Key for Quiz I; F4360; Spring, 2001; 11:00 Class; page 1 of 2
Short answer questions/problems
1. One month from today, you plan to make the first of 5 equal quarterly deposits into a savings account. List the sequence of calculations and what you are solving for in order to determine how much is in your account two years from today. (Ex. future value of a growing annuity, future value of a lump sum, present value of a perpetuity in which solve for the first cash flow).
Future value of an annuity, future value of a lump sum
Use the following information to answer questions 2 through 5 below.
Four months from today, you plan to make the first in a series of semiannual deposits (all of the same amount) into an account paying an interest rate of 4.5% per year compounded continuously. You plan to make the last deposit 2 years and 10 months from today. Three years and 5 months from today, you plan to make the first of 10 quarterly withdrawals from this account. After your initial withdrawal of $1000, you plan for your withdrawals to increase by 1.5% each. In order to solve for how large your deposits need to be, you plan to 1) calculate the present value of a growing annuity, then 2) calculate the present value of a single sum, and then 3) calculate the future value of an annuity in which you solve for the annuity payment.
2. What would you use for g in the equation you use in step 1? .015
3. What would you use for “r” in the equation you use in step 1?
r(1) = e.045 – 1 = .046028;
4. Assume you use the same rate in step 2 that you did in step 1. What would you enter for “N” in a financial calculator or “t” in the equation in step 2? 4/3
5. What would you enter for “N” in a financial calculator or “n” in the equation in step 3? 6
6. Assume your boss has just given you forecasted returns on Dot Not Inc. and Dot Con Inc. List the equations you would need to use in order to calculate the correlation between these two firms.
; ; ; ;
7. The expected return on LoseACent Technology Inc. is 12% and the standard deviation of returns on LoseACent is 18%. You plan to invest in LoseACent then borrow or lend to achieve your desired level of risk. Express the risk you face as a function of the percent of your wealth tied up in LoseACent.
sp = XL * (.18)
Quiz I; F4360; Spring, 2001; 11:00 Class; page 2 of 2
8. Assume that you have chosen to invest funds in Sorrell Biotech Inc. (high risk, high return) and Northwestern Grocery and Supply Inc. (low risk, low return). You have decided to sell a lot of your stock in Sorrell and use your proceeds to purchase additional shares in Northwestern. Demonstrate (and label with an 8) the impact of your decision with a graph of the feasible set for Sorrell and Northwestern.
This graph should have two points representing the two assets (Sorrell should be to the right and above Northwestern) and a curve between the two points (no area….just a curved line). The curve should go to the left due to diversification. The sale of Sorrell should be represented by a shift along the curve away from Sorrell and towards Northwestern. There are no two “correct” points….as long as the shift is along the curve away from Sorrell and towards Northwestern.
9. Assume that in addition to investing in Sorrell and Northwestern you can borrow or lend at the risk-free rate. Discuss how you can determine whether your portfolio in number 8 is the best possible mix of Sorrell and Northwestern.
Should be the point of tangency (on the feasible set) on a line between the risk-free intercept and the feasible set.
10. Assume that you invest 90% of your wealth in T-bills and 10% of your wealth in the portfolio you constructed in number 8. On the same graph that you drew for 8, add in a point (and label with a 10) which shows the risk and return you face from your investment in T-bills and the portfolio of stocks (after you sold the stock in Sorrell).
This graph should have a line extending from the risk-free intercept through the point you shifted to (after selling some of your investment in Sorrell). Since you are lending, you investment will lie between the risk-free intercept and the point of tangency, but since you invest most of your wealth in T-bills, your investment will be very close to the risk-free intercept.