1. Suppose two competing projects have cash flows of the form (-A1, B1, B1, ..., B1) and (-A2, B2, B2, ..., B2), both with the same length and A1, A2, B1, B2 all positive. Suppose B1/A1 > B2/A2. Show that project 1 will have a higher IRR than project 2.
2. There are two cash flows of the form A = (5, 14, -15, -7, 10, 2) and B = (1, 14, 3, -7, -8, 2). You can choose at most one cash flow. Find a range of r satisfying A > B. Find a range of r which you will not take anything.
3. A loan company is offering a loan of $L for 20 years on the Internet with the following characteristics:
• A quote rate of 7.256% (which is used to calculate $p, the monthly payments).
• 3 points (that is, you have to pay 3%. of L when you get the loan) and initiation fee of $1000.
• An actual APR of 7.53% (compounded monthly).
• No closing cost.
Find L and p.
4. Suppose that your aunt and uncle each separately offer you a bond. Both bonds have the same maturity T years and face value F. However, the coupon of your aunt's bond are a1, a2, ..., aT , where ai = ai-1 - d (d is positive constant and i = 2, 3, ..., T); the coupon of your uncle's bond is c every year, where c is the average of the ai 's, i.e. c =1/T∑i=1T ai . It turns out that both your aunt and uncle ask for $100 for the bond. Given that you have only $100 to use, which one would you choose? Assume the interest rate is strictly positive and less than 1.
5. Determine whether it is true or false. Justify your answer providing either a short proof or a (counter) example as appropriate. Given two bonds with the same price, face value, expiration date and yield means that their coupons payments are identical.