In order to understand how the discount rate impacts the company’s pension obligations, it is useful to first understand the finance concepts of time value of money and present value. Note that the discount rate is the most important (and most difficult to assess) assumption in calculating pension obligations.

### Time Value of Money

The concept of time value of money is best explained in a simple way: a dollar today is worth more than a dollar in the future.

Imagine receiving $1,000 today and putting it in a simple bank savings account. That

$1,000 will eventually grow over the years because the bank will pay interest on it. Thus, there is a greater benefit to getting the $1,000 now rather than later. If the amount is to be received later, it would be necessary to ask for more than $1,000 to compensate for the interest that could have been earned had the money been received today.### Present Value

Present value is the current worth of a sum of money to be paid in the future or a stream of future cash flows measured in “today’s dollars.” Money paid or received in the future must be discounted to reflect the current time value of money.

The specified rate of return used to discount future cash payments and receipts is the discount rate. In the example above, we noted that $1,000 received in the future would be worth less than $1,000 received now.

To expand on this example, assume that the bank pays 2% a year in interest. After one year, that $1,000 would earn $20 in interest, and be worth a total of $1,020.

Thus, if the $1,000 was to be paid in a year’s time instead of today, the recipient would want $1,020 to make up for the interest foregone in the year before payment. Therefore, the present value of receiving $1,020 in one year from today, assuming a 2% rate of return, is $1,000.

### Changing the Discount Rate and Timing of Cash Flows

The discount rate and the timing of cash flows have a significant impact on the present value of future cash receipts and payments. Here are some examples, still with the same $1,000 example:

- Instead of one year, assume that the money is to be received 10 years from now. If the money had been received today, it could have earned 10 years’ worth of compounded interest. Using the same discount rate (2%) as above, 10 years of compounded interest would grow the initial $1,000 to $1,219. This means that the present value of receiving $1,219 in 10 years’ time is, again, $1,000. The farther out in time the cash flows are received, the less they are worth today.
- Continuing with the previous example of $1,000, consider a situation where you had to choose between receiving $1,000 today or $1,219 in 10 year’s time. Based on the above example, you would be indifferent because receiving $1,000 today and growing it at a rate of 2% per year would give you the same value as receiving $1,219 in 10 year’s time. Now, instead of a 2% rate of return, assume a 6% rate. At this new rate, investing $1,000 today would yield $1,791 after 10 years. By simply increasing the discount rate, it no longer makes sense to agree to receive $1,219 in 10 year’s time when you should be able to make $1,791 by investing $1,000 today. Said differently, the present value of $1,219 is no longer $1,000—it’s less because the higher rate of return means you only have to invest $688 at a 6% rate to have $1,219 in 10 years.
*Therefore, increasing the discount rate decreases the present value of future cash flows; decreasing the discount rate increases the present value of future cash flows.*

### Understanding How the Discount Rate Impacts Pension Obligation

Understanding the concepts of the time value of money, present value, and discount rates are necessary in any discussion of how to value pension obligations. In simple terms, pensions are promises of future payments to employees when they retire in return for their employment services now.

As these payments are made far out into the future, the mathematical concepts discussed earlier must be applied to determine the value of the company’s pension obligations as of the date of its financial statements.

The company, with the assistance of actuaries, does this by calculating the present value of pension benefits to be paid to current and future retirees into the future. Naturally, the company must determine a discount rate before an actuary can determine the present value of these future cash payments.

### Discount rates used by the company

IFRS prescribe that the discount rate should be set with reference to plan-assets returns or the cost of borrowing. The discount rate used is set at the company’s long-term expected rate of return on the plan assets.

As a result of the time value of money, discussed above, it means that if the discount rate decreases the present value of the pension plan will increase. However, under IAS 26, changes in the discount rate do not immediately impact the company’s pension liability in the year they occur. Changes in the pension liabilities arising from changes in the discount rate are considered actuarial gains and losses. These amounts are considered unamortized actuarial gains (loses) and are then gradually subtracted from (added to) the company’s pension liability over the course of many years (this is over the course of the expected average remaining service life of employees).

### Pension Obligation Sensitivity to Changes in the Discount Rate

The discount rate is one of the most significant assumptions the company makes in valuing its pension obligations. This is why it is required to disclose in the notes to the financial statements a “sensitivity analysis” of how changes in the discount rates would impact pension obligations.

A sensitivity analysis looks at what-if scenarios with respect to a specific assumption, while holding all other assumptions constant. For example, a sensitivity analysis can illustrate what would happen to the company’s pension obligation if the discount rate was changed by an arbitrary number of basis points.

Given the downward trend of discount rates over the last five fiscal years, we looked at what would happen to the company’s total pension obligation if the discount rate was 25 basis points lower (e.g., from 6.25% to 6.00%, 5.75% to 5.50%, and so on).

As at March 31, 2016, an “across the board” decrease in the discount rate of 25 basis points would have increased the company’s total pension obligation by more than $4 billion. While this change would not show up immediately in the company’s total pension liability, it would have a future impact of increasing the pension liability and pension expense over the course of many years.Due to the mathematical properties of present-value formulas, a decrease in the discount rate has more of an impact than an increase of equivalent size. As such, an increase in the discount rate of 25 basis points would have a slightly smaller impact on the pension obligation in the opposite direction.

To further illustrate the sensitivity of the accrued benefit obligation to the discount rate, consider the following. As at March 31, 2016, with respect to the pension plan, the company reported a pension asset before valuation allowance of $10.1 billion using a discount rate of 6.25% for its 50% share of the plan.

This implies a $20.2-billion pension asset before valuation allowance for the pension plan as a whole using the company’s assumptions set in accordance with IFRS. In contrast, the pension plan’s most recently available financial statements reported a deficit (net liability) of $1.8 billion as at December 31, 2015, using a discount rate of 3.25%.

The pension plan sets its discount rate with reference to government bonds (i.e., one of the rates at which the company borrows from investors) in accordance with accounting standards for pension plans and IFRS. It should be noted that there are several other differences between the key economic assumptions used by the pension plan and those of the company. However, by far the most significant difference in assumptions causing the disparity in measurement is the 300 basis point difference in discount rates.

### Looking for benchmarks

The company set up a benchmark of comparable entities with comparable pension plans to see how they discounted their pension plans (which was the discount rate used?).

Research showed the following comparables:

In summary the benchmark discount rate is anywhere from 5% to 6.95% and the company falls inside this range. So there is no obvious reason to change the company’s use of a discount rate of 6.25%.