Chapter 4: Q.20 (page 134)

Consider a bond with a 6% annual coupon and a face value of $1,000. Complete the following table. What relationships do you observe between years to maturity, yield to maturity, and the current price?

Short Answer

Expert verified

The current yield will be:

Step by step solution

Step 1. Introduction

The total return expected if the bond is kept to maturity is known as yield to maturity. It can also be referred as the internal rate of return of bond if it is kept till maturity.

Step 2. Explanation

$A n n u a l C o u p o n = $ 1000 \times 6 % = $ 60 C a s e I C u r r e n t M a r k e t P r i c e = $ 60 \times \frac{1 - {(\frac{1}{1.04})}^{2}}{0.04} + $ 1000 \times {(\frac{1}{1.04})}^{2} = $ 60 \times 1.8861 + $ 1000 \times 0.9246 = $ 1037.77 C u r r e n t Y i e l d = \frac{$ 60}{$ 1037.77} = 5.78 % C a s e - I I C u r r e n t M a r k e t P r i c e = $ 60 \times \frac{1 - {(\frac{1}{1.06})}^{2}}{0.06} + $ 1000 \times {(\frac{1}{1.06})}^{2} = $ 1, 000 C u r r e n t Y i e l d = \frac{$ 60}{$ 1000} = 6 % C a s e - I I I C u r r e n t M a r k e t P r i c e = $ 60 \times \frac{1 - {(\frac{1}{1.06})}^{3}}{0.06} + $ 1000 \times {(\frac{1}{1.06})}^{3} = $ 1000 C u r r e n t Y i e l d = \frac{$ 60}{$ 1000} = 6 % C a s e - I V C u r r e n t M a r k e t P r i c e = $ 60 \times \frac{1 - {(\frac{1}{1.04})}^{5}}{0.04} + $ 1000 \times {(\frac{1}{1.04})}^{5} = $ 1089 C u r r e n t Y i e l d = \frac{$ 60}{$ 1089} = 5.51 % C a s e - V C u r r e n t M a r k e t P r i c e = $ 60 \times \frac{1 - {(\frac{1}{1.08})}^{5}}{0.08} + $ 1000 \times {(\frac{1}{1.08})}^{5} = $ 920.16 C u r r e n t Y i e l d = \frac{$ 60}{$ 920.16} = 6.52 %$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Consider a bond with a 6% annual coupon and a face value of $1,000. Complete the following table. What relationships do you observe between years to maturity, yield to maturity, and the current price?

Short Answer

Step by step solution

Step 1. Introduction

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Study anywhere. Anytime. Across all devices.