Hard debt: Archimedes’ thumb (Part 1)
“Hard debt, one of the four kinds of money, is an essential element in affordable housing,” said Holmes abruptly, “though the very affordability instincts that induce policymakers to offer favorable terms also substantially increase its potential to do harm.”

Watson tossed down the Foreclosure Notices section of the Times
“Harmful?” asked Watson. “But are not the Federal government and state agencies replete with low-cost, high-leverage loan programs?”
“And in that lies the danger,” Holmes said, for as Archimedes and Michael Milken demonstrated, ‘Give me a line of credit long enough and I can buy the world.’”

“Now, all I need is a small down payment“
“A loan is renting money,” Holmes began, with the satisfied rolling tones of a protagonist early in a story of which he is the hero. “I let you use my money for a discrete period of time. You tell me when you will return it (term of the loan), you pay me an agreed formula rent for the interval (interest), and you give me security (a mortgage) as proof of your good intentions.”
Hard debt and hard equity
“In this hard debt is quite different from equity, as shown in the accompanying Table 1,” and with his long mobile fingers he conjured it into being:
Table 1
Hard debt versus hard equity
(comparison of the pure states)
|
|
Debt |
Equity |
|
Consumer’s relation to capital source |
Rents money from source |
Buys money from source |
|
Interest or yield rate |
Defined by formula |
Undefined, depends |
|
Mandatory payments |
Yes |
No |
|
Security or collateral |
Yes, usually a mortgage |
No |
|
When is it paid? |
First |
Last, after all debt |
|
Participates in upside? |
No |
Yes |
|
Risk (from capital source’s point of view) |
Safest |
Riskiest |
|
Yield |
Low |
High |
“Throughout all this, Watson, we are speaking of hard capital, not the soft debt and soft equity we have previously covered.”

Watson dread the thought of having to revisit the soft debt lecture
Leverage, gearing, LTV, and DSC
Hard debt is the fundamental element of real estate finance, the sine qua non. With debt, a given amount of equity (or down payment) can be levered (or geared, as the English say) into a significant multiple thereof. Eighty percent loan-to-value gears $1 of equity with $4 of debt. Ninety percent gears $1 of equity with $9 of debt. This is powerful leverage.
With that leverage, of course, comes increased risk, for an increasing portion of the enterprise’s cash flows are pledged to the lender, leaving less cushion for volatility. Recognizing this, rational lenders cap borrowing at some stipulated loan-to-value (LTV) ratio.
Loan-to-value (LTV) ratio
+ Loan on the property
¸ Property value
= Loan to value (LTV) ratio
Loan-to-value ratios should never exceed 100%; the closer to 100%, the riskier the loan. Lenders normally specify maximum LTV ratios, with the balance to be supplied by equity (down payment).
In income-producing property, lenders add a second test, of debt service coverage:
Debt service coverage (DSC) ratio
+ Net Operating Income
¸ Debt service requirement
= Debt service coverage (DSC) ratio
For an income-producing property to be viable, debt service coverage must always exceed 100%; the closer they are to 100%, the riskier the loan. Lenders normally specify a minimum debt service coverage ratio (e.g. 120%) in their loan underwriting
So in all these matters, lenders wish to assure that there is some hard equity in the transaction.
From the capital source’s point of view, debt is much safer than equity: it is the first money out (equity is the last money out), and it has numerous protections that equity lacks. So as a general rule, in equilibrium markets debt is always cheaper than equity.
Weighted Average Cost of Capital
Every market financing involves at least two sources, one that is principally debt, another that is principally equity. (”Any lender who thinks that the 100% financing is all debt is fooling himself,” muttered Holmes.)
The purest example, and the easiest for our purposes, is the purchase of a single-family home:
Price = mortgage + down payment
Every dollar not funded in mortgage must be funded with down payment
Equity is scarce, and expensive. Getting it from the marketplace works against affordability in both a homeownership and a rental context.
When there are multiple sources of capital, the resulting mixture can be financially homogenized by deriving the Weighted Average Cost of Capital (WACC) as follows:
Weighted Average Cost of Capital
+ Debt cost = Loan x interest rate
+ Equity cost = Equity x yield requirement
= Total cost of capital
/ Total capital raised (sum of debt + equity)
= Weighted Average Cost of Capital
Example:
+ 6.0% Debt cost = 75% loan x 8.0% interest rate
+ 3.0% Equity cost = 25% equity x 12.0% yield requirement
= 9.0% Weighted Average Cost of Capital
From this simple equation, several consequences are readily apparent:
1. Higher leverage (more debt, less equity) reduces Weighted Average Cost of Capital. (For instance, at 90% leverage, the WACC is 8.4%; verify this for yourself.)
2. WACC is equally applicable when there are more than two sources, such as a senior loan, a junior loan, and equity. The calculation is structurally the same.
3. If the equity yield is distributed over time — that is, starts low and rises — then the initial cost of capital (say, for the first year) is quite low (in the example, 6.0%), but it rises rapidly as time passes. As a result, hard equity is antithetical to long-term affordability (but has its uses, as I will discuss when I post on that subject).
Hard capital and affordability tension
Unlike soft capital (which has no direct impact on mandatory debt service or required rent levels, and thus fuels affordability), hard capital has a payment cost, and that cost works directly against affordability. Moreover, equity is more expensive than debt, which is an even greater tension (though hard equity is essential, for reasons we will take up in another post.) We can display this schematically as follows:
Weighted Average Cost of Capital and affordability:
The homeownership relationship
Higher WACC –> higher loan payments –> less affordability
This thus translates into a direct function between lending terms and maximum home prices:
Home prices relative to hard debt
and cost of capital
+ Debt service
¸ Payments-to-income affordability ratio (say 30%)
= Supportable mortgage
+ Down payment
= Maximum affordable home price
The rental equivalent involves more arithmetical steps:
Required Gross Potential Rent (GPR)
Working upwards from financing
+ Debt service (debt cost x loan amount)
+ Coverage (cash flow, which is also equity yield x equity amount)
= Net Operating Income (NOI)
+ Operating expenditures (administration, maintenance, repairs)
+ Deposits to replacement reserves/ capital expenditure fund
= Effective gross income (EGI) required for viability
¸ Financial occupancy (100% minus financial vacancy)
= Gross Potential Rent (GPR) required for viability

“You have an extraordinary genius for minutiae,” I remarked.
“I appreciate their importance.”
– The Sign of the Four, 1890, Chapter 1
but leads to the same functional causality: debt service cost drives rents upwards:
Higher debt service –> higher required NOI –> higher required rent
Yet hard debt is inescapable, because everything else is finite, scarce, expensive, or some combination of all three. Thus policymakers designing affordable housing programs inevitably use hard debt, but then militate against its affordability-defeating cost by pursuing two principal goals:
- Highest leverage (loan-to-value)
- Lowest Weighted Average Cost of Capital
These two goals go together; high leverage also tends to drive down WACC. Both strategies are about multiplying buying power, using OPM financing (Other People’s Money) to make one’s own (assets or income) go further.
(Continue to Part 2.)