1. An annuity pays $1 per year. In the table below fill in the present value of the annuity for different maturity dates and interest rates.

2.
A. A firm discovers that children can be talked into wanting Vegi Babies, and will then harass their parents mercilessly to purchase them. Alas, children appear to tire of each Vegi Baby line after 4 years. In addition, you believe that after 3 Vegi Baby runs (Asparagus Baby, Artichoke Baby, and Turnip Baby) children will have tired of the whole thing and additional lines will be unprofitable. Assume each Vegi Baby line costs $10 million in advertising to launch in period 0, and then produces a net cash inflow of $4 million per year beginning in year 1 and ending in year 4. (Note, here period 0 refers to the launch year, and not calendar time.) Further assume you can only launch one Vegi Baby line per year. If the interest rate equals 12% what is the PV of the Vegi Baby line?

B. After giving the matter some thought you come up with a somewhat more realistic model of the firm’s cash flows. Instead of assuming that after year 4 profits end, you believe a better assumption would be that they will decline at a rate of 10% per year forever. For example, in year 5 profits will equal $3.6 million. (Again year in this case refers to the years from launch date and not calendar time.) Based upon your new model of the cash flows what is the PV of the Vegi Baby line?

3. Amalgamated Rocks is an old firm that has consistently produced profits of $20 million per year. Currently the market expects this to continue forever, and values the firm at $200 million. Alas, Mr. Amalgamated has lost a few rocks of his own and ordered the firm to pursue a new investment strategy. Instead of paying an annual dividend of $20 million per year, he orders the firm to invest 50% of the current year’s profits in 5 year treasury bonds with coupons of 8% if it is an odd year, and in 10 year treasury bonds with coupons of 9% if it is an even year. What is the new value of the firm? Hint: If you have booted up your computer you are making a mistake.

4. That’s Disgusting produces a shampoo for removing fur balls coughed up by cats from rugs. Right now the firm reinvests 40% of its earnings (currently at $20 million) and is growing at a rate of 8% per year.
A) What is the firm’s return on equity (Matthew Spiegel’s terminology)?
or equivalently, A) What is the firm’s return on retained earnings (Geert Rouwenhorst’s terminology)?
B) If the firm has a market value of $1 billion what is the discount rate?
C) Imagine the firm’s product falls out of favor and the return on equity falls by 2%, what will be the firm’s new market value?

5. A real estate company is planing to put up a new building. The building will cost $40 million in period 0 to construct. After that leases will generate $6 million per year for 20 years. In years 5, 10, and 15 you will need to spend $8 million to repair the building’s exterior, and in year 10 another $4 million to replace the roof.
The project’s developer has hired you and demanded that you calculate the internal rate of return (IRR) for the project. You try to talk him out of it, but to no avail. So you try the next best approach and decide to convince him that the IRR criteria will not work here by demonstrating that there exist multiple IRRs.
A) Calculate all of the IRRs.
B) Graph the project’s PV as a function of the interest rate.