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?
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a. To calculate the value of the bonds when the interest rates are different, we need to use the formula for bond valuation.
The formula for valuing a bond is:
Bond Value = (Coupon Payment / Interest Rate) * (1 - (1 / (1 + Interest Rate)^n)) + (Face Value / (1 + Interest Rate)^n)
where:
- Coupon Payment: The annual interest payment
- Interest Rate: The going rate of interest
- Face Value: The amount received at maturity
- n: The number of years to maturity
Let's calculate the value of each bond with different interest rates:
(1) When the interest rate is 5%:
For Bond L (15-year maturity):
Coupon Payment = $100, Interest Rate = 5%, Face Value = $1,000, n = 15
Plug these values into the formula:
Bond L Value = ($100 / 0.05) * (1 - (1 / (1 + 0.05)^15)) + ($1,000 / (1 + 0.05)^15)
For Bond S (1-year maturity):
Coupon Payment = $100, Interest Rate = 5%, Face Value = $1,000, n = 1
Plug these values into the formula:
Bond S Value = ($100 / 0.05) * (1 - (1 / (1 + 0.05)^1)) + ($1,000 / (1 + 0.05)^1)
Repeat this calculation for interest rates of 8% and 12% to find the values of the bonds.
b. The longer-term bond (15-year) fluctuates more than the shorter-term bond (1-year) when interest rates change because of the effect of the present value of future cash flows.
When interest rates rise, the present value of future cash flows decreases. Since the longer-term bond has more future cash flows, it is more impacted by the higher discount rate. This results in a larger decrease in the value of the longer-term bond compared to the shorter-term bond.
Conversely, when interest rates decrease, the present value of future cash flows increases. Again, the longer-term bond benefits more from the lower discount rate, resulting in a larger increase in its value compared to the shorter-term bond.
b. To calculate the preferred stock's required rate of return, we need to use the dividend discount model.
The formula for the required rate of return is:
Required Rate of Return = Dividend / Stock Price
where:
- Dividend: The annual dividend payment
- Stock Price: The current price of the preferred stock
Plug in the given values into the formula:
Dividend = $5
Stock Price = $60
Required Rate of Return = $5 / $60
Calculating this will give us the required rate of return for the preferred stock.