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Answer question 6 and 7

6. What is the value of a $ 1000 par value bond, 8 % coupon paid annually, 5 years to maturity if investors require an 8 % return? 7. What will be the value of the bond in questio

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To calculate the value of a bond, we can use the present value formula, which takes into account the bond's coupon payments and the face value (par value) at maturity.

Value of the bond:

Given data:

Par value (face value) = $1000

Coupon rate = 8% (paid annually)

Years to maturity = 5

Required return (Yield to maturity) = 8%

To calculate the value of the bond, we need to discount the future cash flows (coupon payments and the face value) at the required return rate.

First, let's calculate the annual coupon payment:

Annual coupon payment = Coupon rate * Par value

Annual coupon payment = 8% * $1000 = $80

Next, let's calculate the present value of the bond's cash flows:

PV of coupon payments = (Annual coupon payment / Required return) * (1 - (1 / (1 + Required return)^Years to maturity))

PV of coupon payments = ($80 / 0.08) * (1 - (1 / (1 + 0.08)^5))

PV of coupon payments = $1000 * (1 - (1 / 1.4693))

PV of coupon payments = $1000 * (1 - 0.6806)

PV of coupon payments = $319.4

PV of the face value = Face value / (1 + Required return)^Years to maturity

PV of the face value = $1000 / (1 + 0.08)^5

PV of the face value = $1000 / 1.4693

PV of the face value = $680.6

Value of the bond = PV of coupon payments + PV of the face value

Value of the bond = $319.4 + $680.6

Value of the bond = $1000

Therefore, the value of the bond is $1000.

The value of the bond in question if the required return increases to 10%:

We can use the same formula as in question 6, but with the updated required return of 10%.

PV of coupon payments = ($80 / 0.10) * (1 - (1 / (1 + 0.10)^5))

PV of coupon payments = $800 * (1 - (1 / 1.6105))

PV of coupon payments = $800 * (1 - 0.6209)

PV of coupon payments = $495.2

PV of the face value = $1000 / (1 + 0.10)^5

PV of the face value = $1000 / 1.6105

PV of the face value = $620.9

Value of the bond = PV of coupon payments + PV of the face value

Value of the bond = $495.2 + $620.9

Value of the bond = $1116.1

Therefore, the value of the bond in question, if the required return increases to 10%, is approximately $1116.1.

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