# 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?

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.
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