Actuarial Mathematics for Modelling · Financial instruments and insurance contracts as cashflow models

Equities, Property and Other Real Assets as Cashflow Models

Updated 11 October 2026 · Fact-checked

Equities pay uncertain, usually growing dividends plus a capital value at sale. Property pays rent that is often reviewed upwards, plus a sale value. Neither has a fixed amount or fixed redemption date like a bond. You model expected cashflows with growth assumptions, then discount at a rate that reflects the risk.

Understand Equities, Property and Other Real Assets

A fixed interest asset such as a bond promises amounts and dates in advance. The issuer must pay them. Your only real uncertainty is default. Equities and property make no such promise, so their cashflows are uncertain in both amount and, sometimes, timing.

An equity (share) gives you part ownership of a company. Your cashflows are dividends, which the company chooses to pay and which can rise, fall or stop, and the sale price when you sell. A share has no maturity date. In theory it can pay dividends forever. So you value it as a stream with no end, or you value it up to a chosen sale date.

Property gives you rent from tenants and a sale proceeds value at the end of your holding period. Rents are usually set by lease and reviewed at intervals, often upwards when inflation or demand rises. Property also brings costs: maintenance, management and void periods when nobody rents it. These reduce the net income. Property is hard to trade quickly, so it is illiquid and the sale value is uncertain.

Cash deposits sit at the other end. The capital is stable in money terms, and interest is paid at a rate that may change. Capital value is safe, but the income can vary as rates change, so a deposit is not fully risk-free over the long term.

In actuarial modelling you do not know the actual cashflows, so you work with expected cashflows under stated assumptions, such as a dividend growth rate or a rent review pattern. Because equities and property tend to grow with the economy, they are often seen as a real-return asset, meaning they may keep pace with inflation better than fixed money amounts. That is a tendency, not a guarantee. You should always say this clearly in written answers.

Key rules to remember

Present value of dividends with constant growth (Gordon model): P₀ = D₁ ÷ (i − g), for i > g; D₁ is the dividend due one year from now, g is the constant annual growth rate, i is the effective annual discount rate. Needs dividends to start in one year and continue forever.
Dividend growth: Dₜ = D₀ × (1 + g)ᵗ; Dividend in year t if growth is a constant g each year.
Present value of equity over a holding period: P₀ = Σ Dₜ vᵗ + S × vⁿ, where v = 1 ÷ (1 + i); Dividends for t = 1 to n plus the expected sale price S at time n.
Net rental income: Net rent = gross rent − costs (maintenance, management, voids); Value property on net income, not on gross rent.
Present value of property over a holding period: P₀ = Σ Rₜ vᵗ + S × vⁿ, where Rₜ is net rent; Rent review changes Rₜ in steps, not smoothly, so list the years that apply.
Rent in advance: Rent paid at start of each period is valued like an annuity-due; Check payment timing carefully; property rent is often paid in advance.

How to solve Equities, Property and Other Real Assets questions

Use this method for any question on equity, property or cash cashflows.

1Identify the asset and list its cashflow types: dividends or interest, rent, costs, sale or redemption value.
2Mark each cashflow as certain, uncertain, or dependent on inflation or growth. Note the timing: start or end of period.
3Write the stated assumptions: growth rate g, rent review dates, costs, sale price, holding period.
4Build the expected cashflow for each time point, applying growth or review rules exactly as given.
5Discount each expected cashflow at the stated rate, or use a formula such as D₁ ÷ (i − g) if it applies.
6Add the present values and check the answer is sensible in size.
7If asked to compare with bonds, state the difference in certainty, growth, term and liquidity.

Quickest way: Gordon formula shortcut and cashflow table

When to use it: Use when dividends or rents grow at a constant rate for ever, or when you have only a few periods to list.

