Walter White's life insurance
A companion post.
This post is a supplement to the main post where we discuss how life insurance would have pre-emptively solved most of Walter White’s problems. You definitely should read the main post first; we’re going to jump in assuming you know everything in it.
If you’re reading in the mobile app, the equations below might look ugly. It looks much better if you copy the post link into your browser. When reading in the mobile browser, you have to rotate your phone to horizontal orientation to view the longer equations.
Replace Walt’s future income
How do we calculate a death benefit that replaces 15 years of earnings?
Walt’s gross income is $51,700 in our example. Let’s say we need to replace only one year of income with a death benefit. That would just be the family’s share of earnings: 70% × $51,700 = $36,190.
That was easy. What about two years? The income to be replaced in the second year would be 2.5% bigger: $36,190 × 1.025 = $37,095. But we expect the benefit to grow by 4% each year, so we don’t need the whole amount a year prior to spending it. To replace $37,095 one year from now, we divide by 1.04.
So in this case, the second year’s income adds less to the benefit than the first year’s income. It adds:
If we extend to the third year’s income, it decreases by the same factor:
So over 15 years, the total would be:
The exponent on 1.025/1.04 starts at zero — which makes the ratio equal to 1, essentially absent — and grows to 14 (Walt’s work-life expectancy minus one). With sum notation, that is:
The benefit needed to replace his future income is about $491,000. The calculation is at that link, and you can go there to plug in your own numbers.*
Fund the kids’ college educations
On Walt’s 50th birthday in 2008, there were about three years until his son Walt Jr. was expected to start college. Holly was still cooking and had about 19 years.
For the sake of round numbers, we’ll assume that the total cost of a public university education was $100K, and that those costs will grow at a 5% annual rate. We’ll also assume that we want to be ready to pay the whole cost on the day each kid starts college, because separating individual years or semesters would add complexity to the problem but no substance.
Because we’re replacing a lump sum (college costs) with another lump sum earlier in time (the death benefit), this calculation is straightforward. You only need a solid understanding of exponents and exponential growth. If you want a refresher, check out this post. In three years, we expect the cost of college for Walt Jr. to be:
How much money do we need now to have that amount in three years? We’ll continue with our assumption that the death benefit will be invested with a 4% after-tax rate of return. We divide by 1.04 three times:
And that’s it, you can write the whole calculation as one expression if you want:
This calculation finds the “present value” of the college cost for Walt Jr. in three years. You don’t have to use that term to explain it, but that’s what it is.
To calculate the death benefit we would need to fund Holly’s education, we replace 3 with 19:
Add those results to find that we need about $223K of coverage. The total cost is expected to be $368K. At a 4% annual rate, the $223K benefit would grow enough to fund their educations in full if Walt bought a policy at age 50 and dropped dead on the spot. If he died later, the death benefit wouldn’t have enough time to grow.
Of course, we would expect Walt and Skyler to be able to fund their children’s educations without life insurance. So if they were executing a coherent financial plan — which they were not doing — they would be gradually saving and investing enough to pay for each kid’s education. If they were doing that and Walt died at some point while covered by his 15-year policy, the death benefit would be enough to substitute for the income Walt intended to spend on college.
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As you can see, the math is heavier than most people want to deal with on a Saturday night, but it’s not that complicated. See you next week.
Further resources
Every Money IRL post is organized in The Omni-Post, and all vocab terms are here.
What, you wanted further resources? Check out the main post. There’s a footnote at the bottom though.
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*Big footnote:
If you’re really interested in details, this article is a good description of the difference between an “ordinary annuity” and an “annuity due”. So far, we assumed that the first withdrawal from the death benefit would occur immediately (an annuity due). You can see the formula here. Another method of calculating the death benefit is similar, but it assumes one period (in this case one year) before the first withdrawal. This is an ordinary growing annuity, whose formula is here. As a result of waiting one year before withdrawal, the ordinary annuity calculation results in a slightly smaller death benefit.
I find writing the formulas in sum notation to be clear, because it reflects the process of reasoning and calculation. You can compress the process into a shorter formula, but it’s harder to tell what’s going on.
Here’s the expanded sum for the ordinary annuity method:
It gives us a death benefit of about $472,000. One way the sum can be written is:
The “annuity due” method makes a little more sense to me, which is why I said the result was $491K in the main post.
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