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Finance???
Finance???
Does present value decrease at a linear rate, at an increasing rate, or at a decreasing rate with the discount rate? Why?
Answers:
Chosen Answer
Michael M: PV decreases at a decreasing rate as the discount rate goes up.
PV increases at an increasing rate as the discount rate goes down.
PV is an example of an exponential (not linear) function. Here is a simple single period PV where the we are trying to value $100 with a discount rate of 10%
A. 100/1.10 =90.909 ok. so lets add 1% to the discount rate.
B. 100/1.11=90.090 and add 1% more to the discount rate.
C. 100/1.12 =89.285 and 1% more.
D. 100/1.13=88.495
here are the changes in present value
A to B .819 B to C .804 C to D .790
PV is decreasing at a decreasing rate because of the slowing rate of increase in the discount rate. Every time you add 1% to the discount rate the percentage increase in the discount rate becomes smaller and smaller and the impact of the discount rate on PV diminishes as you keep adding. This is exponential decay.
Here is what 1% represents as a portion of successively higher discount rates
At a rate of 1.11 .01/1.11=.00900%
At a rate of 1.12 .01/1.12=.00892%
At a rate of 1.13 .01/1.13= .00885%
Of course if you go in the other direction and lower the discount rate each 1% decrease gets proportionally larger and larger - this is termed exponential growth.
2008-03-30 20:51:00
Michael M: PV decreases at a decreasing rate as the discount rate goes up.
PV increases at an increasing rate as the discount rate goes down.
PV is an example of an exponential (not linear) function. Here is a simple single period PV where the we are trying to value $100 with a discount rate of 10%
A. 100/1.10 =90.909 ok. so lets add 1% to the discount rate.
B. 100/1.11=90.090 and add 1% more to the discount rate.
C. 100/1.12 =89.285 and 1% more.
D. 100/1.13=88.495
here are the changes in present value
A to B .819 B to C .804 C to D .790
PV is decreasing at a decreasing rate because of the slowing rate of increase in the discount rate. Every time you add 1% to the discount rate the percentage increase in the discount rate becomes smaller and smaller and the impact of the discount rate on PV diminishes as you keep adding. This is exponential decay.
Here is what 1% represents as a portion of successively higher discount rates
At a rate of 1.11 .01/1.11=.00900%
At a rate of 1.12 .01/1.12=.00892%
At a rate of 1.13 .01/1.13= .00885%
Of course if you go in the other direction and lower the discount rate each 1% decrease gets proportionally larger and larger - this is termed exponential growth.
2008-03-30 20:51:00