Check the conditions: constant growth g, first cashflow one period away, and i > g.
Apply P₀ = D₁ ÷ (i − g) and stop.
If the horizon is finite or growth changes, write a short table of year, cashflow and discount factor.
Sum the discounted values and add the discounted sale price.
Do a quick reasonableness check: a higher g or lower i should give a higher value.

Common mistakes in Equities, Property and Other Real Assets

Using D₀ instead of D₁ in the Gordon formula.
The question gives the dividend just paid, and students plug it in directly.
Fix: Compute D₁ = D₀ × (1 + g) first, then divide by (i − g).
Treating equity cashflows as guaranteed like bond coupons.
Students carry the fixed interest mindset into every asset.
Fix: Say that dividends and sale prices are uncertain and that you are valuing expected amounts under assumptions.
Valuing property on gross rent.
The costs are mentioned briefly in the question and get missed.
Fix: Subtract maintenance, management and void allowances before discounting.
Applying the Gordon formula when i ≤ g.
The formula looks like it always works.
Fix: Check i > g first. If not, the infinite sum does not converge and the formula is invalid.
Applying a rent review in the wrong year.
Students grow the rent every year when it only changes at review dates.
Fix: Keep rent constant between reviews and change it only in the review year.
Forgetting the sale value at the end of the holding period.
Students focus on income and ignore the capital cashflow.
Fix: Always add S × vⁿ when the asset is sold at time n.

Worked examples

Example 1

A share has just paid a dividend of ₹10. Dividends are expected to grow at 4% a year for ever, with the next dividend due in one year. Find the present value at an effective annual rate of 9%.

Show the solution

D₀ = 10, g = 0.04, i = 0.09, so i > g and the formula applies.
D₁ = 10 × 1.04 = 10.40.
P₀ = D₁ ÷ (i − g) = 10.40 ÷ (0.09 − 0.04).
P₀ = 10.40 ÷ 0.05 = 208.

Answer: ₹208

Example 2

A property is bought to be held for 3 years. Net rent is ₹1,00,000 a year, paid at the end of each year, with no change during the period. It is then sold for ₹20,00,000. Find the present value at an effective annual rate of 10%.

Show the solution

v = 1 ÷ 1.10 = 0.909091.
Rent annuity: 1,00,000 × a₃ at 10%, where a₃ = (1 − v³) ÷ 0.10.
v³ = 1 ÷ 1.331 = 0.751315, so a₃ = 0.248685 ÷ 0.10 = 2.48685.
PV of rent = 1,00,000 × 2.48685 = ₹2,48,685.
PV of sale = 20,00,000 × 0.751315 = ₹15,02,630.
Total = 2,48,685 + 15,02,630 = ₹17,51,315.

Answer: About ₹17,51,315

Exam tips

In written questions, always add a sentence on how the asset differs from a bond: uncertain amount, no fixed term, possible growth, liquidity.
State every assumption you use, such as constant growth or rent paid annually in arrears.
Check payment timing before choosing annuity-immediate or annuity-due.
In MCQs, watch for options that confuse D₀ with D₁ or gross with net rent.
Show the formula in notation first, then the numbers, then the result with the unit.

Practice questions from Financial instruments and insurance contracts as cashflow models

Equities, Property and Other Real Assets in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

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Equities, Property and Other Real Assets: frequently asked questions

How do equity cashflows differ from bond cashflows?

Bond cashflows are fixed in amount and date by contract. Equity dividends are uncertain, usually grow over time, and have no maturity date. The sale price of a share is also uncertain.

How are dividends modelled in actuarial work?

You usually assume a dividend now and a growth rate, then project expected dividends. A constant growth rate gives a simple stream you can discount with the Gordon formula if i > g.

Why is property cashflow harder to model than a bond?

Rent depends on leases and reviews, there are costs and void periods, and the sale value is uncertain. Property is also illiquid, so selling may take time.

Are equities and property protected against inflation?

They often tend to keep pace with inflation over the long term because dividends and rents may rise with prices. This is not guaranteed, so state it as a tendency.