Real Interest Rates and Business Investment

Why Real Interest Rates Matter for Investment

A firm considering a new machine, facility, or software system weighs the expected return from using that capital against the cost of funds tied up in the project. That cost is not just the interest rate printed in a loan offer. If prices are expected to rise, part of a nominal interest payment compensates lenders for the expected loss of purchasing power. The relevant baseline comparison is therefore between a project’s expected real return and its real financing or opportunity cost.

This comparison helps explain why a higher real interest rate can reduce investment spending: some projects that were worthwhile at a lower hurdle rate no longer offer a sufficient expected return. The decision also depends on risk, taxes, depreciation, and other project-specific factors, so the basic comparison is a model rather than a complete description of every firm’s decision. This treatment is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.

Definition: The ex ante real interest rate is the purchasing-power-adjusted rate of return expected over a period, calculated using expected inflation over that same period. In a one-year model, let $i$ be the effective annual nominal interest rate, let $\pi^e$ be expected annual inflation, and let $r$ be the ex ante real interest rate. Then $1+r=(1+i)/(1+\pi^e)$, so $r=(1+i)/(1+\pi^e)-1$.

The formula assumes that $i$ and $\pi^e$ refer to the same one-year period and that inflation is measured by the price index relevant to the purchasing power being considered. The project return and financing cost must also use a consistent period and real-versus-nominal basis. When rates are small, $r$ is often approximated by $i-\pi^e$, but the ratio formula gives the exact result under these assumptions.

Why the Fisher Conversion Works

The exact formula follows from comparing what one unit of purchasing power can buy at the start and end of the year. Start with one unit of real funds. At nominal rate $i$, it becomes $1+i$ units of money. If the price level is expected to rise by $\pi^e$, the expected price index at year-end is $1+\pi^e$ times its initial level. Dividing the nominal amount by that price-level change gives its expected value in initial purchasing power:

1+r=\frac{1+i}{1+\pi^e} \qquad\Longrightarrow\qquad r=\frac{1+i}{1+\pi^e}-1

This is an ex ante rate because it uses expected inflation, not the inflation that eventually occurs. The ex post real rate instead uses realized inflation. In a firm’s decision, expected inflation matters when the firm commits to a nominal loan or evaluates future nominal receipts before the inflation outcome is known.

Comparing a Project Return with Its Real Hurdle

For a simple project comparison, suppose the firm knows its real cost of capital today and has an estimate of the project’s expected real return over the same period. Assume the project’s return is net of operating costs, the return and financing rate cover the same horizon, and the firm compares projects with comparable risk. In this baseline model, a project is attractive if its expected real return exceeds the real hurdle rate. A return below the hurdle does not compensate for the cost of funds; equality leaves the firm indifferent in the simplified model.

In practice, the relevant hurdle may include a risk premium, taxes, or other costs. A firm should not compare a risky project’s raw expected return with a safe borrowing rate as if risk were irrelevant. Funds supplied by owners also have an opportunity cost: using retained earnings for one project means they cannot be used for another investment or returned to owners. “Internal funds” do not automatically make a project costless.

Worked Example: Converting a Loan Rate and Testing a Project

A firm can borrow at an effective annual nominal rate of 8%. Expected inflation over the coming year is 2%. A proposed equipment upgrade costs $100,000 in today’s purchasing power and is expected to generate a net real value of $106,500 one year later. Assuming comparable risk and a one-year horizon, should the firm proceed under the baseline rule?

Method: convert the nominal financing rate to a real rate, then compare returns. First calculate the exact ex ante real rate:

r=\frac{1.08}{1.02}-1 =\frac{1.08-1.02}{1.02} =\frac{0.06}{1.02} =0.0588235\ldots

The real financing hurdle is about 5.8824% per year. The project’s expected real return is calculated from its expected real gain relative to its real cost:

\frac{\$106{,}500-\$100{,}000}{\$100{,}000} =\frac{\$6{,}500}{\$100{,}000} =0.065 =6.5\%

Since 6.5% is greater than 5.8824%, the expected real return exceeds the real financing rate by about 0.6176 percentage points. Under the stated assumptions, the firm should proceed. This comparison avoids treating the 8% nominal rate as if it were the real cost of borrowing.

Check: The calculation uses a one-year nominal rate and one-year expected inflation. The project return and financing hurdle are both expressed in real annual terms, and the project’s $6,500 real gain is 6.5% of its $100,000 real cost.

How a Higher Real Rate Can Reduce Investment

Firms typically have projects with different expected returns. A firm or economy can rank potential projects from highest to lowest risk-adjusted expected real return. At a given real interest rate, projects with returns above that rate meet the baseline hurdle; projects below it do not. Raising the real rate raises the hurdle, so projects near the old threshold may be postponed, scaled down, or canceled.

This is a change in the quantity of investment desired at the new financing cost: the set of projects that pass the comparison can shrink. It does not mean every firm cuts investment by the same amount, or that all investment stops. Projects with high expected returns may remain worthwhile. Nor does the simple comparison establish that interest rates are the only cause of an investment change: expected sales, technology, uncertainty, available capacity, and access to credit can also affect decisions.

Worked Example: Applying a Higher Real Hurdle to a Project List

A firm is reviewing four independent projects. The figures below give each project’s expected risk-adjusted real annual return and its required capital in millions of dollars. Assume all returns and the real financing hurdle refer to the same period, and accept projects only when expected return is strictly above the hurdle. Find planned investment at real rates of 4% and 6%.

