PRIN.OF CORPORATE FINANCE
PRIN.OF CORPORATE FINANCE
13th Edition
ISBN: 9781260013900
Author: BREALEY
Publisher: RENT MCG
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Chapter 3, Problem 35PS

Prices and spot interest rates What spot interest rates are implied by the following Treasury bonds? Assume for simplicity that the bonds pay annual coupons. The price of a one-year strip is 97.56%, and the price of a four-year strip is 87.48%.

Chapter 3, Problem 35PS, Prices and spot interest rates What spot interest rates are implied by the following Treasury bonds?

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Summary Introduction

To determine: The spot interest rates implied by treasury bonds.

Explanation of Solution

Determine r1:

$97.56=$100(1+r1)(1+r1)=$100$97.56=2.50%

Hence, r1 is 2.50%.

Determiner4:

$87.48=$100(1+r4)(1+r4)=$100$87.48=3.40%

Hence, r1 is 3.40%.

Determiner5:

r5 can be solved by eliminating the 1-4 cash flow of 1.5 times 2% coupon bond and 3% coupon bond.

(1.5×$928.90)$974.30=[1.5×$1,020($1,030)](1+r5)5=0.036or3.6%

Determiner3:

r3 can be solved by reducing the 3-year, 5% coupon bond and 2.5 times of reduced 5-year 2% coupon bond which eliminates the 2-year cash flow:

$928.90=$201.025+$20(1+r2)2+$20(1+r3)3+$201.0344+$1,0201.0359555.....(1)$1,054.20=$501.025+$50(1+r2)2+$1,050(1+r3)3   $1,005.419512=$50(1+r2)2+$1,050(1+r3)...........(2)

Solve equation 1 and 2

$1,005.419512(2.5×$37.030021)=$1,050(2.5×$20)(1+r3)3=$912.844459$1,000(1 +r3)3r3=0.030863, or 3.0863%

Determiner2:

r2 can be solved by 3-year bond and r3 and r1

$1,054.20=$501.025+$50(1+r2)2+$1,0501.0308633$46.932036=$50(1+r2)2=0.0322

Hence, the spot rates are 2.50%, 3.22%, 3.09%, 3.40% and 3.60 for years 1 to 5.

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PRIN.OF CORPORATE FINANCE

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