Question 1 [12 points] Consider the two assets with the following cash flow streams: Asset A generates $3 at t=1 $1 at t=2 and $10 at t=3. Asset B generates $2 at t=1 $X at t=2 and $10 at t=3. Suppose X=4 and the interest rate r is constant. (a) For r=0.2 calculate the present value of the two assets.[2p] (b) Determine the set of all interest rates {r} such that asset A is more valuable than asset B.[3p] (c) Draw the present value of the assets as a function of the interest rate.[2p] (d) Suppose r=0.25. Find the value X such that the present value of asset B is 10.[2p] (e) Suppose the (one-period) interest rates are variable and given as follows: r1=0.1 r2=0.2 r3=0.1. Calculate the yield to maturity of asset A. (You can use Excel or a scientific calculator to find the solution numerically.)[3p]? ? ? Question 2 [8 points] Suppose you have $100 000 today that you want to save for 10 years. Compare the following two savings plans. Bank A offers you the following alternative: For the first $50 000 you obtain 6% p.a. (per annum) for 10 years. For the other amount you obtain 4% p.a. for the first four years. Then you obtain 3% p.a. Bank B offers you the following alternative: The interest in year 1 is 2% in year 2 is 4% in year 3 is 8% in year 4 is 20% then for years 5 to 10 you obtain 1% p.a. For both plans interest payments are reinvested. (a) You maximize the amount at t=10. Which plan is better? How much more can you spend at t=10 if you choose the better one?[4p] (b) Suppose bank B wants to match the offer of bank A. Interest rates for years 2 to 10 are as above. What interest rate for the first year must bank B offer you so that you get the same amount as from bank A?[4p] ? ? Question 3 [6 points] An entrepreneur has a project which generates the following (sure) cash flow stream: t=1 t=2 t=3 $10 $20 $40 in million dollars. The initial investment costs (at t=0) are $20 millions. In addition the entrepreneur has to incur the following operating costs (in million dollars) to run the business in the subsequent periods: t=1 t=2 t=3 $12 $10 $3 The entrepreneur can borrow and save any amount at any date at the one period interest rate r=10% from a bank. (a) Should the entrepreneur undertake the project?[3p] (b) Suppose a private equity firm wants to buy the whole project (at t=0). Once the private equity firm owns the project it has to finance all costs (setup cost and operating costs) itself. What is the minimum price it has to pay so that the entrepreneur accepts the offer? What is the maximum price the private equity firm is willing to pay?[3p] Question 4 [4 points] A firm with an AA-rating plans to issue one million shares of a 4 year-10% bond with face value $100. After the financial crisis this firm is downgraded to a B rating. The risk free rate is 1%. The default spreads are given in the table below. (a) What is the initial amount (before downgrading) the firm wants to raise?[1p] (b) How much can this now B-rated firm raise?[1p] (c) If the firm wants to raise the planned amount how many more bonds does it issue? [2p] Rating Default spread AAA 0.20% AA 0.40% A 0.60% A 0.80% A- 1.00% BBB 1.50% BB 2.00% BB 2.50% B 3.25% B 4.00% B- 6.00% CCC 8.00% CC 10.00% C 12.00% D 20.00% ? ? ? ?