Project	Expected real return	Capital required
A	9%	$20 million
B	7%	$30 million
C	5%	$25 million
D	3%	$40 million

Method: apply the return-above-hurdle rule separately at each rate. At a 4% real rate, Projects A, B, and C pass because $9\%>4\%$, $7\%>4\%$, and $5\%>4\%$. Project D fails because $3\%<4\%$. Planned investment is therefore:

\$20\text{ million}+\$30\text{ million}+\$25\text{ million} =\$75\text{ million}

At a 6% real rate, only A and B pass: $9\%>6\%$ and $7\%>6\%$. Projects C and D fail because $5\%<6\%$ and $3\%<6\%$. Planned investment is:

\$20\text{ million}+\$30\text{ million} =\$50\text{ million}

The higher real rate reduces planned investment in this example by $25 million, from $75 million to $50 million. The result follows from the project list, not from an assumption that every project is equally affected. The common mistake avoided here is counting projects whose returns are below the new hurdle.

Check: At 4%, three projects pass and their capital totals $75 million. At 6%, two pass and their capital totals $50 million. No project has a return exactly equal to either hurdle.

Inflation Expectations Can Change the Comparison

A nominal borrowing rate alone does not determine the real financing cost. Holding the nominal rate fixed, a higher expected inflation rate lowers the exact ex ante real rate, because the same nominal repayment is expected to have less purchasing power. This arithmetic does not imply that inflation expectations can change independently of the nominal rate in every setting. It isolates how the real-rate calculation changes when the two inputs are specified.

Worked Example: Same Nominal Rate, Different Inflation Expectations

A firm evaluates a project with an expected real return of 4%. Its effective annual nominal borrowing rate is 7%. Compare the project decision under expected inflation of 1% and 4%, using the baseline rule and assuming comparable risk.

Method: calculate the exact real rate under each inflation expectation. With expected inflation of 1%:

r_1=\frac{1.07}{1.01}-1 =\frac{0.06}{1.01} =0.0594059\ldots \approx 5.9406\%

The project’s 4% expected real return is below 5.9406%, so it fails the baseline hurdle. With expected inflation of 4%:

r_2=\frac{1.07}{1.04}-1 =\frac{0.03}{1.04} =0.0288462\ldots \approx 2.8846\%

Now the project’s 4% expected real return is above 2.8846%, so it passes. The decision changes because the expected real cost changes while the stated nominal rate and project return remain fixed. This is a conditional comparison, not a claim that firms should ignore any other effect of changing inflation expectations.

Check: In both cases, subtracting 1 is equivalent to subtracting the denominator from the numerator and then dividing by the denominator. For the second case, $1.07-1.04=0.03$, giving $0.03/1.04$, not $0.03$.

Common Mistakes and Exam Traps

Using the nominal rate as the real hurdle. If expected inflation is positive, the exact real rate is generally below the nominal rate. Convert using the same period for both rates.
Subtracting inflation as if the approximation were exact. The shortcut $r\approx i-\pi^e$ can be useful for small rates, but the exact one-year relation is $r=(1+i)/(1+\pi^e)-1$.
Subtracting 1 incorrectly. For example, with $i=8\%$ and $\pi^e=2\%$, $1.08/1.02-1$ equals $(1.08-1.02)/1.02=0.06/1.02$, or about 5.8824%. It does not equal 6%: the difference in the numerator must still be divided by $1.02$.
Mixing real and nominal project returns. A nominal expected return should not be compared directly with a real financing rate. Put both quantities on a consistent purchasing-power basis and over the same horizon.
Ignoring risk and opportunity cost. A project with a higher raw expected return is not automatically worthwhile if its risk, taxes, or other costs require a larger hurdle. Internal funds still have alternative uses.

Key takeaway: In the baseline model, a firm compares a project’s expected real return with its real financing or opportunity cost. A higher real rate raises the hurdle, so fewer projects in a ranked set may qualify. The comparison is informative only when rates, returns, periods, and risk treatment are made consistent.

Check Your Understanding

For each problem, use the exact one-year real-rate formula when inflation expectations are given. Treat the stated project return as risk-adjusted and apply the strict return-above-hurdle rule.

A firm faces an effective annual nominal borrowing rate of 6% and expected inflation of 2%. Its project’s expected real return is 3.8%. Find the real rate and state whether the project passes. (Answer: real rate $=3.9216\%$; it does not pass.)
A small manufacturer’s nominal financing rate is 9%, with expected inflation of 5%. A retrofit is expected to earn 4.2% in real terms. Calculate the real rate and determine whether the retrofit passes. (Answer: real rate $=3.8095\%$; the retrofit passes.)
A real-rate hurdle is 5.5%. Four independent projects have expected real returns of 8%, 6%, 4%, and 3%, with required capital of $12 million, $18 million, $22 million, and $15 million, respectively. What is planned investment? (Answer: $30 million.)
A nominal rate is 5%, expected inflation is 3%, and a project’s expected real return is 2%. Compute the real financing rate and decide whether to proceed under the baseline rule. (Answer: real rate $=1.9417\%$; the project passes.)
A project’s expected real return is 5.5%. The nominal rate is 10%. Compare its status when expected inflation is 2% and when it is 6%. (Answer: at 2% inflation, the real rate is $7.8431\%$ and the project fails; at 6% inflation, the real rate is $3.7736\%$ and the project passes.)

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