Answer:
$59.8 million.
Explanation:
At the beginning of the year, the Projected Benefit Obligation (PBO) was $48 million, however, during the year this amount was affected by several factors that are explained in the problem statement: the service cost ($13 million), the interest costs (defined by a discount rate of 10%) and the pension benefits paid by the company ($6 million).
To understand how it was modified exactly, first, we will do a theoretical analysis and then present it more <em>graphically</em> as a financial statement.
1. Theoretical analysis
Firstly, a Projected Benefit Obligation (PBO) is a measure that reflects how much a company needs at the present time (December 31, 2018) to cover future pension liabilities. We know that the year began with a PBO of $48 million. However, this amount must be added to the service costs ($13 million), which is the increase in the present value of the liabilities, because the employees have completed another year in the company and that implies an increase in their pension credit.
Therefore, so far, the PBO at December 31, 2018 is $61 million. To this amount must be added the interest cost which is the annual interest amount on the unpaid balance of the PBO. In this case, an interest rate of 10% is handled. Therefore the amount of interest is equal to $48 million (original PBO) * 10% = 4.8 million.
So far, the PBO at December 31, 2018 is $61 + $4.8 = $65.8 million
Finally, the pension benefits paid by the trustee during 2018 should be subtracted, since they are a partial payment of the PBO.
Therefore, we have: $65.8 - $6 = $59.8
2. As a financial statement.
Pension obligations
Year Ended At December 31, 2018
Change in benefit obligations
Beginning PBO $48
Service cost $13
Interest cost $4.8
Benefits paid ($6.0)
Ending PBO $59.8
