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.

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

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

We sincerely hope that we have managed to present this information in an easily understandable manner without compromising correctness.

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

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

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

We sincerely hope that we have managed to present this information in an easily understandable manner without compromising correctness.