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.