The choice of a discount rate is very important in calculating a cost benefit ratio. In a project where the costs are incurred in the first 5 years and the revenues grow steadily over the remaining 25 years, what will be the effect of a high discount rate (say 15%) on the stream of benefits and costs over a 30-year period, compared to a low discount rate (such as 5%)?

Select a single answer.

Question

The choice of a discount rate is very important in calculating a cost benefit ratio. In a project where the costs are incurred in the first 5 years and the revenues grow steadily over the remaining 25 years, what will be the effect of a high discount rate (say 15%) on the stream of benefits and costs over a 30-year period, compared to a low discount rate (such as 5%)?

Select a single answer.

BlackTom AI · Accepted Answer

Future cash flows are converted to present value by PV = CF / (1 + r)^t, so a higher discount rate disproportionately shrinks the present value of cash flows that occur far in the future.

1) Relevant concepts
- Present value (PV) and discounting: PV = CF/(1+r)^t.
- Time sensitivity: later-year cash flows are divided by (1+r)^t with larger t, so they fall faster as r increases.
- Cost timing: costs in years 1–5 are near-term; benefits in years 6–30 are long-term.

2) Step-by-step reasoning
- Early costs (years 1–5) are discounted only a few periods; later benefits (years 6–30) are discounted many periods. Increasing r reduces both, but the reduction is much larger for the distant benefits.

3) Calculations (intermediate steps shown) — illustrate with unit cash flows of 1 per year:
- PV of benefits as an annuity of 1 from t=6 to 30 equals PV of a 25-year annuity deferred 5 years:
  - At r = 5%: PV25 = (1 - 1/1.05^25)/0.05 ≈ 14.09; deflate to t=0 by 1/1.05^5 (≈0.7835) → PV ≈ 14.09 × 0.7835 ≈ 11.04.
  - At r = 15%: PV25 = (1 - 1/1.15^25)/0.15 ≈ 6.465; deflate by 1/1.15^5 (≈0.4972) → PV ≈ 6.465 × 0.4972 ≈ 3.21.
  - Comparison: benefits PV falls from ≈11.04 (5%) to ≈3.21 (15%) — a reduction to about 29% (a very large drop).
- PV of costs as annual 1 from t=1 to 5:
  - At r = 5%: PV5 = (1 - 1/1.05^5)/0.05 ≈ 4.33.
  - At r = 15%: PV5 = (1 - 1/1.15^5)/0.15 ≈ 3.35.
  - Comparison: costs PV falls from ≈4.33 to ≈3.35 — a modest reduction (~23%).

4) Why the correct answer is correct
Because benefits occur far into the future, a high discount rate (15%) heavily reduces their present value compared to a low rate (5%). The numerical example shows benefits are far more “penalized” than early costs.

5) Why other options are incorrect
- “Significantly reduce the value of the costs” / “reduce the value of the costs”: costs occur early and are much less reduced by a higher r.
- “There is negligible effect”: incorrect because long horizons amplify the effect on distant benefits.
- “It will reduce the value of the benefits”: true but understates the magnitude; the correct choice emphasizes the strong (significant) reduction.

6) Conclusion
The high discount rate will significantly reduce the value of the benefits — confirming the provided answer.

Similar Questions

Complete the following statement: Making decisions today using an economic analysis with a high discount rate, means that large costs and benefits in the future... Select a single answer.

Which of the following does not assign a value to a business opportunity using time-value measurement tools?

Because "present value" refers to the value of cash flows that occur at different points in time, a series of present values of cash flows should not be summed to determine the value of a capital budgeting project.

Which of the following correctly describes the time value of money?

Which of the following best explains the reason behind the time value of money?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler