Quote of the Day

Great things are not done by impulse, but by a series of small things brought together.

## Introduction

I recently went into a home center and was shocked to see a 2‑in x 4‑in stud now costs $11 that used to cost $2.50. A 4‑foot x 8‑foot sheet of plywood now costs $100 that used to cost $25. These prices were so high that I decided to delay building a shed until the prices had dropped to more sane levels.

Unfortunately, a perfect storm of COVID panic and bizarre trade policies has caused a massive rise in US lumber prices (Figure 1). Lumber prices are typically around $300 per 1000 board-feet (units discussed below). These prices recently peaked at over $1700 per 1000 board-feet.

What impact did these high lumber prices have on the price of a home? Time to do a little math …

For this post, I will be performing my calculations using a new tool called Maple Flow. I want to give it a test drive.

## Background

### Yet Another Apology for Units

While my raw US Forest Service Wood Product data is metric, the commodity price data is in US Customary units. Because this post is focused on the US housing market, my final results will in the form that US readers can use directly.

### Definitions

- Board-Feet
- Wood volume in the US is usually expressed in board-feet, which has units of ft
^{2}·in. There are 423.8 board-feet in a cubic meter of wood. - House Area
- House area in the US is usually expressed in square feet, which has units of ft
^{2}.

### Wood Usage Per Home Data

All of my calculations will be based on 2019 data from this US Forest Service document, where Table 3 contains this information.

I am only interested in the single-family house data. Here is the information critical to my analysis (Figure 2):

- Floor Area Per Unit: A
_{SFH }:= 234.5 m^{2}(2524 ft^{2}) - Wood Volume Per Unit: V
_{Wood }:= 44.0 m^{3}(18.65E3 board-feet/home)

## Analysis

### Wood Cost Increase

Figure 1 provides the following information:

- Maximum wood cost per board-foot: $1,733.50/1000 board-feet
- Average wood cost per board-foot (pre-COVID); $392.81/1000 board-feet (data mean before 1-Jan-2021)

The price rise in wood products can be computed as shown in Equation 1.

Eq. 1 | $latex \displaystyle \Delta W=\$1733.50-\$392.81=\$1,340.69 \text{ per 1000 board-feet}$ |

For those who like to follow along, my Excel workbook of historical lumber data is available here.

### Mean Board-Feet Per Square Foot of Housed

Equation 1 shows how we can calculate the mean board feet (BfA) per square foot of the home. This number includes both lumber and sheet goods. I should mention that a quick Google search will give you a rough number of 6.3 board-feet per square foot of house area (example). I find this number to be a bit low.

Eq. 1 | $latex \displaystyle k_{BdFtPerSqFt}=\frac{{{{V}_{{Wood}}}}}{{{{A}_{{SFH}}}}}=\frac{{18.65E3}}{{2524}}=7.34\frac{{\text{bdft}}}{{\text{f}{{\text{t}}^{2}}}}$ |

### Estimate Home Cost Increase at the Peak of the Wood Cost Boom

Assuming that houses built in 2019 and 2021 are similar, we now can compute that impact of the recent wood cost increase on the price of a typical home using Equation 2.

Eq. 2 | $latex \displaystyle \Delta C=\Delta W\cdot k_{BdFtPerSqFt}\cdot {{A}_{{SFH}}}= {1,340.69}\cdot 7.34\cdot 2524=24,999\ \text{USD}$ |

Here is a screenshot of all my calculations in Maple Flow.

## Conclusion

At the peak of the recent wood cost increase, the cost of a typical home increased $25K just for wood alone. I should point out that other materials, such as drywall, have also increased in price. Fortunately, we are seeing the wood prices decrease rapidly as more supply is coming online.

I feel bad for the young people trying to buy a house in recent years. Between the Great Recession and COVID, young people entering both the housing and job markets have been subjected to terrible uncertainty.

Mark, there seems to be a Covid inflation aftershock for basic materials. For example, I wanted to upgrade my graphics card so that I can do Blender 3D modeling. Unfortunately, those card prices have gone up also,

I've been using Maple for a number of years.

Have fun,

Ronan

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