A comp. has issued a bond with the following characteristics: Principal=1000, Time to maturity=20yrs. Coupon Rate=8%, compounded semiannually with semiannual payments. Calculate the value of this bond if the stated interest rate, compounded semiannually is 6%
My attempt: 1000(.08)/2 * (1-1/1.06^20) + (1000/1.06^20) = 40(11.4699) + 311.80 = 770.60
I get a different answer.
An excel spreadsheet is very helpful for these types of problems. (However, I am aware that finance instructors are into using look-up tables rather that calculating everything out). I presume you can use EXCEL to calculate.
Anyway, find V where:
V = C/(1+i) + C/(1+i)^2 + ... C/(1+i)^n + P/(1+i)^n
Where V is the bond value, C is the coupon payment, i is the interest rate, n is the number of payments, and P is the Principal.
Since payments are semiannual, I presume that C=$80/2=$40 and i=.06/2 = .03, n=40, and P=1000
I get V=1236.40
Thanks, I know now where I went wrong. I need to ask something else.
Comp. Q has just paid a dividend of $1.40 per share. Its dividend is expected to grow at 5% per year perpetually. If the required return is 10%, what is the value of a share in Company Q?
I think I use formula p0 = Div/r-g but I don't know where the required rate of return comes into play.
I know:
g=.05
r=
Retention Ratio=90%
Req. rate of return=10%
growth rate in Div. of (.9*.1)=9%
To calculate the value of the bond, you can use the formula for the present value of a bond:
PV = (C / (1 + r)^n) + (F / (1 + r)^n)
Where:
PV = Present value of the bond
C = Coupon payment per period
r = Interest rate per period
n = Number of periods
F = Face value of the bond
In this case, the face value (F) is $1000, the coupon payment (C) is $40 (0.08 * $1000 / 2), the interest rate (r) is 6% per semiannual period (0.06 / 2), and the number of periods (n) is 20 years multiplied by 2 (since there are semiannual periods).
Plugging in the values, we get:
PV = (40 / (1 + 0.03)^40) + (1000 / (1 + 0.03)^40)
= (40 / (1.03)^40) + (1000 / (1.03)^40)
≈ 770.60
So, the value of this bond, with a stated interest rate of 6% compounded semiannually, is approximately $770.60.