A project generates $100 forever with certainty and cash flows grow at the inflation rate. The nominal interest rate is 4% (real interest rate = 2% and inflation = 2%). Ignore taxes. What is the project’s value?

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BlackTom AI · Accepted Answer

The problem describes a perpetuity that pays $100 every period and whose cash flows grow at the inflation rate. Since the nominal discount rate is 4% and the cash flows grow at g = 2%, we can use the growing perpetuity formula with the standard convention that the first cash flow occurs at t = 1.

Option by option analysis:
- Infinity: This would require that the discount rate minus the growth rate be zero or negative (i > g is necessary for convergence). Here i = 4% and g = 2%, so i − g = 2% > 0. Therefore the present value is finite, not infinite.

- $2500: If one erroneously uses a denominator of i − g = 0.04 − 0.04 or misapplies the formula, one might land at 2500, but the correct difference is 0.04 − 0.02 = 0.02. With the first cash flow being 100, this option does not align with the correct calculation.

- $5000: This matches the standard formula PV = CF1 / (i − g) when CF1 = 100 (the first cash flow at t = 1) and i − g = 0.04 − 0.02 = 0.02. Computing 100 / 0.02 gives 5000, which is the correct present value under the given assumptions.

- $10,000: This would require a larger numerator or a smaller denominator. If someone uses CF1 = 100 and i − g = 0.01, they could reach 10,000, but the actual i − g here is 0.02, not 0.01, so 10,000 is not correct. Alternatively, treating CF0 differently would also lead away from 10,000, so this option is inconsistent with the problem data.

Summarizing the key point: in a growing perpetuity with first cash flow 100 at t = 1, discount rate 4%, and growth 2%, the value is 100 / (0.04 − 0.02) = 5000. The other numbers arise from incorrect application of the growth formula or incorrect interpretation of the timing of the first cash flow.

IFEPIA7022_001_2025_3 - Economics of Finance EOF Final - Dec 16, 2025

A project generates $100 forever with certainty and cash flows grow at the inflation rate. The nominal interest rate is 4% (real interest rate = 2% and inflation = 2%). Ignore taxes. What is the project’s value?

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