Redirecting Taxable investments to Roth 401(k) - An Improved Analysis

This is a follow-up to Redirecting Taxable investments to Roth 401(k). The analysis is conducted in terms of capital appreciation and dividend yield rates. It also incorporates the additional basis created in a taxable account by dividend reinvestment.

Redirecting Taxable investments to Roth 401(k)

Preface

This article is for those in the USA who

• have access to after-tax 401(k) contributions with immediate in-plan conversion to Roth 401(k), aka, Mega Back Door Roth (MBDR), and
• have a taxable brokerage account with sufficient assets that can be leveraged to facilitate the MBDR.

Introduction

Usually, people focussed on saving and investing set their retirement contributions so that their net pay covers living expenses. Assuming one is already maxing out contributions to tax-advantaged retirement accounts and has accumulated a nontrivial amount of investments in a taxable brokerage, the question naturally arises:

Does it make financial sense to take advantage of the MBDR even if it means that one has to draw down on the taxable brokerage to fund living expenses?

Comparing mortgages for buying or refinancing a house

Questions that come up in scenarios related to buying or refinancing a home:

1. Is mortgage A better than mortgage B?
• Each mortgage may be amortized over a different duration (e.g., $15$ vs. $30$ years)
2. Given that I'm part-way through mortgage C, should I refinance to mortgage D?

Setting aside the emotional aspects, there is almost always a clear answer based on the Net Present Value ($NPV$) calculation of the cashflows related to the principal, interest, and loan fees. For a fixed-rate mortgage with no taxes or unusual features:$$\begin{align*}NPV &= F + P_0 + \sum_{k=1}^N \frac{PMT_k}{(1+d)^k}\\&=F + P_0 + PMT\left[\frac{1-(1+d)^{-N}}{d}\right]\;\text{for a fixed-rate loan}\end{align*}$$where

• $F$ is the amount in fees paid to acquire the loan
• $P_0$ is the initial cash outflow ("downpayment"), if any, outside of fees
• $N$ is the total number of payment periods
• For a $30$ year mortgage with monthly payments, $N = 30 \times 12 = 360$
• $PMT_k$ is the payment due at the end of the $k^\text{th}$ period
• The $PMT$ is a constant for a fixed-rate mortgage
• $d$ is the chosen discount rate per period

The $NPV$ formula, as specified above, assumes that the first payment will be due at the end of the first period immediately following the loan origination.

I've made available a Mortgage Comparison Template.ods file that implements the calculations referred to in this post.