicated case, we can only use second method which is mentioned at Tutorial: Basic Internal Rate of Return,IRR, Calculation and Explanation, that is, the trial and error plus linear interpolation approach.
$6000.00 + $6000.00*(P|A, IRR, 29) = $455,996.00*(P|F, IRR, 30)
4. Since the equation of (P|A, IRR, N) = ((1 + IRR)^N - 1) / ( IRR*(1 + IRR)^N), then
(P|A, IRR, 29) = ((1 + IRR)^29 - 1) / ( IRR*(1 + IRR)^29)
5. Divide the equation $6000.00 + $6000.00*(P|A, IRR, 29) = $455,996.00*(P|F, IRR, 30) by $455,996.00, so
0.013158 + 0.013158*(P|A, IRR, 29) = (P|F, IRR, 30)
6. Rearrange, again.
0.013158 = (P|F, IRR, 30) - 0.013158*(P|A, IRR, 29)
7. Using previous equations to get the follow value:
(P|F, 4%, 30) = 0.3083
(P|F, 5%, 30) = 0.2314
(P|F, 6%, 30) = 0.1741
(P|A, 4%, 29) = 16.9837
(P|A, 5%, 29) = 15.1411
(P|A, 6%, 29) = 13.5907
(P|F, 4%, 30) - 0.013158*(P|A, 4%, 29) = 0.0848
8. Obviously, the IRR is between 5% and 6%. Now, we can using linear interpolation as we did last time.
(P|F, 5%, 30) - 0.013158*(P|A, 5%, 29) = 0.03217
(P|F, IRR, 30) - 0.013158*(P|A, IRR, 29) = 0.013158
(P|F, 6%, 30) - 0.013158*(P|A, 6%, 29) = - 0.00473
(6% - 5%) / (-0.00473 - 0.03217) = (IRR - 5%) / (0.013158 - 0.03217 )
Therefore, IRR = 5.5%
9. Now, let's check the answer by using IRR = 5.5%.
(P|A, 5.5%, 29) = ((1 + 5.5%)^29 - 1) / ( 5.5%*(1 + 5.5%)^29) = 14.3331
(P|F, 5.5%, 30) = 1/(1 + 5.5%)^30 = 0.2006
PW = $455,996.00*(P|F, IRR, 30) - $6000.00*(P|A, IRR, 29) = 5494.26
Note: Due to the use of linear approximation approximation, a small difference is reasonable.
That's all for today. More fascinating articles and sharing will be updated from time to time in Xaivier Blog. So, you are welcome to subscribe our feed, look at our sitemap or simply visit our Homepage.
Written by: Xaivier Chia
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2 comments:
ok...im totally blur n dont understand...i try to understand it...if face by face sure can get it easily...T_T
thank you very much...
Take it easy. A journey of a thousand miles, begins with a single step.
Actually, I had spent half semester time to learn IRR during my degree program. Therefore, I suggest you to familiar previous examples before try example 3.
You are welcome. Good luck.
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