1.4 Capital Needs: Preservation and Depletion

Capital needs: define the payment timing first

Capital-needs analysis translates a household's spending gap into a required portfolio. Subtract reliable income from the expense budget, include taxes consistently, and decide whether the figures are nominal or inflation-adjusted. A real-return model pairs today's purchasing-power spending with a real return. Do not combine inflation-adjusted expenses with a nominal return without adjustment.

Two deterministic models illustrate a trade-off. Capital preservation funds spending while retaining a specified principal amount. Capital depletion deliberately spends principal and earnings over a finite horizon. Neither formula predicts volatile markets or guarantees that a retiree will have enough money. Both require a return assumption, payment timing, and a clear definition of the ending balance.

Preservation with end-of-year payments

For constant annual real spending E paid at each year-end and constant positive real return r, the perpetual-preservation reserve is:

$$P_{\text{ordinary}}=\frac{E}{r}$$

At E = 60,000 and r = 0.04, this is 1,500,000. The reserve earns 60,000 during the first year, then pays that amount at year-end. The balance after payment returns to 1,500,000. Repeating the assumed return and payment preserves that real principal indefinitely in the model.

This formula does not fund an immediate first payment while also retaining the same initial balance at the corresponding point in every year. If spending starts today, the household needs an additional payment in reserve. Identify the timing before comparing formulas.

Preservation with beginning-of-year payments

For perpetual beginning-of-year payments, measured immediately before each payment, the required initial capital is:

$$P_{\text{due}}=\frac{E(1+r)}{r}$$

At 60,000 and 4%, this is 1,560,000. The first immediate 60,000 payment leaves 1,500,000 invested. One year of 4% real growth restores 1,560,000 immediately before the next payment. The same annual cycle repeats. Thus the before-payment balance is preserved at 1,560,000 and the after-payment reserve at 1,500,000. State the observation point when describing preserved principal.

Actual returns will vary. Fees, taxes, inflation surprises, unexpected care, and different payment frequencies change the result. A legacy objective may justify a partial reserve or a finite bequest target rather than perpetual preservation of all capital. If the assumed real return is zero or negative, dividing by a positive r is not an available solution for positive perpetual spending.

Depletion: the present value of an annuity due

For n beginning-of-year payments of PMT, the deterministic requirement is:

$$PV_{\text{due}}=PMT\left[\frac{1-(1+r)^{-n}}{r}\right](1+r)$$

Consider an age-65 retiree needing 60,000 in real annual portfolio spending, beginning immediately, for 25 payments. Assume a constant 4% real return. The ordinary-annuity factor is approximately 15.62207994; multiplying by 1.04 produces the annuity-due factor 16.24696314. Multiplying by 60,000 gives 974,817.79, rounded to 974,818.

The payments occur at ages 65 through 89. The account reaches zero immediately after the final payment; age 90 marks the end of the 25-year horizon. It does not provide an additional payment at age 90. If payments instead occur at year-end, omit the final multiplication by 1.04. At a zero return, the finite-horizon limit is simply PMT × n.

Compare like timing with like timing

Both columns below fund beginning-of-year spending. Amounts are rounded to whole dollars; premiums compare the extra preservation capital with the depletion requirement.

Longer finite horizons approach the perpetual requirement. A smaller depletion target helps explain why a client may retire sooner, but it also leaves less protection if life, expenses, or poor returns extend beyond the modeled horizon. Compare multiple horizons, a survivor budget, and a care reserve. Social Security, pension survivor options, or an annuity can cover part of the spending need under their respective terms.

Accumulation: saving early and often

The funding gap also depends on time remaining before retirement. With no starting balance, constant year-end savings C, annual return r, and n contributions, the future value is:

$$FV=C\frac{(1+r)^n-1}{r}$$

Saving 10,000 at each year-end for 20 years at an assumed 5% produces approximately 330,660; 30 years produces approximately 664,388. Ten extra contributions double the modeled outcome approximately because earlier deposits also earn returns longer. These are hypothetical, fee-free nominal results, not guaranteed returns. Beginning-of-year contributions multiply each result by 1.05. An existing balance requires adding its separate compounded future value.

Monte Carlo: uncertainty rather than a promise

A Monte Carlo model generates many possible return and inflation paths instead of repeating one average return. Specify expected asset returns, volatility, correlations, fees, inflation, tax treatment, withdrawal timing, longevity horizon, and rebalancing. A model that assumes independent annual returns differs from one using historical blocks or changing economic regimes. The choice can materially change results.

If 850 of 1,000 hypothetical paths finish the selected horizon with assets remaining, the model reports an 85% success rate under its assumptions. This is not an observed 85% personal survival probability or a guarantee of sustaining every desired expense. Define failure: any shortfall, depletion by the horizon, or inability to fund essential spending can produce different classifications.

Inspect the size and timing of shortfalls as well as the percentage. A small shortfall at age 100 and depletion at age 78 require different responses. Test lower returns, higher inflation, earlier market losses, longer life, and spending adjustments. Document whether pension and Social Security cash flows continue for the survivor. Revisit the model when circumstances change; a precise percentage does not repair uncertain inputs.