Harmonica has been a nanny for the Petersons, whose six children range from age 6 to age 30, for over 20 years. Harmonica’s salary is $50,000 per year and her compensation includes room and board since she is required to be available to assist with the children at all times. Harmonica’s twin brother, Hondu, earns $50,000 per year working as a contractor. Hondu’s employer typically offers lodging near the building site for $100 per week, but Hondu rarely takes advantage of this offer. Which of the following statements is correct for Harmonica and Hondu?

Question

BlackTom AI · Accepted Answer

Employer-provided lodging changes the worker’s effective pre-retirement consumption and therefore the percent of pre-retirement income they must replace in retirement (the wage replacement ratio). The wage replacement ratio is defined as the retirement income required to maintain pre-retirement living standards divided by pre-retirement earnings. In-kind benefits (room and board) reduce a worker’s out-of-pocket living costs while employed but are unlikely to be provided in retirement, so they raise the percentage of pre-retirement earnings that must be replaced by retirement income.

Step-by-step reasoning:
1) Identify components: Both Harmonica and Hondu have $50,000 cash salary. Harmonica also receives employer-provided room and board (an in-kind benefit) because she must live on-site and be available. Hondu rarely accepts the lodging offer, so his pre-retirement living costs are paid out of his cash wages.
2) Effect on required retirement income: Harmonica’s pre-retirement standard of living includes the value of lodging. In retirement she will have to pay housing out of retirement income; thus to maintain the same standard of living she needs replacement income that covers both ordinary living expenses and housing that was previously provided in-kind.
3) Numerical illustration: Suppose the lodging is worth $12,000/year. Harmonica’s pre-retirement consumption = $50,000 cash + $12,000 lodging = $62,000. If she targets 70% replacement of that consumption, she needs 0.70 × $62,000 = $43,400 in retirement. Expressed as a percent of her $50,000 cash salary that’s $43,400 / $50,000 = 86.8% replacement. Hondu’s 70% target on $50,000 is $35,000, i.e., 70% of his cash salary. Thus Harmonica’s replacement ratio (relative to cash salary) is higher.
4) Why the correct answer fits: Because Harmonica consumes an employer-provided benefit now that won’t automatically be available in retirement, the percent of pre-retirement (cash) earnings she must replace is likely higher than Hondu’s.
5) Why other options are incorrect: Option 1 asserts she’s taxed on lodging and therefore below 70%—tax treatment doesn’t guarantee a lower replacement need; option 2 wrongly claims reduced-cost employer housing is automatically tax-free; option 3 incorrectly states both have tax-free lodging. Those are not generally true without meeting strict tax-code conditions.

Conclusion: Harmonica’s wage replacement ratio is likely to be higher than Hondu’s, matching the provided answer.

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