A 'Dave Problem':
You just purchased three securities, a one-year to maturity Bond, a four-year to maturity bond, and a perpetuity.
The one-year bond promises $1100 on this date next year.
The four-year bond promises annual payments of $100 every year on this date for the next four years and repayment (face value) of $1000 on this date four years from today.
The perpetuity promises $100 per year (on this date) forever.
The interest rate is 10%.
(a) Show the formula for pricing (determining the present value) of each of these bonds using the values given and show the present values.
(b) The interest rate rises from 10% to 20% just after you buy these securities. What are the new present values of these securities?
(c) The interest rate falls from 10% to 5% just after you buy these securities. What are the new present values of these securities?
(d) Calculate the percentage changes in prices for each security between (a) and (b) and (a) and (c).