Time Value of Money and Present Value of Expected Cash Flows

Updated for the 2026-2027 CFA® Level I curriculum.

A dollar available today can be invested and earn a return, which makes it more valuable than the same dollar received later. The time value of money gives you a consistent way to compare cash flows that occur on different dates.

For CFA Level I, the main application is present value. You will discount expected fixed-income and equity cash flows back to the valuation date, add those values, and interpret how timing and the required return affect the result.

Key Takeaways

• The time value of money connects cash flows that occur on different dates.

• Present value moves a future cash flow back to the valuation date.

• Future value moves a current amount forward through compounding.

• Each cash flow must be discounted for the correct number of periods.

• The discount rate and the cash-flow timing must use consistent time units.

• Fixed-income value commonly comes from coupon and principal payments.

• Equity value may come from expected dividends, shareholder cash flows, and a future sale or terminal value.

• A higher required return produces a lower present value, all else equal.

What You Need to Know for CFA Level I

For CFA Level I, focus on:

• Explaining why a future cash flow is worth less than an equal amount received today.

• Moving between present value and future value.

• Drawing and interpreting a cash flow timeline.

• Discounting one future cash flow or several uneven cash flows.

• Valuing fixed-income instruments from expected coupon and principal payments.

• Valuing equity instruments from expected distributions and future value.

• Matching the discount rate’s period with the timing of the cash flows.

• Interpreting how changes in the discount rate, timing, and expected amount affect present value.

What Is the Time Value of Money?

The time value of money reflects the opportunity to earn a return on funds that are available today. Receiving money earlier gives you more time to invest it, while waiting for a future payment carries an opportunity cost.

Compounding moves a current value forward through time. Discounting reverses that process and moves a future amount back to the valuation date.

The future value relationship is:

Where:

• Inline equation code = future value at the end of period

• Inline equation code = value at the current date

• Inline equation code = rate of return per period

• Inline equation code = number of compounding periods

Rearranging the equation gives the present value formula:

Where:

• Inline equation code = present value at the current date

• Inline equation code = future amount received at the end of period

• Inline equation code = discount rate per period

• Inline equation code = number of periods until the amount is received

These equations describe the same relationship from opposite directions. Compounding starts with today’s value. Discounting starts with the future amount.

How Do You Read a Cash Flow Timeline?

A cash flow timeline places each amount at the date when it occurs. The current valuation date appears at time zero, and future dates move from left to right.

A simple three-period timeline may look like this:

t = 0          t = 1          t = 2          t = 3
   |--------------|--------------|--------------|
  Valuation       CF₁            CF₂            CF₃
    date

Where:

• Inline equation code = current valuation date

• Inline equation code = end of the first period

• Inline equation code = end of the second period

• Inline equation code = end of the third period

• Inline equation code = cash flow received at time

A timeline helps you identify the correct discount exponent. A cash flow at inline equation code is discounted for one period, while a cash flow at inline equation code is discounted for three periods.

How Do You Calculate the Present Value of Expected Cash Flows?

When an instrument produces several expected cash flows, discount each payment separately and then add the results.

For a simplified valuation using one required return across all periods:

Where:

• Inline equation code = present value of the full expected cash-flow stream

• Inline equation code = expected cash flow received at time

• Inline equation code = required return or discount rate per period

• Inline equation code = number of periods until a particular cash flow is received

• Inline equation code = final period in the cash-flow stream

Each expected cash flow has its own discount exponent because each payment occurs at a different point in time.

For example, a payment received in three years is divided by inline equation code . Discounting it for only one year would overstate its current value.

How Is Present Value Used for Fixed-Income Instruments?

A standard fixed-rate bond generally provides two types of cash flows:

• Coupon payments during the bond’s life

• Repayment of principal at maturity

When one required return is used for all periods, the bond value is:

Where:

• Inline equation code = current value of the bond

• Inline equation code = coupon payment received each period

• Inline equation code = required return per period

• Inline equation code = period in which each coupon is received

• Inline equation code = total number of periods until maturity

• Inline equation code = principal or face value repaid at maturity

The final period includes both the last coupon and the repayment of principal.

Fixed-Income Example

A two-year bond has a $1,000 face value and pays a 5% annual coupon. The required annual return is 6%.

First, calculate the annual coupon:

The bond pays:

• $50 at the end of year 1

• $1,050 at the end of year 2, including the final coupon and principal

Discount both payments to the current date:

The bond’s present value is approximately $981.67.

