Bond valuation
The Garraty Company has two bond issues outstanding. Both bonds pay $100 annual interest plus $1,000 at maturity. Bondf L has a maturity of 15 years, and Bond S a maturity of 1 year.
a. What will the value of each of these bonds when the going rate of interest is (1) 5 percent, (2) 8 percent, and (3) 12 percent? Assume that there is only one more interest payment to be made on Bond S.
b. Why does the longer-term (15 year) bond fluctuate more when interest rates change than does the shorter-term bond (1 year)?
Preferred stock evaluation
Fee Founders has preferred stock outstanding that pays a dividend of $5 at the end of each year. The preferred stock sells for $60 a share. What is the preferred stock's required rate of return?
To calculate the value of each bond at different interest rates, you need to use the concept of present value. The present value of a bond is the sum of the present value of its future interest payments and its future maturity payment.
Here's how you can calculate the value of each bond at different interest rates:
For Bond L (15-year maturity):
1. Calculate the present value of the annual interest payment of $100 using the formula for the present value of an ordinary annuity:
PV = PMT * (1 - (1 + r)^(-n)) / r, where PV is the present value, PMT is the payment, r is the interest rate per period, and n is the number of periods.
For Bond L, PMT = $100, r = interest rate / 100, and n = 15.
2. Calculate the present value of the maturity payment of $1,000 using the formula for the present value of a single sum:
PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate per period, and n is the number of periods.
For Bond L, FV = $1,000, r = interest rate / 100, and n = 15.
3. Add the present value of the interest payments and the present value of the maturity payment to get the total value of Bond L.
Repeat the same steps for Bond S (1-year maturity), but this time n = 1.
To answer the second part of your question:
The longer-term (15-year) bond fluctuates more when interest rates change compared to the shorter-term (1-year) bond due to the concept of duration. Duration measures a bond's sensitivity to interest rate changes. Generally, the longer the duration, the greater the bond's sensitivity to interest rate changes. This means that when interest rates increase, the value of the longer-term bond decreases more than the shorter-term bond, and vice versa.
To calculate the required rate of return for the preferred stock:
The rate of return, also known as the yield or the required rate of return, is the rate of return an investor expects to earn from an investment. In the case of preferred stock, the rate of return can be calculated using the formula:
Rate of Return = Dividend / Stock Price
In this scenario, the preferred stock pays a dividend of $5 and the stock price is $60. Therefore, the required rate of return for the preferred stock is:
Rate of Return = $5 / $60
You can simplify this to get the required rate of return.