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A1. (Bond Valuation) A $1,000 Face Value Bond Has A Remaining Maturity Of 10 Years And A Required Return Of 9%. The Bond's Coupon Rate Is 7.4%. What Is The Fair Value Of This Bond?

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Iris Phillips Profile
Iris Phillips answered
If a face value bond of $1,000 has 10 years as its remaining maturity, and a coupon rate of 7.4 %, with a necessary return of 9%, then the bond has a fair value of $897.31. How to get to this figure involves working out a variety of factors, details of which are shown in the step by step calculations below.

In the calculations below, a equals the necessary return of 9 %, n equals the amount of years, namely 10 years, and PV signifies a present value.

  • Calculating the PV (PV1) Using the Coupon Rate
First, the cash flow using the coupon rate is determined:
Cash flow = $1000 x 7.4 % = $74

The PV factor (PV1) is determined using this formula: PV1 factor = (1/a)x(1- 1/(1+a)^n) . Therefore, (1/9%)x(1-1(1+9%)^10), which equals 6.4176.

The present value PV1 is determined by multiplying the cash flow by the PV1 factor, hence the PV1 equals $74 x 6.4176, which is $474.9024

  • Calculating the PV (PV2) Using the $1000 Cash Flow
The PV2 factor here is determined by this formula: 1/(1+i)^n.
Therefore, PV2 factor = 1/(1+9%)^10 = 0.42241

The present value PV2 is again calculated by multiplying the cash flow and the PV2 factor, so the PV2 equals $1000 x 0.42241, resulting in $422.21

  • Calculating the Fair Bond Value
The fair value of the bond is calculated by adding PV1 to PV2. Consequently the fair value of the bond is $474.9024 plus $422.21, which equals $897.3124. This figure is then rounded down to $897.31.

We sincerely hope that we have managed to present this information in an easily understandable manner without compromising correctness.
Anonymous Profile
Anonymous answered
A1. (Bond Valuation) A $1,000 Face Value Bond Has A Remaining Maturity Of 10 Years And A Required Return Of 9%. The Bond's Coupon Rate Is 7.4%. What Is The Fair Value Of This Bond?
Anonymous Profile
Anonymous answered
The semi-annual coupon=PT=1000*0.074/2=37, rate=0.09/2=0.045, n=2*10=20  FV=1000
PV= 895.94

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