1. Corporate Finance Introduction to Financial Math Hannes Wagner Felix Suntheim Arie E. Gozluklu 15 September 2010

2. Contact Information Email: – arie.gozluklu@unibocconi.it – felix.suntheim@unibocconi.it Office Hours: Thursday 6-7pm. Current Office: Grafton Building, 2-C3-02 New office: Grafton Building, 2-E2-fm03

3. Q1) BMA Chp. 2, PQ 19(Page 33) For an outlay of $8 million you can purchase a tanker load of bucolic acid delivered in Rotterdam one year hence. Unfortunately the net cash flow from selling the tanker load will be very sensitive to the growth rate of the world economy: a) What is the expected cash flow? Assume the three outcomes for the economy are equally likely. b) What is the expected rate of return on the investment in the project? c) One share of stock Z is selling for $10.The stock has the following payoffs after one year Calculate the expected rate of return offered by stock Z. Explain why this is the opportunity cost of capital for your bucolic acid project. d) Calculate the project’s NPV. Is the project a good investment? Explain why. SlumpNormalBoom $8million$12million$16million SlumpNormalBoom $8$12$16

4. Q2) BMA Chp. 2, CQ 20(Page 34) In real life the future health of the economy cannot be reduced to three equally probable states like slump, normal, and boom. But we’ll keep that simplification for one more example. Your company has identified two more projects, B and C. Each will require a $5 outlay immediately. The possible payoffs at year 1, are in millions: You have identified the possible payoffs to investors in three stocks X, Y, and Z: SlumpNormalBoom Project B$4$6$8 Project C55,56 Current PricePayoff at Year 1 per ShareSlumpNormalBoom X$95,65$80$110$140 Y40 4448 Z1081216

5. Q2) BMA Chp. 2, CQ 20(Page 34) a) What are the expected cash inflows of project B and C? b) What are the expected rates of return offered by stocks X,Y, and Z? c) What are the opportunity costs of capital for projects B and C? (Hint: Calculate the percentage differences, slump versus normal and boom versus normal, for stocks X,Y, and Z. Match up to the percentage differences in B’s and C’s payoffs.) d) What are the NPVs of projects B and C? e) Suppose B and C are launched and $5 million are invested in each. How much will they add to the market value of your company’s shares?

6. Q3) BMA Chp. 3, PQ 19(Page 56) As winner of a breakfast cereal competition, you can choose one of the following prizes: a) $100.000 now. b) $180.000 at the end of five years. c) $11.400 forever. d) $ 19000 each of 10 years. e) $6.500 next year and increasing thereafter by 5% a year forever. If the interest rate is 12%, which is the most valuable price?

7. Q4) BMA Chp. 3, CQ 38(Page 58) You own a pipeline which generate a $2 million cash return over the coming year. The pipeline’s operating costs are negligible, and it is expected to last for a very long time. Unfortunately, the volume of oil shipped is declining, and cash flows are expected to decline by 4% per year. The discount rate is 10%. a) What is the present value (PV) of the pipeline’s cash flows if its cash flows are assumed to last forever? b) What is the PV of the cash flows if the pipeline is scrapped after 20 years?

8. Q5) BMA Chp. 4, PQ 7(Page 81) The following table shows the prices of a sample of U.S Treasury strips in August 2006. Each strip makes a single payment of 1000 at maturity. a) Calculate the annually compounded, spot interest rate for each year. b) Is the term structure upward- or downward-sloping or flat? c) Would you expect the yield on a coupon bond maturing in August 2010 to be higher or lower than the yield on the 2010 strip? d) Calculate the annually compounded, one year forward rate of interest for August 2008. Now do the same for August 2009. MaturityPrice(%) August 200795,53 August 200891,07 August 200986,2 August 201081,08

9. Q6) BMA Chp. 4, CQ 35(Page 84) What spot and forward rates are embedded in the following Treasury bonds? The price of one-year (zero-coupon) Treasury bill is 93,46%. Assume for simplicity that bonds make only annual payments. Hint: Can you devise a mixture of long and short positions in these bonds that gives a cash payoff only in year 2? In year 3? A- three year bond with a 4% coupon is selling at 95%. Is there a profit opportunity here? If so, how would you take advantage of it? Coupon(%)MaturityPrice(%) 4294,92 83103,64

10. Long Term Yields