# EBF 401 EBF401 Midterm 1 Review Problems (Penn State University)

EBF 401 EBF401 Midterm 1 Review Problems (Penn State University)

Problem 1

You are considering a savings bond that will pay $100 in 10 years. If the interest rate is 2%, what should you pay today for the bond?

Problem 2

Consider the following alternatives:

i. $100 received in one year;

ii. $200 received in 5 years;

iii. $300 received in 10 years

(a) Rank the alternatives from most valuable to least valuable if the interest rate is 10% per year.

(b) What is your ranking if the interest rate is 5% per year?

(c) What is your ranking if the interest rate is 20% per year?

Problem 3

Your grandfather put some money in an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money for the first time. The account currently has $3,996 in it and pays an 8% interest rate.

(a) How much money would be in the account if you left the money there until your 25^{th} birthday?

(b) What if you left the money until your 65^{th} birthday?

(c) How much money did your grandfather originally put in the account?

Problem 4

Your grandmother has been putting $1,000 into a savings account on every birthday since your first (that is, when you turned one). The account pays an interest rate of 3%. How much money will be in the account immediately after your grandmother makes the deposit on your 18^{th} birthday?

Problem 5

You are thinking of building a new machine that will save you $1,000 in the first year. The machine will then begin to wear out so that the savings decline at a rate of 2% per year forever. What is the present value of the savings, if the interest rate is 5% per year?

Problem 6

Consider again the 5-year, $1,000 bond with a 2.2% coupon rate and semiannual coupons in HW 2. Suppose interest rates drop and the bondâ€™s yield to maturity decreases to 2% (expressed as an APR with semiannual compounding). What price is the bond trading for now? And what is the effective annual yield (or effective annual rate) on this bond?

Problem 7

Consider three 30-year bonds with annual coupon payments. One bond has a 10% coupon rate, one has a 5% coupon rate, one has a 3% coupon rate. If the yield to maturity of each bond is 5%, what is the price of each bond per $100 face value? Which bond trades at a premium, which trades at a discount, and which trades at par?

Problem 8

Suppose you expect Company X to pay an annual dividend of $0.56 per share in the coming year and to trade for $45.50 per share at the end of the year. If investments with equivalent risk to Company Xâ€™s stock have an expected return of 6.8%, what is the most you would pay today for this stock? What dividend yield and capital gain would you expect at this price?