Question

after reading the​ Novy-Marz and Rauh paper regarding unfunded pension liabilities you decide to compute the total obligation of the state that you live in. After some research you determine that your​ state's promised pension payments amount to $1.8 billion dollars​ annually, and you expect this obligation to grow at 1.6% per year. You determine that the riskiness of this obligation is the same as the riskiness of the​ state's debt. Based on the pricing of that debt you determine that the correct discount rate for the​ fund's liabilities is 2.7% per annum.​ Currently, based on actuarial calculations using 7.9% as the discount​ rate, the plan is neither over nor underfundeddash–the value of the liabilities exactly matches the value of the assets. What is the extent of the true unfunded​ liability

Answer 1

Present value of the current liability = PVIFA * Perpetuity
PVIFA = 1 / (i - g)
= 1 / (0.079 - 0.016)
= 1 / 0.063
= 15.873
Perpetuity = $1.8 billion

Present value of the current liability = 15.873 * 1.8 = $28.5714 billion

Value of new perpetuity = Perpetuity * PVIFA
PVIFA = 1 / (i - g)
= 1 / (0.027 - 0.016)
= 90.9091

Value of total liabiltiy = 90.9091 * 1.8 = $163.6364 billion

Unfunded liability = $163.6364 billion - $28.5714 billion = $135.06 billion

Unfunded liability = $135.06 billion