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VEE Accounting and Finance · Project and Divisional Discount Rates · Tutorial 692 of 996

Consequences of Applying a Companywide Hurdle Rate

Learn to identify when a companywide hurdle rate distorts project NPV and how to compare the resulting decisions with project-specific required returns.

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What You'll Learn

  • Explain why a single companywide hurdle rate is appropriate only for projects with comparable risk and financing characteristics.
  • Calculate and compare project NPVs using companywide and project-specific required returns.
  • Identify how an excessive discount rate can cause a safer value-creating project to be rejected.
  • Identify how an insufficient discount rate can cause a riskier value-destroying project to be accepted.
  • Apply a consistent decision rule and avoid common hurdle-rate interpretation errors.

Why One Companywide Hurdle Rate Can Mislead

A companywide hurdle rate is a convenient screening rule, but it is not automatically the right rate for every investment. A firm may have a stable core business and also consider projects with substantially different operating risks. Applying the same rate to both can make their NPVs look more alike than their risk-adjusted values warrant.

The direction of the distortion matters. If a project is safer than the company’s existing operations, the companywide rate may be too high, discounting its cash flows too heavily and causing managers to reject a value-creating investment. If a project is riskier, the companywide rate may be too low, making its cash flows appear too valuable and causing managers to accept a value-destroying investment. These errors can occur even when the companywide rate is a reasonable estimate for the firm’s existing business.

Definition: A companywide hurdle rate is a required return used as a common investment-screening rate across a firm. A project-specific required return is the rate appropriate to the risk of a project’s operating cash flows and its relevant financing policy. A project’s net present value (NPV) is the present value of its expected incremental cash flows, discounted at the rate appropriate to that project, less its initial investment.

For a conventional investment with an initial outflow followed by nonnegative future cash flows, the NPV at required return \(k\) is

$$ \operatorname{NPV}(k)=-I_0+\sum_{t=1}^{n}\frac{E[CF_t]}{(1+k)^t}, $$

where \(I_0\) is the initial investment, \(E[CF_t]\) is the expected cash flow at time \(t\), and \(k\) is an annual effective rate consistent with the timing and risk of those cash flows. Accepting a project when its appropriately measured NPV is positive is the relevant value-creation rule. The companywide rate is suitable only when the project’s risk and financing characteristics are sufficiently comparable to those represented by that rate. It is not a general-purpose rate for every proposal.

How the Wrong Rate Changes Project Value

For positive future cash flows, increasing the discount rate reduces their present value. Each cash flow is divided by a larger accumulation factor, so the NPV falls. The calculation therefore has a predictable direction when comparing rates for a conventional project: using a rate above the project-specific rate understates its NPV; using a rate below the project-specific rate overstates its NPV.

A level perpetuity makes the effect especially transparent. Assume a project pays a constant amount \(C\) at each year-end forever, with the first payment one year from now, and has a constant positive required return \(k\). Its present value is

$$ PV=\frac{C}{1+k}+\frac{C}{(1+k)^2}+\frac{C}{(1+k)^3}+\cdots=\frac{C}{k}. $$

To justify the result, let \(v=1/(1+k)\). The present value is the infinite geometric series \(Cv+Cv^2+Cv^3+\cdots\). For \(k>0\), \(0<v<1\), so the series converges to \(Cv/(1-v)\). Since \(v/(1-v)=[1/(1+k)]/[k/(1+k)]=1/k\), the value is \(C/k\). This formula assumes level payments forever, paid at year-end, beginning one year from now, and a constant positive discount rate. It does not apply without adjustment to a finite-lived project, a growing perpetuity, or cash flows whose timing differs.

Worked Example: A Safer Project Is Rejected at the Company Rate

A hypothetical insurer is considering a project that costs $250,000 today and is expected to pay $24,000 at each year-end forever, beginning one year from now. The companywide hurdle rate is 12%, but the project-specific required return is 8%. Determine the NPV under each rate and explain the decision error. Assume level perpetual cash flows and constant annual effective rates.

Method. Apply the perpetuity formula at each rate, then subtract the initial cost. The common mistake is to use the companywide rate simply because it is the firm’s usual screening rate, without checking whether the project has comparable risk.

At the project-specific rate of 8%, the present value of the inflows is

$$ PV_{\text{project}}=\frac{\$24{,}000}{0.08}=\$300{,}000. $$

Therefore, the appropriate NPV is \(\$300{,}000-\$250{,}000=\$50{,}000\). The project creates value at its risk-appropriate rate.

