1. Test 1 Solution Sketches Note for multiple-choice questions: choose the closest answer. Exam date: 1 February 2016 Econ 134A, John Hartman

2. 1. Present value calculation

3. 2. Present value calculation

4. 3. Relationship between IRR and NPV A project has a cash outflow today, a cash inflow one year from today, and a cash outflow two years from today. (Note that a cash outflow means you have to pay money and a cash inflow means you receive money.) Two internal rates are found, 13% and 40%. Darryl is trying to determine whether or not net present values (NPVs) are positive for 5%, 20%, and 60% discount rates. For which of these three discount rates will the NPV be positive? We know the graph will look like this: 13%20%40% discount rate NPV $0 If the discount rate is high, then less weight is put on the last inflow, more weight is put on the other payments, and NPV is negative. If the discount rate is low, then more weight is put on the last inflow, less weight is put on the other payments, and the NPV is negative. If the discount rate is between these two, then more weight is put on the inflow in the middle, and the NPV becomes positive. Two IRRs means the line crosses the x-axis twice. The ordering of outflow, inflow, outflow means that the line begins negative, crosses (being positive for a bit), then becomes negative at high rates. r=20% has a positive NPV.

5. 4. Inflation

6. 5. Annuity factor

7. 6. Partial amortization

8. 7. IRR