When it comes time to sell your property, there really are only 3 types of options available for you to use:
To clarify, option 1 simply involves working with a real estate agent to handle all the necessary work involved in selling your property. Option 2 is literally you sell the property yourself (and handle all the necessary work), hence FSBO means For Sale By Ower. And finally, option 3 involves selling the property directly to what is known as a cash buyer but is basically a real estate investment company. That is really what you are considering when you are looking to sell your property.
But really, when we look at the underlying differences between these three types of options, we see that the differences are only numerical:
\[\begin{align*} P_{agent} &= C_m \cdot (1 - (c_a + c_{closing})) \\ P_{fsbo} &= C_m \cdot (1 - (c_b + c_{closing})) \\ P_{cash} &= C_m \cdot ( 1 - (d_c + c_{closing})) \end{align*}\]The different $P$ values stand for profit made from selling the property (e.g. profit from selling with an agent vs. fsbo vs. cash buyer). The $C_m$ is the market value of your property, and the $c_a$ and $c_b$ variables are the buyer and seller agent commissions. Finally the $d_c$ value is the discount % that the cash buyer will take (i.e. the percent difference between the price they offer you and the market value $C_m$).
We can further simplify things by expressing this in terms of a system of linear equations:
\[\mathbf{P} = C_m \cdot \begin{bmatrix} 1 - (c_a + c_{\text{closing}}) \\ 1 - (c_b + c_{\text{closing}}) \\ 1 - (d_c + c_{\text{closing}}) \end{bmatrix}\]Where $P$ is the profit vector:
\[\mathbf{P} = \begin{bmatrix} P_{\text{agent}} \\ P_{\text{fsbo}} \\ P_{\text{cash}} \end{bmatrix}\]The simplest application of the above problem definition is to find the maximum element in the profit vector $\mathbf{P}$:
\[\max(\mathbf{P}) = \max \begin{bmatrix} p_1 \\ p_2 \\ p_3 \\ p_4 \\ \vdots \end{bmatrix}\]Now imagine we have multiple options: several agents, a few cash buyers, and of course fsbo. We can just collect all those equations in a matrix like we did before, and use linear algebra to calculate the profit vector like so:
\[\boldsymbol{P} = \boldsymbol{S} \cdot \boldsymbol{C}\]Where $\mathbf{C}$ represents the cost matrix with $x_i$ and $y_i$ variables representing the commission/discount percent and closing costs respectively:
\[\mathbf{C} = \begin{bmatrix} 1 -x_1 -y_1 \\ 1 -x_2 -y_2 \\ 1 -x_3 -y_3 \\ 1 -x_4 -y_4 \\ \vdots \end{bmatrix}\]and $\mathbf{S}$ is the diagonal matrix representing the different selling prices that the property will be sold for (as opposed to $C_m$ which is just the market value of the property):
\[\mathbf{S} = \begin{bmatrix} s_1 & 0 & 0 & 0 & \cdots \\ 0 & s_2 & 0 & 0 & \cdots \\ 0 & 0 & s_3 & 0 & \cdots \\ 0 & 0 & 0 & s_4 & \cdots \\ \vdots & \vdots & \vdots & \vdots & \ddots \end{bmatrix}\]Put it all together and you have:
\[\begin{align*} \begin{bmatrix} p_1 \\ p_2 \\ p_3 \\ p_4 \\ \vdots \end{bmatrix} &= \begin{bmatrix} s_1 & 0 & 0 & 0 & \cdots \\ 0 & s_2 & 0 & 0 & \cdots \\ 0 & 0 & s_3 & 0 & \cdots \\ 0 & 0 & 0 & s_4 & \cdots \\ \vdots & \vdots & \vdots & \vdots & \ddots \end{bmatrix} \cdot \begin{bmatrix} 1 -x_1 -y_1 \\ 1 -x_2 -y_2 \\ 1 -x_3 -y_3 \\ 1 -x_4 -y_4 \\ \vdots \end{bmatrix} \\ &= \begin{bmatrix} s_1 & -s_1 x_1 & -s_1 y_1 & \cdots \\ s_2 & -s_2 x_2 & -s_2 y_2 & \cdots \\ s_3 & -s_3 x_3 & -s_3 y_3 & \cdots \\ s_4 & -s_4 x_4 & -s_4 y_4 & \cdots \\ \vdots & \vdots & \vdots & \ddots \end{bmatrix} \end{align*}\]To illustrate this method more clearly, we are going to generate some fake data, apply some linear algebra, and find the best (i.e. maximum) profit. First we must generate some fake data to populate the cost matrix $\mathbf{C}$:
1.000 -0.041 -0.018 agent
1.000 -0.059 -0.020 agent
1.000 -0.052 -0.023 agent
1.000 -0.048 -0.021 agent
1.000 -0.035 -0.019 agent
1.000 -0.035 -0.024 agent
1.000 -0.032 -0.017 agent
1.000 -0.056 -0.019 agent
1.000 -0.048 -0.020 agent
1.000 -0.051 -0.022 agent
1.000 -0.030 -0.027 fsbo
1.000 -0.294 -0.018 cash
1.000 -0.266 -0.023 cash
1.000 -0.142 -0.024 cash
1.000 -0.136 -0.016 cash
Then create some more fake data to populate the sales price matrix $\mathbf{S}$ (based on the Q2 2024 median US house price of $\textdollar361,282$):
372036 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 328334 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 317787 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 406171 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 407845 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 392122 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 341743 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 321049 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 379705 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 355297 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 323486 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 360800 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 314721 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 402214 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 337160
Now calculate the profit vector $\mathbf{P}$:
$350,091 agent
$302,696 agent
$294,007 agent
$377,967 agent
$385,802 agent
$369,042 agent
$325,054 agent
$296,853 agent
$353,685 agent
$329,331 agent
$304,986 fsbo
$248,238 cash
$223,703 cash
$335,304 cash
$285,891 cash
The maximum profit possible from the above profit vector $\mathbf{P}$:
Max Profit: $385,802
Sales Price: $407,845
Total Costs: $22,044
Commission: 3.4681%
Option Type: agent
What the above calculations really show, is that regardless of what is the commission or closing costs involved in the sales options selected for selling your property, it is the profit that is the important number (in this calculation). Whatever option you choose, regardless of what commission or discount the agent or cash buyer wants, as long as the sales price is high enough it may be favorable. An agent with a higher commission, but also a significantly higher sales price (assuming they can indeed find a buyer for that price), could very well be more profitable than a agent at a lower commission (and also a lower sales price). Of course, in the actual decision process there are more things to consider than just “profit” (e.g. time, complexity, reputation, etc). But at as a first approach the method outlined can be used to initially filter the options for selling your property.