At the companywide rate of 12%, the same expected cash flows have present value

$$ PV_{\text{company}}=\frac{\$24{,}000}{0.12}=\$200{,}000. $$

The companywide-rate NPV is \(\$200{,}000-\$250{,}000=-\$50{,}000\). Thus, the common rate changes the decision from accept to reject and understates NPV by \(\$100{,}000\). Because this project is safer than the company’s typical operations, the higher companywide rate discounts its cash flows too severely.

Check. The inflow is positive and the companywide rate exceeds the project rate, so its present value must be lower: \(\$200{,}000<\$300{,}000\). The calculated values have the expected ordering.

Worked Example: A Riskier Project Is Accepted at the Company Rate

A hypothetical firm can invest $250,000 in a project expected to pay $32,000 at each year-end forever, beginning one year from now. The project-specific required return is 16%; the companywide hurdle rate is 12%. Calculate both NPVs and identify the consequence of using the companywide rate. Assume level perpetual cash flows and constant annual effective rates.

Method. Value the perpetuity separately at the project-specific and companywide rates. The trap is to treat a positive NPV at the firm’s usual rate as sufficient, even though that rate does not reflect this project’s higher risk.

At the project-specific rate of 16%,

$$ PV_{\text{project}}=\frac{\$32{,}000}{0.16}=\$200{,}000, \qquad \operatorname{NPV}_{\text{project}}=\$200{,}000-\$250{,}000=-\$50{,}000. $$

At the companywide rate of 12%,

$$ PV_{\text{company}}=\frac{\$32{,}000}{0.12}=\$266{,}666.6667, \qquad \operatorname{NPV}_{\text{company}}=\$266{,}666.6667-\$250{,}000=\$16{,}666.6667. $$

Rounded to the nearest cent, the companywide-rate NPV is $16,666.67, whereas the project-specific NPV is −$50,000. The appropriate decision is to reject because the project-specific NPV is negative. Using the companywide rate would falsely indicate that the project creates value and would lead to acceptance.

Check. The companywide rate is lower than the project’s required return, so it must produce a higher present value of positive inflows. The companywide value of $266,666.67 exceeds the project-specific value of $200,000, as expected.

Comparing Rates in a Finite Project

The same issue arises for projects with finite cash flows. Calculate each dated cash flow at its own discount factor, keeping the payment timing unchanged. Do not use the companywide rate for one year and the project-specific rate for another; that would not represent either consistent valuation model.

Worked Example: A Finite Safer Project Has Opposite Decisions

A hypothetical project costs $190,000 now and is expected to generate $80,000 at the end of each of the next three years. Its project-specific required return is 10%, while the companywide hurdle rate is 15%. Find both NPVs and determine whether the companywide rate changes the decision. Assume annual year-end cash flows and constant annual effective rates.

Method. Discount each of the three inflows at the same rate for the valuation being calculated, sum the present values, and subtract the initial cost. The common mistake is to round each intermediate present value too early or to assume that the rate difference cannot change the accept/reject outcome.

At 10%, the present values of the inflows are

$$ \frac{\$80{,}000}{1.10}=\$72{,}727.2727,\quad \frac{\$80{,}000}{1.10^2}=\frac{\$80{,}000}{1.21}=\$66{,}115.7025,\quad \frac{\$80{,}000}{1.10^3}=\frac{\$80{,}000}{1.331}=\$60{,}105.1841. $$

Using unrounded values, their total present value is $198,948.1593. The NPV at the project-specific rate is \(\$198{,}948.1593-\$190{,}000=\$8{,}948.1593\), or $8,948.16 to the nearest cent. The project should be accepted.

At 15%, the corresponding present values are

$$ \frac{\$80{,}000}{1.15}=\$69{,}565.2174,\quad \frac{\$80{,}000}{1.15^2}=\frac{\$80{,}000}{1.3225}=\$60{,}491.4934,\quad \frac{\$80{,}000}{1.15^3}=\frac{\$80{,}000}{1.520875}=\$52{,}601.2986. $$

Their total, using unrounded values, is $182,658.0094. Thus the companywide-rate NPV is \(\$182{,}658.0094-\$190{,}000=-\$7{,}341.9906\), or −$7,341.99 to the nearest cent. The companywide rate would cause the firm to reject a project that has positive NPV at its appropriate rate.

Check. Every future cash flow is positive, and 15% exceeds 10%, so the total present value at 15% must be lower. The results, $182,658.01 versus $198,948.16, satisfy this condition.

