# Accretion of Discount

Journalists covering state, local and school district pension obligations need to add an esoteric phrase to their vocabularies: “Accretion of Discount.”

As explained by Investopedia: “Accretion of discount is the increase in the value of a discounted instrument as time passes and the maturity date looms closer. The value of the instrument will accrete (grow) at the interest rate implied by the discounted issuance price, the value at maturity and the term to maturity.”

In the case of public pensions, “discounted instrument” = the present value of pension liabilities. Eg, assume a government obligates itself to make a $100 pension payment in 20 years. To report a present value of that obligation when created, the future payment of $100 must be “discounted.” Once a present value is established, ** the obligation will grow at the discount rate**.

Let’s say the government chooses a 7.5 percent discount rate. Discounted at that rate, $100 due in 20 years has a present value of $24. The discount — $76 — will accrete over the succeeding 20 years. One year later, the liability will accrete to $25. After five years, $34. After ten years, $49. After 15 years, $70. Finally, at 20 years, the liability has fully accreted to $100. ** That growth is automatic. It’s built in up front by the discount. **Also, changing the discount rate during the 20 year period wouldn’t change the end result — that must always be $100. It would just change the pace at which the $100 is accreted.

For a real-life example, take a look at these figures from CalPERS:

Liabilities (second column) grew 76 percent in nine years, from $248 billion to $436 billion. That translates into a compounded annual growth rate of 8.11 percent, close to the discount rates CalPERS employed during that period.

CalPERS is slowly lowering its discount rate to 7 percent but it doesn’t make much difference at this stage. That’s because its plan is increasingly mature and its assets are so much smaller than liabilities. Assets of $298 billion cannot keep up with liabilities of $436 billion accreting at 7 percent, much less 8 percent. Even if $436 billion of liabilities accrete at “only” 7 percent, $298 billion of assets must grow at more than 10 percent just to keep the unfunded liability (the difference between liabilities and assets) from growing.