Problem 1:  Calculate the annual internal rates of return (IRR) for the following investments (time t is in years):

1. At t = 0, the cost is $100.  The cash flows are $100 at t = 1 and $250 at t = 3.

2. At t = 0, the cost is $150.  The cash flows are $100 at t = 1 and $250 at t = 3.  

3. At t = 0, the cost is $100.  The cash flows are $100 at t = 1 and $250 at t = 2.

4. At t = 0, the cost is $100.  The cash flows are $250 at t = 1 and $100 at t = 3.

Which of these investments has the highest IRR?  Why?

Problem 2:  Consider a 10-year bond that pays a 5 percent coupon semi-annually with a face value of $1000.

1. What is the price of this bond if the annualized yield to maturity of 4 percent (i.e., the stated rate is .04 compounded semi-annually)?  

2. What is the price of this bond if the annualized yield to maturity of 5 percent (i.e., the stated rate is .05 compounded semi-annually)?  

3. What is the price of this bond if the annualized yield to maturity of 6 percent (i.e., the stated rate is .06 compounded semi-annually)?  

4. What is the price of this bond if the annualized effective rate is 5 percent?

Problem 3:  Consider the bond described in Problem 2 above but let the coupon be paid annually.  Answer questions a through c in Problem 2 above for this annual coupon paying bond.

Problem 4:  The price of a 10-year zero-coupon bond is $670 per $1000 in face value.

1. What is its yield to maturity on this bond?

2. If you buy this 10-year bond today (at t = 0) for $670, hold it for 5 years, and sell it then (when it is a 5-year zero) for $850, what is your holding period yield?  If this happens, will the yield to maturity when you sell this bond be higher or lower than its current yield to maturity?  

3. What price would this bond current 10-year zero have to sell for in 5 years for the holding period yield to be its current yield to maturity?