Assume annual compound interest unless stated otherwise.
1. If the interest rate is 4%, what are the proceeds of a $5,000 investment after 10 years?
a) assuming simple interest
b) assuming compound interest
2. What if interest in #1 is compounded semi-annually? What if monthly?
3. How much do you need to deposit into a bank in order to receive proceeds of $200,000 in 5 years if the interest rate is 2.5%
What if interest is compounded quarterly?
4. What is the present value of $200,000 to be received in 5 years if the rate of discount is 2.5%?
5. What is the price today of a $200,000 cash flow in 5 years if the discount rate is 2.5%
6. What is the price today of $200,000 to be received in 6 years if the rate of discount is 2.5%? Compare to #5.
7. What is the price today of $200,000 to be received in 5 years if the rate of discount is 3%? Compare to #5.
8. Calculate the percentage price change between your answer in #5 and your answer in #7. This is known as the interest rate “sensitivity.”
9. a) What must be the interest rate in order for an investment of $1,000 to produce proceeds of $2,000 in 20 years?
b) If a cash flow of $2,000 in 20 years has a price today of $1,000, what must be the discount rate?
These are known as “implied” rates.
10. An asset promises to pay $50,000 in five years and $100,000 in ten years. What is its price if the 5-year rate of discount is 10% and the 10-year rate of discount is 5%?
11. An asset promises to pay $1,000 in each of the next two years.
a) What is its present value assuming the one-year rate of discount is 1.5% and the two-year is 2.2%?
b) What is its present value assuming both discount rates are 1.85%?
12. An asset promises to pay $60 in each of the next three years. Assume the rate of discount is 5% for each of the years.
a) Calculate its price the “long” way; i.e., just as you have been doing for #11 and #12, by discounting each future cash flow and summing.
b) Calculate its price using the annuity formula.
13. For the annuity in #12, what happens to it price if the rate of discount increase to 6%?
14. For the annuity in #12, what happens to it price if:
a) its maturity is raised to four years?
b) it never matures (a “perpetuity”)?
15. What are the proceeds of $1,000,000 deposited in a bank today (Sept 9) for 1 month at 1.5%? Take care to apply “money market” rules and use the proper “day count.”
16. What is the present value of $1MM to be paid March 9 2018 at a (discount) rate of 2%. (Same instructions as in 15.)
17. An asset promises to pay the following:
$60 each year for the next ten years: and $1,000 in ten years
Assume all the cash flows are discounted by 6%. Use the annuity formula to get the price of the first part. Use the standard discounting formula to get the price of the second part. Add them together, and you have the price of a bond!
This is a bond with a coupon rate of 60/1,000 = 6% and a maturity of ten years. Its yield-to-maturity is 6%.
18. Consider a bond with a coupon rate of 5%, face value $100,000 and twenty year maturity.
a) What is its price if the yield-to-maturity is 5%? What about 6%? 4%? Calculate these as explained in #17, or use the bond formula in the Lecture Notes.
b) Repeat the three parts of a) but for a thirty-year maturity.