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Q-10-281

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Essentials Of Investments
Found in: Page 330
Essentials Of Investments

Essentials Of Investments

Book edition 9th
Author(s) Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus
Pages 748 pages
ISBN 9780078034695

Short Answer

Question: A two-year bond with par value $1,000 making annual coupon payments of $100 is priced at $1,000. What is the yield to maturity of the bond? What will be the realized compound yield to maturity if the one-year interest rate next year turns out to be:

( a ) 8%,

( b ) 10%,

( c ) 12%?

Answer

a. 9.91%

b. 10.00%

c. 10.09%

See the step by step solution

Step by Step Solution

Step 1: Given information

The bond is selling at par value.

Its yield to maturity equals the coupon rate, 10%.

If the first-year coupon is reinvested at an interest rate of r percent, then total proceeds at the end (1 + r) + 1100].

Step 2: Calculation of the realized compound YTM

Therefore, realized compound yield to maturity of the second year will be a function of r as given below:

r

Total proceeds

Realized YTM = √Proceeds / 1000 -1

8%

$1208

√1208/1000 - 1 = 0.0991 = 9.91 %

10%

$ 1210

√1210/1000 - 1 = 0.1000 = 10.00 %

12%

$ 1212

√1212/1000 - 1 = 0.1009 = 10.09 %

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