How sensitive is a multi-decade gifting plan to errors in the growth rate $r$ and planning horizon $N$?

The sensitivity is huge — small changes in $r$ or $N$ produce large changes in terminal wealth. Here's the quantitative picture and the practical implications.

Sensitivity table ($PMT = \$19{,}000$ per year, baseline $r = 5\%$, $N = 30$):

Practical implications:

1. A $1\%$ error in $r$ changes FV by $\sim 20\%$ at a 30-year horizon. So predicting $4\%$ vs. $5\%$ growth shifts the plan by hundreds of thousands of dollars.

1. A 5-year error in $N$ changes FV by $\sim 30\%$. If you assume 30 years and live 35, you've underestimated the transferred wealth by a third.

1. Compounding is asymmetric. Higher $r$ AND higher $N$ both push FV higher — they don't cancel. A combined $+1\%$ on $r$ and $+5$years on$N$adds$\sim 60\%$ to FV.

How to think about uncertainty:

For $r$ (growth rate):

• Be conservative. Use a realistic after-tax growth rate, not aspirational. For a balanced trust portfolio, that's typically 4-$6\%$ real, not 8-$10\%$ nominal.
• Tax matters. If the trust pays income tax, use after-tax growth. Trust tax brackets compress quickly ($37\%$ at $> \$13K$ of trust income in 2024), so high-yield strategies can be tax-disadvantaged.
• Sensitivity-test. Run the plan at $r - 1\%$, $r$, and $r + 1\%$. Show the client the spread.

For $N$ (planning horizon):

• Use median life expectancy as baseline.
• Model upside scenarios at $+5$years and downside at$-5$ years.
• Consider longevity insurance if the family wealth depends critically on the upper-bound case.

Real-world planner mindset:

A wealth advisor typically presents the client with THREE scenarios:

1. Conservative: $r - 1\%$, $N - 5$. Likely floor on transferred wealth.
2. Base case: advisor's point estimate of $r$ and $N$.
3. Optimistic: $r + 1\%$, $N + 5$. Likely ceiling.

The advisor then frames decisions around the base case but tests for robustness against the conservative and optimistic outcomes. If the plan only works in the optimistic case, that's a fragile plan.

The "rich get richer" effect:

High-net-worth clients can afford to be conservative on assumptions because they have a margin of safety. Lower-net-worth clients trying to stretch retirement income often have to be aggressive on $r$ — which is risky because if the realisation is below the assumption, they run out of money.

This is one of the structural advantages of being wealthy: the ability to use conservative planning assumptions and still meet life goals. The math is the same; the wealth gives you a buffer against the variance.

For the exam:

CFA Level III vignettes often include sensitivity tables. Be ready to compute the impact of bumping $r$ or $N$. The exam loves to ask "what is the additional wealth transferred if $r$ is $6\%$ instead of $5\%$" — that's a sensitivity question.