Why the Distortion Occurs

For a conventional project with nonnegative future cash flows, compare the NPVs at a companywide rate \(k_c\) and project-specific rate \(k_p\):

$$ \operatorname{NPV}(k_c)-\operatorname{NPV}(k_p) = \sum_{t=1}^{n} E[CF_t] \left[ \frac{1}{(1+k_c)^t}-\frac{1}{(1+k_p)^t} \right]. $$

The initial investment cancels because it is the same under both valuations. If \(k_c>k_p\), then for each \(t\geq 1\), \((1+k_c)^t>(1+k_p)^t\), and hence \((1+k_c)^{-t}<(1+k_p)^{-t}\). Multiplying by a nonnegative expected cash flow makes each bracketed contribution nonpositive. Therefore \(\operatorname{NPV}(k_c)\leq\operatorname{NPV}(k_p)\). If \(k_c<k_p\), the inequalities reverse, so the companywide rate overstates NPV. The comparison relies on conventional cash flows; with later negative cash flows, the direction of the effect need not be uniform.

The rate difference represents a difference in required compensation for risk, not a change in the project’s cash-flow forecast. Project discount rates should reflect the risk of the project’s cash flows and the relevant financing assumptions. In particular, the companywide rate should not be treated as an automatic minimum for every investment. A low-risk project can be attractive even if its return falls below the companywide rate, while a high-risk project can destroy value even if its return exceeds that rate.

This does not mean that managers should choose whichever rate produces a preferred decision. The project-specific rate must be supported by a defensible assessment of risk and financing policy. Estimating it poorly can also distort NPV. The practical question is whether the companywide rate is a suitable proxy for the project, not whether a different rate would make the proposal pass a screen.

Decision Process and Common Exam Trap

1
Describe project risk.
Compare the project’s operating risk and relevant financing characteristics with those represented by the companywide rate.
2
Select the appropriate required return.
Use a project-specific rate when the project’s risk differs materially from the company’s existing operations.
3
Calculate NPV consistently.
Discount the project’s expected incremental cash flows at the selected rate, with periods and cash-flow timing matched.
4
Compare the decision, not just the rates.
Positive NPV supports acceptance and negative NPV supports rejection when the rate is appropriate. State whether the companywide rate changes the decision and in which direction.

Common mistake: “The project earns more than the companywide rate, so it must create value.” This comparison is not sufficient if the project is riskier than the firm’s existing operations. For a project whose appropriate required return is 16%, comparing its return only with a 12% companywide rate can make a risky investment look attractive when its risk-adjusted NPV is actually negative. The correction is to value it at the rate appropriate to its risk and then apply the NPV decision rule.

Key takeaway: A companywide hurdle rate can overstate safer projects’ discount rates and understate riskier projects’ discount rates. Match the required return to project risk before interpreting NPV; otherwise, a common screening rule can reject value creation and approve value destruction.

Check Your Understanding

For each problem, compare the companywide-rate result with the project-specific result. Assume annual effective rates and year-end cash flows where applicable.

  1. A hypothetical low-risk project costs $180,000 and pays $18,000 at each year-end forever, beginning one year from now. Its project-specific rate is 9%, and the companywide rate is 12%. Find both NPVs and state whether the common rate changes the decision. (Answer: Project-specific NPV = $20,000; companywide NPV = −$30,000; the companywide rate causes a value-creating project to be rejected.)
  2. A hypothetical high-risk project costs $300,000 and pays $39,000 at each year-end forever, beginning one year from now. Its project-specific rate is 15%, and the companywide rate is 10%. Find both NPVs and state the error from using the companywide rate. (Answer: Project-specific NPV = −$40,000; companywide NPV = $90,000; the companywide rate falsely supports acceptance.)
  3. A project costs $150,000 and pays $90,000 at the end of each of the next two years. The project-specific rate is 8%, and the companywide rate is 14%. Calculate both NPVs to the nearest cent and identify the decision change. (Answer: Project-specific NPV = $10,493.83; companywide NPV = −$1,800.55; the companywide rate changes acceptance to rejection.)
  4. A hypothetical risky project costs $240,000 and pays $30,000 at each year-end forever, beginning one year from now. Its project-specific rate is 14%, while the companywide rate is 10%. Calculate both NPVs and explain why their signs differ. (Answer: Project-specific NPV = −$25,714.29; companywide NPV = $60,000; the companywide rate is too low for the project’s risk and falsely indicates value creation.)

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