Crossfade Corporation has a bond with a par value of $2,000 that sells for $1,917.12. The bond has a coupon rate of 7.02 percent and matures in 20 years. If the bond makes semiannual coupon payments, what is the YTM of the bond?Single choice
A
7.42%
B
5.57%
C
3.71%
D
7.05%
E
6.68%

Question

Crossfade Corporation has a bond with a par value of $2,000 that sells for $1,917.12. The bond has a coupon rate of 7.02 percent and matures in 20 years. If the bond makes semiannual coupon payments, what is the YTM of the bond?Single choice

A

7.42%

B

5.57%

C

3.71%

D

7.05%

E

6.68%

BlackTom AI · Accepted Answer

YTM is the discount rate that makes the bond’s price equal to the present value of its semiannual coupon payments plus the redemption (par) value. Set up the bond-price equation and solve for the per-period rate, then annualize.

1) Relevant knowledge and concepts
- Coupon (annual) = coupon rate × par. For semiannual payments, each period’s coupon = (annual coupon)/2.
- Number of periods N = years × 2.
- Price = PV of an annuity (coupons) + PV of a lump sum (par).
- YTM (quoted) for semiannual-pay bond is the nominal annual rate = 2 × (semiannual rate).

2) Step-by-step reasoning and setup
- Par = $2,000.
- Annual coupon = 0.0702 × 2,000 = $140.40 → semiannual coupon = 140.40/2 = $70.20.
- N = 20 × 2 = 40 semiannual periods.
- Price P = $1,917.12.
Form equation for semiannual yield i:
1917.12 = 70.20 × [1 − (1 + i)^−40]/i + 2000 × (1 + i)^−40

3) Calculations (intermediate steps)
This equation must be solved numerically. Using trial/financial-calculator methods:
- Try i ≈ 0.03710 (3.710% per half-year):
  (1 + i)^40 ≈ 4.295 → (1 + i)^−40 ≈ 0.2327
  Annuity factor = [1 − 0.2327]/0.03710 ≈ 20.68
  PV(coupons) ≈ 70.20 × 20.68 ≈ 1,452.6
  PV(par) ≈ 2000 × 0.2327 ≈ 465.4
  Total PV ≈ 1,918.0 (very close to 1,917.12)
Refining i slightly to ≈ 0.037095 gives PV essentially equal to 1,917.12. Therefore semiannual rate ≈ 3.7095%.

4) Why the correct answer is correct
Annual nominal YTM (with semiannual compounding) = 2 × semiannual rate ≈ 2 × 3.7095% ≈ 7.419% → rounded to 7.42%. This is the rate that equates the given price to the bond’s cash flows.

5) Why other choices are incorrect
- 3.71%: This is approximately the semiannual rate, not the quoted annual YTM (the quoted YTM doubles the semiannual rate).
- 5.57%, 7.05%, 6.68%: These annual rates would produce different present values and do not satisfy the price equation for the given coupons and maturity.

6) Conclusion
Solving the bond price equation yields a semiannual rate ≈ 3.7095%, so the nominal annual YTM = 2 × 3.7095% ≈ 7.42%, which matches the provided correct answer (7.42%).

Crossfade Corporation has a bond with a par value of $2,000 that sells for $1,917.12. The bond has a coupon rate of 7.02 percent and matures in 20 years. If the bond makes semiannual coupon payments, what is the YTM of the bond?Single choice

Similar Questions

You own a bond that pays $64 in interest annually. The face value is $1,000 and the current market price is $1,021.61. The bond matures in 11 years. What is the yield to maturity?

Question at position 8 An excess of growth hormone (GH) before puberty can result in the development ofgigantism.Graves' disease.acromegaly.pituitary dwarfism.Clear my selection

Question at position 6 The most abundant supporting cells in the central nervous system are called Question Blank 1 of 1[input].

Question at position 5 In the eye, the lens functions tofocus light on the retina at the back of the eye.protect the surface of the eye.increase vision in low-light conditions.move the eye side to side.Clear my selection

Question at position 4 Olfactory (odor) receptors are chemoreceptors. TrueFalse

If the pKa of HCHO2 is 3.74 and the pH of an HCHO2/NaCHO2 solution is 3.00, which of the following is TRUE?

Identify the missing particle in the following nuclear equation: 92 236 𝑈 → 38 90 𝑆 𝑟 + ? + 2 0 1 𝑛 + 4 0 0 𝑔

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