Handle this for me
9. Assume that you plan to buy a share of XYZ stock today and to hold it for 2 years. Your expectations are that you will not receive a dividend at the end of Year 1, but you will receive a dividend of $9.25 at the end of Year 2. In addition, you expect to sell the stock for $150 at the end of Year 2. If your expected rate today? of return is 16 percent, how much should you be willing to pay for this stock a. $164.19 b. $75.29 c. $107.53 d. $118.35 e. $131.74 10. You have just purchased a 10-year, $1,000 par value bond. The coupon rate on this bond is 8 percent annually, with interest being paid each 6 months. If you expect to earn a 10 percent rate of return on this bond, how much did you pay for it? a. $1,122.87 b. $1,003.42 c. $875.38 d. $950.75 e. $812.15 11. The primary function of the money markets is to provide liquidity to businesses, governments, and individuals so that they can meet their short-term needs for cash. a. True b. False 12. The last dividend on Apple Bite's common stock was $4.00, and the expected growth rate is 10 percent. If you require a rate of return of 20 percent, what is the highest price you should be willing to pay for this stock? a. $44.00 b. $38.50 c. $40.00 d. $45.69 e. $50.001. This question is about some basic properties of projection operators. Remember from class that if W is a subspace of R" which has the orthonormal basis {1'51\" . . ,ii'P}, then the (orthogonal) projection onto W is given by multiplication by the matrix P = U UT, where U = [t'il . . . 113,] is the n x p matrix whose columns are the basis vectors of W. Also remember that UTU = I, and that any vector :i." can be written in exactly one way in the form =t+5 oemsewi. By the way, be careful of the terminology here. The matrix P of an orthogonal projection is not generally an orthogonal matrix. Remember that an orthogonal matrix S is one such that S\"1 = ST. In particular, it must be invertible. The only projection which is invertible is I. (Don't blame me; I didn't invent the terminology!) (a) Show that P2 = P and PT = P. (b) Dene Q = I P. Show that Q2 = Q, QT = Q, and P0 = QP = 0, the zero matrix. (c) Explain why Col(P) = Coi(U). (For this, remember that the column space of a matrix A is the same as the range of the linear transformation whose matrix is A. That is, the vectors in Col(A) are precisely the vectors of the form A5.) (d) Show that if a e Col(P) and 5' 6 (301(0), then a. i; = o. (Hint: Remember that a. 5' = 5T3.) (e) Explain why :i.' = Pf + inf. This means that 001(0) = Col(P)-". (Remark: It is true that if P is any n x 11. matrix such that P2 = P and PT = P, then P is the matrix of an orthogonal projection. If all you have is the P2 = P, then P is still a projection, but it doesn't have to be an orthogonal projection. That is, instead mapping vectors onto a subsPace in a direction perpendicular to the subspace, it will instead map in some oblique direction.) (1') Let A be any n x p matrix with linearly independent columns. The p x p matrix ATA must then be invertible. (You don't need to explain why this is true, but you should at least think about it and try to gure out a reason why it's true.) Dene R = A(ATA)'1AT. Show that 32 = R and RT = R. (Remark: In light of the previous remark, then, R is an orthogonal projection. In fact, it's the projection onto the column space of A. The difference here is that while the columns of A are a basis for the column space, they aren't necessarily an orthonormal basis.) (3) Show that S = I - 2P is an orthogonal matrix. (Not an orthogonal projection!). 1. (4 points) Suppose the following diagram shows the demand (D) and marginal revenue (MR) curves for a monopolist producer of caviar. The diagram also shows the monopolist's marginal cost (MC) and average total cost (ATC). 900 800 700 MC 600 500 ATC 400 300 200 100 MR D 5 10 15 20 25 30 35 40 45 Quantity in thousands of pounds a. What this monopolist's profit-maximizing level of output? b. What price should this monopolist charge to maximize its profit? C. How much profit will this monopolist make if it is maximizing profit
