# OPC Calculations

Ok, I’m in a mathematical mood today so I’m going to test out the $\LaTeX$ functions in wordpress and present some of my calculations and observations on our Off Peak Car (OPC).

Let $C$ be the COE of the car, $O$ be the OMV of the car, and $P$ be the PARF of the car.

Let us consider the PARF of a normal plated car at each year within the lifespan of the COE of 10 years. For simplicity, we will consider integer number of years $t$.

$P_{normal}(t)=\left\{\begin{array}{l l}C\times\frac{10-t}{10}+O\times0.75&\quad\mbox{if }0

For an OPC, the 17000 rebate is deducted first from the COE, then from the OMV. Let us assume that $C\leq17000$ and $C+O>17000$. Then, the COE will be completely deducted and the PARF of an OPC at each year is defined as follows.

$P_{OPC}(t)=\left\{\begin{array}{l l}(C+O-17000)\times0.75&\quad\mbox{if }0

Next, we substitute $P_{normal}(10)=0.5O$ into $P_{OPC}(10)$.

$\begin{array}{rcl}P_{OPC}(10)&=&(C+O-17000)\times\frac{100-(10\times5)}{100}\\&=&0.5C+0.5O-8500\\&=&P_{normal}(10)+0.5C-8500\end{array}$

This equation shows us that if $C=0$ then OPC owners receive 8500 less in PARF compared to normal car owners at the end of 10 years. That is, OPC owners received 17000 rebate when they bought the car but recovers 8500 lesser when they scrap the car, meaning the net rebate enjoyed is only (17000-8500=) 8500. If, however, $C\geq17000$ then OPC owners will receive the same amount in PARF as normal car owners at the end of 10 years, and they enjoy the full 17000 rebate.

This means that OPC owners who got their COE at prices lower than 17000 do not enjoy the full 17000 rebate by virtue of the fact that they will receive a lesser amount when their car is scrapped. In the worse case scenario, the OPC owner will receive only 8500 in rebate if their COE is zero or near zero (i.e. $2 COE in Nov 08). Of course, there are other factors to be considered such as the actual sale price of the car, the interest rate, amount of loan to take, length of loan, etc. This is only a very simplified calculation to find out the maximum and minimum rebates an OPC owner can get. Yes, in times of high COE, you get the maximum savings, but you might also end up paying more in absolute terms becos of the higher cost of the car and interest payable on loan amount. It’s like buying a brand-less backpack at full price of$20 or a designer brand backpack at 70% off the usual price of $1000. Sure, you saved$700 but you also just spent an extra (300-20=) \$280 more than just getting the brand-less one.

Lastly, typing $\LaTeX$ equations are fun! <-geek!

-Dear1