Discounting and Firm Value

Education Program Lecture 6

November 14, 2026

Time Value of Money

Time Value of Money

Question: Would you rather have $100 now or $100 later?

Time Value of Money

Question: Would you rather have $100 now or $100 later?

ANSWER: $100 Today. Money today is worth MORE than money tomorrow. In other words, $100 today is worth more than $100 in 5 years.

• Many people misunderstand this point and think that future money is less valuable because of inflation. While inflation also makes future money less valuable today, the REAL reason is that you could invest money today and earn more in the future.
• Invest in the stock market, treasury / corporate bonds, savings account, etc.
• Cash Flows in the future are worth less to me today, the day of my investment decision (Both timing and magnitude of cash flows matters)

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Time Value of Money

Question: Would you rather have $100 now or $100 later?

ANSWER: $100 Today. Money today is worth MORE than money tomorrow. In other words, $100 today is worth more than $100 in 5 years.

• Many people misunderstand this point and think that future money is less valuable because of inflation. While inflation also makes future money less valuable today, the REAL reason is that you could invest money today and earn more in the future.
• Invest in the stock market, treasury / corporate bonds, savings account, etc.
• Cash Flows in the future are worth less to me today, the day of my investment decision (Both timing and magnitude of cash flows matters)

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QUICK EXERCISE!

Time Value of Money

South Korea Real Estate System:

전세 (Jeon-se)

월세 (Wol-se)

You pay an upfront deposit for 50-80% of the apartment’s value, but you pay no monthly rent, and you get the deposit back at the end.

You pay an upfront deposit for 5-10% of the apartment’s value, but you pay monthly rent, and you still get that deposit back at the end.

• Deposit of $150K (75% of apartment’s value).

• No monthly rent.

• Get back $150K deposit after 2 years.

Let’s use some specific numbers and say that the apartment is worth $200,000 ($200K).

• Deposit of $10K (5% of apartment’s value).

• Monthly rent of $1K.

• Get back $10K deposit after 2 years.

Which option would you choose and why?

Time Value of Money

The answer is that it depends, but it will probably worth more to choose the second option.

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• Because $150K received back in 2 years is worth LESS than $150K today. Even if we receive back “the same amount” in the future, it’s worth less than it is today
• Paying $140K more for the deposit means that you CANNOT invest that $140K elsewhere and earn something with it. So, there’s an opportunity cost associated with a higher deposit.

Invested 140,000 into high-yield investments, returning 10% every year

Present Value

Since money today is worth more than money tomorrow, you must discount future money to its value today, or its “Present Value,” when you’re analyzing it.

Example: What is the $150,000 deposit that I will receive back in 2 years actually worth today?

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Depends on your opportunity cost… But going with the fact that you’re earning 10% each year for 2 years:

• PV of Payoff:
• -$150,000 + $150,000 / (1+10%)^2 = -$150,000 + $123,966.94
• = ~ - $26,000

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Meanwhile…

• PV of Payoff:
• - $10,000 - $12,000/(1+10%) - $12,000/(1+10%)^2 + $10,000/(1+10%)^2 = -$22,561.98
• = ~ - $22,562
• But we are forgetting the 2 Year Pay-Off $140,000 * (1+10%)^2 = $169,400
• It’s present value is $140,000…. why?
• So total PV of Payoff is: $140,000 - $22,562 = $117, 438

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Present Value, IRR, and WACC

Present Value, IRR, and WACC

Since money today is worth more than money tomorrow, you must discount future money to its value today, or its “Present Value,” when you’re analyzing it.

The “opportunity cost” is called the Discount Rate, and it depends on your other, similar investment options

• It matters because it lets you calculate present value (aka. What the future cash flow is worth today)
• Put simply, present value is essentially calculating the intrinsic value of an asset (comparing it to the asking price to make an investment decision)
• A higher discount rate means risk and potential returns are both higher.
• Ex: Stock market, your discount rate (potential return) will be high as annual return has been 10%, but it also means your risk is also quite high.
• In real life, no investor just invests in one asset class, we look at the weighted average of these discount rate across all the asset classes, aka WACC or Weighted Average Cost of Capital

What do all these terms mean?

= Discount Rate (of future cash flows)

= “Opportunity Cost” (for investors)

= Required Rate of Return (for investors)

= Cost of capital (for companies)

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Present Value, IRR, and WACC

What about for companies? What are the two funding options for companies?

• Equity means that the company will raise money by selling stock to investors. In exchange, each investor will own a small percentage of the company.
• Debt means that the company will raise money by borrowing it from lenders. The lenders do not own any portion of the business, but they receive interest payments, and they get their entire principal back in the future.
• WACC: A way to measure the total cost a company has to bear against the capital received from debt and equity weighted by the percentage it contributes to the total capital, added together.

E = Market Value of Equity

D = Market Value of Debt

R_e = Cost of Equity

R_d = Cost of Debt

T = Tax Rate

We’ll go into more detail on this formula in future lectures

Equity and Enterprise Value

Equity and Enterprise Value

When valuing a company, we can choose to value the entire firm (enterprise value) or only the equity in the firm

Equity Value:

• The value of the residual claim on the company’s assets
• The value of only the equity in the firm

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Enterprise Value:

• The value of all of the company’s operating assets
• The value of the entire firm (what an acquirer would have to pay to buy the business)

Equity Value

The value of Everything a company has (Net Assets), but only to Equity Investors

• If the company’s capital structure (% of Equity vs. Debt) changes, the Equity Values changes

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• Method of calculation for current equity value:
• Method #1: Equity Value = Market Cap = Current Share Price * Shares Outstanding
• Method #2: Market Value of Total Assets - Market Value of Total Liabilities
• Method #3: Company’s value in its last round of funding or its valuation in an outside appraisal (for private companies). 
• Equity Value changes only if Common Shareholders’ Equity changes; if it does, both CSE and Equity Value change by the same amount
• Equity value is concerned with what is available to equity shareholders. Debt and debt equivalents, non-controlling interest, and preferred stock are subtracted as these items represent the share of other shareholders.

Enterprise Value

The value of the company’s core business operations (Net operating Assets = Operating Assets - Operating Liabilities), but to all investors (Equity, debt, preferred, and possibly others).

• It excludes non-operating assets and non-operating liabilities. 
• We use enterprise value when analyzing companies because it lets us reach the same conclusion without worrying about the company’s capital structures. 
• Method of Calculation for current enterprise value:
• Enterprise Value = Market Value of Assets – Market Value of Liabilities – Non-Operating Assets + Liability and Equity Items That Represent Other Investor Groups
• Enterprise Value = Current Equity value + Debt + Preferred Stock + Noncontrolling interests - Cash & Investments
• Cash and cash equivalents are assumed to be nonoperating assets you do not need to run core operations of the business
• Other non-operating assets: Financial investments, owned properties, side businesses, assets held for sale associated with discontinued operations, equity investments, non-operating losses
• An Asset is Non-Core or Non-Operating if the company does not need that Asset to sell products/services and deliver them to customers.

Example

Next Time: Valuation Part 1

• Next week we’ll begin to discuss how to compute Equity and Enterprise Value
• If you have questions, please feel free to reach out to Presidents Tao (tazhu@princeton.edu) and Kate (kateliu@princeton.edu) or Director of Education Erica (ehsueh@princeton.edu)