2. On 1/1/10, the following is observed for grade AAA (risk-free) bonds:

- A bond maturing on 12/31/12 with coupon 6.0% and face value $1000 is selling at $1112.80

- A bond maturing on 12/31/12 with coupon 5.0% and face value $1000 is selling at $1084.00

- A T-bill maturing on 12/31/10 is quoted with a yield to maturity of 2.0408%.

Assume that bond coupons are paid annually on 12/31.

a) (3 point) Find the price as of 1/1/10 of $1 delivered in one year (p1).

b) (3 points) Find the prices as of 1/1/10 of $1 delivered in two years and three years (p2 and p3). (HINT: You may need to solve a system of equations)

c) (3 point) Write down the cash flows of a three-year risk-free bond that has face value of $1,000 and pays coupon C each year-end.

d) (3 points) What is the coupon rate (coupon divided by face value) which must be paid for a newly-issued (on 1/1/10) three-year risk-free bond with face value of $1000 to sell at par? (sell at Parmeans market value = face (or principal) value.) Use your prices from a) and b).

e) (3 points) What is the coupon rate which must be paid for a newly-issued (on 1/1/10) two-year risk-free bond to sell at par?

3. (15 points) You are a senior manager at Poeing Aircrafts and have been authorized to spend up to $200 million for projects. The three projects that you are considering have the following characteristics:

Project A: Initial Investment of $150 m. Cash flow of $50 m. at year 1 and $100 m. at year 2. This is plant expansion project, where the required rate of return is 10%. Project B: Initial Investment of $200 m. Cash flow of $200 m. at year 1 and $100 m. at year 2. This is new product development project, where the required rate of return is 20%.

Project C: Initial Investment of $100 m. Cash Flow of $100 m. at year 1 and $100 m. at year 2. This is a market expansion project and the required rate of return is 20%.

Assume that corporate discount rate is 10%. Please o?er your recommendations for the projects choice backed up by your analysis. Specically, for each project, nd its NPV, PI, Payback, and IRR. When computing IRR, please also do the IRR on incremental cash ows (if it is needed in your opinion). Say

1. which project(s) each rule suggests to choose and whether you should trust the rule in this particular case.

A B C Implications

NPV IRR Incremental IRR PI Payback

(Note: The solutions to quadratic equation of form ax2 + bx + c = 0 are x1 = b+pb24ac 2a and x2 = bpb24ac 2a ). To nd the IRR you can use your calculator, Excel, or the formula for solutions to quadratic equation.

Problem Set 3 (Due Feb 13) 1. Three years ago you took out a 30-year amortizing loan. The loan has a 6% APR with monthly payments (and monthly compounding). a) (5 points) What are your monthly payments if your current loan balance is $368; 600? b) (5 points) How much interest did you pay on the loan in the past year? 2. On 1/1/10, the following is observed for grade AAA (\"risk-free\") bonds: - A bond maturing on 12/31/12 with coupon 6.0% and face value $1000 is selling at $1112.80 - A bond maturing on 12/31/12 with coupon 5.0% and face value $1000 is selling at $1084.00 - A T-bill maturing on 12/31/10 is quoted with a yield to maturity of 2.0408%. Assume that bond coupons are paid annually on 12/31. a) (3 point) Find the price as of 1/1/10 of $1 delivered in one year (p1 ). b) (3 points) Find the prices as of 1/1/10 of $1 delivered in two years and three years (p2 and p3 ). (HINT: You may need to solve a system of equations) c) (3 point) Write down the cash ows of a three-year risk-free bond that has face value of $1,000 and pays coupon C each year-end. d) (3 points) What is the coupon rate (coupon divided by face value) which must be paid for a newly-issued (on 1/1/10) three-year risk-free bond with face value of $1000 to sell at par? (\"sell at Par\" means market value = face (or principal) value.) Use your prices from a) and b). e) (3 points) What is the coupon rate which must be paid for a newly-issued (on 1/1/10) two-year risk-free bond to sell at par? 3. (15 points) You are a senior manager at Poeing Aircrafts and have been authorized to spend up to $200 million for projects. The three projects that you are considering have the following characteristics: Project A: Initial Investment of $150 m. Cash ow of $50 m. at year 1 and $100 m. at year 2. This is plant expansion project, where the required rate of return is 10%. Project B: Initial Investment of $200 m. Cash ow of $200 m. at year 1 and $100 m. at year 2. This is new product development project, where the required rate of return is 20%. Project C: Initial Investment of $100 m. Cash Flow of $100 m. at year 1 and $100 m. at year 2. This is a market expansion project and the required rate of return is 20%. Assume that corporate discount rate is 10%. Please oer your recommendations for the projects choice backed up by your analysis. Speci...cally, for each project, ...nd its NPV, PI, Payback, and IRR. When computing IRR, please also do the IRR on incremental cash ows (if it is needed in your opinion). Say 1 which project(s) each rule suggests to choose and whether you should trust the rule in this particular case. A B C Implications NPV IRR Incremental IRR PI Payback (Note: pThe solutions to quadratic equation of form ax2 + bx + c = 0 are p 2 2 b 4ac b 4ac and x2 = b 2a ). To ...nd the IRR you can use your x1 = b+ 2a calculator, Excel, or the formula for solutions to quadratic equation. 2