Expected Value and Time Value of Money in Real Estate

Book: Real Estate by the Numbers | Authors: J Scott and Dave Meyer | Chapters: 7-8

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Two of the most useful tools in an investor’s decision-making toolkit are covered in Chapters 7 and 8 of Real Estate by the Numbers. The first helps you choose between options with uncertain outcomes. The second helps you understand what money is actually worth at different points in time. Together, they change how you look at deals.

Chapter 7: Expected Value

Some decisions you make once and live with for a long time. Others you make over and over, dozens or hundreds of times. Expected value (EV) is a tool designed for that second category.

The book defines it this way: expected value is the long-term average result you should expect when you make the same financial decision over and over.

A Simple Game

The authors start with a game. You roll a six-sided die and guess which number it lands on. Guess right, you win $10. Guess wrong, you win nothing. Either way, it costs you $2 to play.

Should you play?

Two outcomes are possible:

• You guess right (1 in 6 chance, or 16.7%): net gain of $8 ($10 win minus $2 to play)
• You guess wrong (5 in 6 chance, or 83.3%): net loss of $2

The EV formula:

EV = (E1 × P1) + (E2 × P2) + … + (En × Pn)

Where E = the financial result of each outcome and P = the probability of that outcome.

Plugging in the numbers:

EV = ($8 × 16.7%) + (-$2 × 83.3%) EV = $1.34 - $1.67 EV = -$0.33

The expected value is negative. On average, playing this game will cost you $0.33 each time. Play 1,000 times and expect to lose about $330. Don’t play.

Choosing Between Investments

EV gets more useful when you’re comparing two real investments with different risk profiles.

Say you have $10,000 and you can invest in Company A or Company B. You can only pick one.

Company A (high risk, high potential):

• 70% chance of losing everything: -$10,000
• 20% chance of breaking even: $0
• 10% chance of a $250,000 profit: +$250,000

Company B (safer, steadier):

• 10% chance of losing everything: -$10,000
• 60% chance of a $10,000 profit: +$10,000
• 30% chance of a $30,000 profit: +$30,000

Running the EV:

Company A: (-$10,000 × 70%) + ($0 × 20%) + ($250,000 × 10%) = $18,000

Company B: (-$10,000 × 10%) + ($10,000 × 60%) + ($30,000 × 30%) = $14,000

Purely by EV, Company A looks better. But the book is honest here: Company A also has a 70% chance of wiping you out. EV doesn’t capture that risk. You’d want to consider whether a 70% chance of losing everything is something you can absorb. EV is a guide, not the whole answer.

J’s Real Insurance Example

The book includes a great real-world story. J (one of the authors) was doing about 200 house flips and spending roughly $1,000 per property on insurance. He wondered if self-insuring might save money.

His estimates based on past experience:

• 97.5% of flips: no claim
• 2% of flips: small claim around $10,000
• 0.5% of flips: big claim around $100,000

EV of self-insuring: ($0 × 97.5%) + ($10,000 × 2%) + ($100,000 × 0.5%) = $700

Compare that to $1,000 for insurance. On average, self-insuring saves $300 per flip. For a high-volume investor doing hundreds of flips, that math adds up quickly.

The key caveat: EV is only as good as the probabilities you feed it. If your estimates are off, your conclusion will be off. Use it where you have data or solid reasoning to back up your probabilities.

Chapter 8: Time Value of Money

The time value of money (TVM) is one of the foundational ideas in all of finance. The concept:

Money in hand today is worth more than money in hand at some future time.

Why? Because money today can be invested and grow. $1,000 today invested at a 12% annual return becomes $1,126.83 in one year. So receiving $1,000 today is not the same as receiving $1,000 a year from now - the first is more valuable.

Future Value

The question “what will this money be worth later?” is answered by the future value formula:

FV = PV × (1 + i)^n

Where:

• FV = future value
• PV = present value (today’s amount)
• i = interest rate per compounding period
• n = number of compounding periods

Example: $1,000 today, 12% annual return compounded monthly (1% per month), held for 12 months.

FV = $1,000 × (1 + 0.01)^12 FV = $1,000 × 1.126825 FV = $1,126.83

The book shares a real story from J. He was selling a property for $120,000 and an investor offered to buy it but couldn’t pay for seven months. J used the FV formula to figure out that $120,000 now was equivalent to about $129,401 in seven months (at his 13% annual lending rate). He countered at $130,000 for a seven-month wait, the investor agreed, and the deal actually closed five months early, increasing J’s effective return even more.

Present Value

The flip side: “what is that future money worth to me right now?”

PV = FV ÷ (1 + i)^n

Say someone offers you $1,000 a year from now. You could earn 12% compounded monthly on your money otherwise. How much would you pay today for that future $1,000?

PV = $1,000 ÷ (1 + 0.01)^12 PV = $1,000 ÷ 1.126825 PV = $887.45

So $887.45 today equals $1,000 a year from now, assuming you can earn 1% per month. Pay more than $887.45 for that $1,000 promise and you’re getting a worse deal than your alternative investment. Pay less and it’s a great deal.

The Discount Rate

When you use PV to work backwards from a future value, the interest rate is sometimes called the discount rate. Same math, slightly different framing. You’re “discounting” a future value back to what it’s worth today.

The discount rate you choose matters a lot. It typically represents:

• The return you could earn elsewhere (your opportunity cost), or
• The return you need to make a deal worth doing (your “hurdle rate”)

If you believe you can reliably earn 10% on your money elsewhere, then 10% is your discount rate. Any investment that doesn’t beat that rate isn’t worth your capital.

Why This Matters for Real Estate

Every time you evaluate a property, you’re dealing with TVM questions:

• How much should you pay today for a stream of future rental income?
• Is a seller’s deferred-payment offer worth accepting?
• Would you rather have a lower price now or higher payments later?

The PV and FV formulas give you a framework to answer those questions with actual numbers instead of gut feelings. The next chapters build on TVM to create even more powerful analysis tools.

Quick Reference

Future Value:

FV = PV × (1 + i)^n

Present Value:

PV = FV ÷ (1 + i)^n

Expected Value:

EV = (E1 × P1) + (E2 × P2) + ... + (En × Pn)

These are the building blocks. Keep them in mind as we move into discounted cash flow analysis, which takes TVM and applies it to real multi-year investment scenarios.

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