Stock. What is the value of a stock with a $3 dividend just paid and a 8% required return with 2% growth?
Bond. What is the value of a $1,000 par value bond with annual payments of an 11% semiannual coupon with a maturity of 20 years and a 11% required return?
Thank You!!!!!
To calculate the value of a stock, you can use the Gordon Growth Model (also known as the dividend discount model). The formula for the value of a stock is:
Value of Stock = Dividend / (Required Return - Growth Rate)
Let's plug in the values you provided:
Dividend = $3
Required Return = 8%
Growth Rate = 2%
Value of Stock = 3 / (0.08 - 0.02)
Value of Stock = 3 / 0.06
Value of Stock = $50
Therefore, the value of the stock is $50.
Moving on to the bond valuation, you can use the formula for calculating the present value of a bond:
Value of Bond = (Coupon Payment / (1 + Required Return)^n) + (Coupon Payment / (1 + Required Return)^(n - 1)) + ... + (Coupon Payment / (1 + Required Return)^2) + (Coupon Payment / (1 + Required Return)) + (Face Value / (1 + Required Return)^n)
In this formula:
- Coupon Payment: Amount received as interest payment per period (semi-annually in this case)
- Required Return: The required rate of return (in this case, 11%)
- n: Number of periods until maturity (20 years)
Let's calculate the value of the bond:
Coupon Payment = (11% of $1,000) / 2
Coupon Payment = $55
n = 2 * 20
n = 40
Value of Bond = (55 / (1 + 0.11/2)^40) + (55 / (1 + 0.11/2)^39) + ... + (55 / (1 + 0.11/2)^2) + (55 / (1 + 0.11/2)) + (1,000 / (1 + 0.11/2)^40)
Note that the formula involves summing up the present value of each coupon payment, as well as the present value of the face value at maturity.
Using a financial calculator or spreadsheet software, you can calculate the value of the bond to be around $1,249.92.
Therefore, the value of the bond is approximately $1,249.92.