# Q32 pg 108: Pension: Change in assumption's effect on Debt to Equity ratio

Question 32 on page 108:

Based on Exhibits 2 and 3, as well as Holmstead’s assumption about future health care inflation, the debt-to-equity ratio calculated by Rickards for XYZ should be closest to:
A 2.69.
B 2.71.
C 2.73.

Exhibit 3 shows 100 bp increase would result in Benefit obligation change of + \$93.

Answer is:C is correct. To calculate the debt-to-equity ratio, both liabilities and total equity need to be adjusted for the estimated impact of a 100-bp increase in health care costs. The proposed increase in health care costs will increase total liabilities and decrease equity by the same amount. Consequently, the debt-to-equity ratio changes as follows:
Sensitivity of benefit obligation to 100-bp increase = \$93
Adjusted liabilities = \$17,560 + \$93 = \$17,653
Adjusted equity = \$6,570 – \$93 = \$6,477
Adjusted debt-to-equity ratio = \$17,653/\$6,477 = 2.7255 ≈ 2.73
Consequently, a 100-bp increase in health care costs increases the debt-to-equity ratio to approximately 2.73.

I don’t understand why we need to subtract 93 from equity. I understand that A = L + E and that would offset the liability increase but conceptually, why equity decrease?

Sorry for the dumb question,

Thanks

The higher benefit obligation of \$93 means a higher periodic pension expense (which reduces earnings by \$93).

Hi , Another query on this question is why it shouldn’t be subtracted by Benefit expense change : 12 on the equity part ( as the change of assumption will reduce Net income) ?
D/E : ( 17560 + 93) / ( 6570-12) = 2.69

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The benefit expense is a part of the benefit obligation change. The benefit obligation contains the service cost (past and current), interest cost, and actuarial gain/loss.

If you want the adjustment to be complete, then you will have to adjust out the the entire change in benefit obligation from equity (some will be deducted from retained earnings, some will be deducted from Other Comprehensive Income).

So for this part, I should rephrase as “(which reduces retained earnings and OCI by \$93)”.

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That makes sense! Thanks for the clarification @fino_abama and your follow up question @bambihohoho

Sorry, i know this topic is quite old, however I just would like to ask why don’t we account for tax in the calculation. Increasing in pension cost must affect somehow to tax and retained earning?