Its 5% coupon rate is below the investor’s 6% required return, so the bond is valued below its $1,000 face value. The lower price allows the investor to earn the higher required return from the bond’s fixed payments.

How Is Present Value Used for Equity Instruments?

Equity instruments do not usually have a fixed maturity date or guaranteed principal payment. Their value depends on expected future benefits to shareholders.

Depending on the valuation model, these benefits may include:

• Expected dividends

• Expected free cash flow to equity

• Proceeds from selling the shares

• A terminal value representing cash flows beyond the explicit forecast period

For a one-period dividend and sale-price model:

Where:

• Inline equation code = current value of the equity investment

• Inline equation code = expected dividend received at the end of period 1

• Inline equation code = expected sale price at the end of period 1

• Inline equation code = required return for the period

Both expected amounts occur at the end of the same period, so they can be added before being discounted.

Equity Example

An investor expects a $2 dividend and a $40 share price one year from now. The required return is 10%.

The present value of the expected dividend and sale price is approximately $38.18.

The calculation depends on the estimated dividend and future share price. Changes in either assumption will change the current value.

How Does Present Value Differ for Fixed Income and Equity?

The discounting process is similar, but the underlying cash flows have different characteristics.

For both instrument types, the current value comes from future cash flows rather than the asset’s label. The timing, amount, risk, and required return drive the calculation.

Why Does the Discount Rate Matter?

The discount rate represents the return an investor requires for waiting and bearing the risk associated with the cash flows.

A higher discount rate applies a larger reduction to future payments. A lower discount rate leaves more of the future amount in present-value terms.

This relationship becomes stronger for cash flows that occur further in the future. A small change in the discount rate has a larger effect on a payment received in ten years than on one received next year.

Why Must the Rate and Cash-Flow Period Match?

The discount rate must use the same time unit as the cash-flow timeline.

For example:

• Annual cash flows require an annual rate.

• Semiannual cash flows require a semiannual periodic rate.

• Monthly cash flows require a monthly periodic rate.

Suppose a quoted annual rate compounds monthly. Before discounting monthly cash flows, convert the quoted rate into the applicable monthly rate and count the number of monthly periods.

Using an annual rate directly with a monthly exponent mixes two time conventions and produces an incorrect value.

Worked Example: Uneven Expected Cash Flows

An investment is expected to pay:

• $100 at the end of year 1

• $150 at the end of year 2

• $200 at the end of year 3

The required return is 8% per year.

Step 1: Discount the First Cash Flow

Step 2: Discount the Second Cash Flow

Step 3: Discount the Third Cash Flow

Step 4: Add the Present Values

Where:

• Inline equation code = value of the full cash-flow stream at the current date

• Inline equation code = present value of the year 1 cash flow

• Inline equation code = present value of the year 2 cash flow

• Inline equation code = present value of the year 3 cash flow

Substitute the calculated values:

The expected cash-flow stream has a present value of approximately $379.96.

Notice that the $200 payment has the largest dollar amount but also receives the largest discount because it arrives last.

How Should You Approach Present Value Questions?

A consistent process helps prevent most timing errors.

1. Identify the Valuation Date

Most questions use the current date, represented by inline equation code .

2. Draw the Timeline

Place every cash flow at the date when it is expected to occur.

3. Identify the Periodic Discount Rate

Confirm whether the rate is annual, semiannual, quarterly, or monthly.

4. Discount Each Cash Flow Separately

Use the number of periods between the valuation date and the payment date as the exponent.

5. Add the Present Values

Once every amount has been moved to the same valuation date, combine them.

6. Interpret the Result

Explain what the value represents and how the timing, cash flows, and required return contributed to it.

Common Exam Traps

Common mistakes include:

• Discounting every cash flow for the same number of periods.

• Placing a payment at the wrong point on the cash flow timeline.

• Adding cash flows from different dates before moving them to a common valuation date.

• Using an annual rate with monthly or semiannual periods without converting it.

• Forgetting to include the bond’s principal repayment.

• Leaving out an equity investment’s expected sale price or terminal value.

• Treating an expected equity cash flow as a guaranteed payment.

• Using the coupon rate as the discount rate without checking the required return.

• Assuming a higher discount rate produces a higher present value.

• Rounding each discounted cash flow too early and carrying the rounding error into the total.

Practice Question

A share is expected to pay a $3 dividend and sell for $55 one year from now. The required return is 10%.

The share’s present value is closest to:

1. $50.00

2. $52.73

3. $58.00

FAQs About Time Value of Money and Present Value