MP Tony Pua made a statement that expropriating the LDP highway is cheaper than maintaining status quo.[1] This is not necessarily true. As typical in the realm of economics, the answer is it depends.
What exactly does it depend on?
The biggest assumption lies in the discount rate. The discount rate is required to incorporate the time value of money in any calculation. In a calculation that spans for a very long time, the slightest change in the discount rate could imply a very different solution to a particular fork. In our case, the time length is 20 years because the contract between the government and the operator of LDP only ends in 2028.
Before we inspect Mr. Pua’s comparison which leads him to call for expropriation, a brief introduction to theory of time value of money is most appropriate.
Time value of money says that rational individuals prefer to have money now rather than later. An ice-cream, for instance, is worth more today than tomorrow with all else being equal. The discount rate acts, as the name suggests, to discount the value of the ice-cream as we progress along a certain timeline.
Next, two crucial variables will need clarification.
The first is the cost of expropriation which is RM1.327 billion. This is the cost the government will have to pay if it ever plans to exercise its rights in eminent domain. The cost in my calculation is assumed to be paid in one lump sum as soon as possible.
The second cost is the cost of compensation which the cost at 0.00% discount rate is RM1.929 billion. The compensation is presumably, as it should, paid in the year that the compensation is required. After all, the compensation is really a subsidy of RM0.50 the government gives to the operator in order for the operator to reduce the toll from RM2.10 to RM1.60. While I have not read the agreement relating to the Highway, it seems that the arrangement is more or less a pay-as-you-go.
For expropriation to be desirable, the expropriation cost must be cheaper than the compensation cost.
With that out of our way, let us get down to business.
If the discount rate is 0.00%, Mr. Pua would be right. At 0.00% discount rate, the cost of expropriation does not exceed the cost of compensation. Under this scenario, it makes sense to expropriate the highway from an economic point of view.
As the rate goes higher, however, the narrative veers to the direction of the other side as the differential between the two costs shrinks; the time value of money reduces the cost of compensation. This is so because all future compensations are redefined in present terms.
At approximately 3.89%, the difference becomes zero. This is where the philosophically agnostics celebrate their existence on this fair planet of ours.
Anything above 3.89%, with all else being equal, empirically leads to the logical conclusion to oppose expropriation. This is where libertarians hold wild party with contrabands filling the cocktail table.
For Mr. Pua to be right, he needs to pray that the government’s discount rate is less than 3.89%.
The following table illustrates how various discount rate affects the compensation rate and the case for expropriation.
Finally, caveat.
Mr. Pua places total compensation as RM2.2 billion with 0.00% as the discount rate while I estimate it to be only RM2.0 billion at the same rate. Why is the difference?
First of all, Pua includes a 2008 sunk cost of RM0.6 billion. Sunk cost however is irrelevant in this comparison. We are interested at projecting the future and our decisions cannot change the past, unless we decide to cook the books. To include the extra RM0.6 billion is to commit logical fallacy. A fair comparison must align the stream of payments together and only then an apple to apple comparison is possible. Regardless, Mr. Pua has been careful with that and has added the necessary qualification with respect to the RM0.6 billion. Therefore, this is hardly an issue.
Secondly, Mr. Pua mentioned that the toll is scheduled to increase to RM3.10 from RM2.10 in 2016. Yet, he did not include that in his calculation. In effort to paint a more accurate picture, I incorporate that increase into the compensation calculation while holding the fraction of subsidy (approximately 23.81% with a RM0.50 subsidy over total toll of RM2.10) constant from 2009 to 2028.
The effect of the exclusion and the inclusion of the two factors lead to the difference of RM0.2 billion.
There are several other assumptions made but I think those caveats are insignificant unless the wonks come out of their caves with their arrows and spears. In any case, the calculation is available here for public consumption.
Finally, the consideration for the time value of money is not the only indicator we should concern ourselves with if we want to expropriate the LDP. Even if the time value of money proves that it is cheaper to expropriate it, several questions remain. One of them is: can the government operate the highway more cheaply than the current operator?
It is possible that even if the expropriation cost is lower than status quo, the operation of the highway by the government may actually impose greater overall cost on the government where everybody, including those who do not use the highway. All taxpayers of which a majority do not use the highway would have to support a small group of taxpayers who use the highway.
That is not fair.
[1] — I have blogged earlier that after reviewing the agreement of several toll concessions, including Lebuhraya Damansara-Puchong (LDP), Cheras Grand Saga Highway, KESAS and Butterworth Outer Ring Road (BORR), the Government is able to ‘expropriate’ these highways by giving between 3 to 6 months’ notice at ‘reasonable’ prices. [Cheaper to expropriate LDP. Philosophy Politics Economics. January 7 2009]
A version of this article was first published in The Malaysian Insider on January 9 2009.
