P = present
F = Future
A = Annual
W = Worth
N = number of year
Basically, two equations are involved in this tutorial
1. PW = FW (P|F, IRR , N)
2. (P|F,IRR, N) = 1/(1 + IRR)^N
(1 + IRR)^N means (1 + IRR) to power N.
Example 1:
1. Let present worth, PW in a six years cash flow is:
present worth, PW = -(capital) + (annual return)(P|A,IRR,6) + (book value)(P|F,IRR,6).
2. Let's say in trial and error approach with different value of IRR, you found that,
PW1 = positive value when IRR = 20%
PW2 = negative value when IRR = 25%
therefore, obviously, IRR is between 20% to 25%
3. Now, one can using a linear interpolation to find approximation of IRR since the IRR is between 20% to 25%.
Example 2:
What is the IRR for the case of PW is $180,000.00, period is 30years, and the return is $455996 after the end of period?
First method : Manually calculation
1. present worth, PW = (FW)(P|F,IRR,N).
PW = $180,000.00
N = 30
FW = $455,996.00
2. (P|F,IRR,N) = PW / FW = 0.3947
3. (P|F,IRR,30) = 1/(1 + IRR)^30 = 0.3947
4. (1 + IRR)^30 = 2.5336
5. IRR = 0.03147 or 3.147%
Second Method: Trial and Error + reference table
1. (P|F,IRR,30) = PW / FW = 0.3947
2. From reference table, we can found that,
(P|F,3%,30) = 0.4120
(P|F,4%,30) = 0.3083
Therefore, IRR is between 3% and 4%.
3. Using linear interpolation,
we have (3% - 4%) / (0.4120 - 0.3083) = (IRR - 4%) / (0.3947 - 0.3083)
As a result, the IRR from second method approach is 3.1668%
Note: The first method is limited to simple calculation like example 2. The second method is more popular since it is workable almost every question.
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Written by: Xaivier Chia
