Yield to maturity approximation for perpetuities is called:

Question

BlackTom AI · Accepted Answer

For a perpetuity the yield is simply the annual cash payment divided by the current price: r = C / P, which is the definition of the current yield.

1. Relevant knowledge points and concepts
- Perpetuity: a security that pays a fixed cash flow C forever.
- Present value of a perpetuity: P = C / r, where r is the constant discount rate (yield).
- Current yield: annual coupon (or payment) divided by bond price, C / P.
- Yield-to-maturity (YTM) for a perpetuity is the discount rate that equates present value of infinite cash flows to the price; algebra shows this equals C / P and therefore equals the current yield.

2. Step-by-step reasoning
- Start from the perpetuity PV formula: P = C / r.
- Rearrange to solve for r: r = C / P.
- Recognize that C / P is exactly the definition of current yield.

3. Calculations with intermediate steps
- Given P = C / r.
- Multiply both sides by r: Pr = C.
- Divide both sides by P: r = C / P.
- Example numeric check: C = $50 annual, P = $1,000 → r = 50/1000 = 0.05 = 5%. That 5% is both the perpetuity’s YTM and the current yield.

4. Why the correct answer is correct
- Because for an instrument with infinite life there is no principal repayment or time-dependent capital gain/loss to account for; the only return comes from the perpetual payment C. Solving the present-value equation yields r = C / P, so the YTM equals the current yield exactly.

5. Why other options are incorrect
- a. future yield: not a standard term for YTM approximation of perpetuities.
- b. discount yield: typically refers to the bank discount yield for money market instruments (e.g., T-bills), not the perpetuity YTM approximation.
- c. star yield: not a recognized finance term.
- d. current yield: matches the derived expression and is the standard name.

6. Conclusion
- Therefore the yield-to-maturity approximation for perpetuities is called the current yield, confirming answer d.

Yield to maturity approximation for perpetuities is called:Single choice

Similar Questions

A $1,000 par value corporate bond that pays $45 annually in interest was issued last year. Which one of these would apply to this bond today if the current price of the bond is $989.42?

Expansionary fiscal policy in an open economy with a floating exchange rate will likely:

Contractionary monetary policy in an open economy with a floating exchange rate will likely:

Contractionary monetary policy in an open economy with a fixed exchange rate will likely ____ a trade surplus.

Which is expansionary monetary policy?

Which is contractionary fiscal policy?

Which is expansionary fiscal policy?

What would raise aggregate supply (AS)?

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