LTV and the time value of money

Published on Wed 20 May 2026

Here, we review the time value of money concept and its application to optimizing marketing (or other asset investment) spend.

Time value of money

A popular lifetime value (LTV) variant is built on top of the "time value of money" concept. Essentially this says that we'd rather have a dollar now than in the future. To formalize this, we imagine we have a source of capital that comes with an associated interest rate. This capital source could be a line of credit, or it might be our own capital that would otherwise be allocated to some other "baseline" investment. As we explain below, the capital source's interest rate sets the time value of money.

A common application of LTV is to set marketing budgets: We can think of LTV as the effective value of a revenue stream, and we will want to acquire the stream provided its cost is less than this effective value. When this holds:

If the capital source is a loan, we should borrow the money to purchase the asset. Its resulting revenue will then be enough to both pay back the loan and generate excess profit on top of that.
If the capital would instead come from reallocating funds from a baseline investment, the asset here offers a higher rate of return. We should therefore shift capital toward this asset if possible, continuing until diminishing returns cause the marginal returns of the two investments to become equal.

Evaluating LTV as a discounted sum of profits

We'll demonstrate how to evaluate LTVs by example.

Example 1

Suppose we can borrow capital at a $20\%$ interest rate, say, and are considering purchasing an asset for $$C$ that will deliver $ $p_T$ in $T$ years. Is this a profitable thing to do?

To check, suppose we do borrow the $$C$ now to buy the asset. Then in $T$ years when the profit $p_T$ comes in, we check if we have enough to pay back the loan. The amount we owe after $T$ years is

\begin{equation} \text{compounded debt owed} = \$C \cdot 1.2^T \tag{1}\label{1} \end{equation}

Therefore, if

\begin{eqnarray} \tag{2}\label{2} p_T = \$C \cdot 1.2^T, \end{eqnarray}

the asset will return just enough money to pay back the loan. With this, we then define

\begin{eqnarray} \tag{3} \label{3} \text{LTV} \equiv \frac{ p_T}{ 1.2^T} \end{eqnarray}

and note that if the asset's cost $C < LTV$, the asset will generate enough revenue to (i) pay back the compounded debt (\ref{1}), and then (ii) have some excess that we can pocket as profit. On the other hand, if $C > LTV$, we won't be able to pay back the loan from the asset's revenue. We see then that (\ref{3}) is precisely the amount we should be willing to pay for the asset: below this the asset will make a profit, above it will not (or in the case of a baseline investment, this determines whether or not we'd have been better off sticking with that baseline).

The factor of $1.2^{-T}$ in (\ref{3}) is called the discount factor. This effectively reduces the amount of value we place on revenue that comes in at time $T$. Higher interest rates force us to more strongly discount future earnings, and the larger $T$ is, the less we value that future revenue. This is the time value of money.

Example 2

Suppose now we pay $$C$ and get back a profit stream with $p_t$ coming in at year $t$, for $t = 0, 1, 2, \ldots$. Is this profitable?

In this case, we can write the LTV of the full stream as a sum of the LTVs of the individual payments. These can be read out using (\ref{3}), so the full LTV is

\begin{equation} \text{LTV} = \sum_t \text{LTV}_t = \sum_{t=0}^{\infty} \frac{p_t}{1.2^t} \tag{4}\label{4} \end{equation}

This is the full "discounted sum of profits" formula for LTV. If this is larger than $C, we'll again have enough to gradually pay back the loan and then pocket the excess as profit (or obtain a better rate of return than a baseline investment).

Example 3

Suppose a bond pays out $1 every year off to infinity. How much is it worth to us if our discount rate is again 20%? From (\ref{4}) this is

\begin{equation} \text{LTV} = \sum_{t=0}^{\infty} \frac{1}{1.2^t} = \frac{1}{1 - 1/1.2} = 6 \tag{5}\label{5} \end{equation}

Although the bond will eventually pay out an infinite amount of money, we have to pay up front to get it. It's a profitable thing for us to do, provided the cost of the bond is less than $6.

Practical application challenges

In practice one is often concerned with marginal returns: As you ramp up spend on a given acquisition channel you may see diminishing returns. In this case, early spend might allow you to acquire revenue streams whose LTV is larger than their costs, but as you spend more, the LTV of the new acquisitions go down.

In a situation like this, you need to calculate the return on each individual dollar invested, setting spend to the value where the marginal LTV captured is exactly equal to one dollar. That is, at this point, if you spent one more dollar you'd capture an additional one dollar of LTV, but above that point the LTV would be less than the next dollar spent. This is the profit-maximizing operating point.

A second practical concern is risk. If the asset under consideration has an uncertain value, one thing you can do is increase your discount rate. E.g., risk is often the result of uncertain forecasts, and these can become more uncertain the further out you are forecasting. The discounting strategy is well-suited to situations such as this, as near-term revenue (which is less subject to forecast error) will not be discounted too heavily, while far out revenue (which is relatively uncertain) will be.