QUESTIONS. Assuming that the two securities above are the only investment vehicles available:

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Hilary Maurice Cameron
5 years ago
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1 NUMBER ONE QUESTIONS (a) Let R and R be the returns from two securities with E(R ) = 3% and E(R ) = 8%, VAR(R ) = 0.0, VAR(R ) = 0.05, and COV(R R ) = 0.0. Assuming that the two securities above are the only investment vehicles available: (i) Security? (ii) Security. If we want to minimize risk, how much of our portfolio will we invest in (5 marks) Find the mean and standard deviation of a portfolio that is 40% in (5 marks) (b) You are given that assets A and B are perfectly correlated such that R y = R X and the probability distribution of A is: Probability Return on X, R X % What is the percentage of your wealth to put into asset A to achieve zero variance? (0 marks) (Total: 0 marks) NUMBER TWO TiquiBank Ltd must decide whether to open a new branch. The current market value of the bank is Ksh.00 million. According to company policy (and industry practice), the bank s capital structure is highly leveraged. The present (and optimal) ratio of debt to total assets is 0.9. Tiqui S debt is almost exclusively in the form of demand, savings, and time deposits. The average return on these deposits to the bank s clients has been 5% over the past five years. However, recently interest rates have climbed sharply, and as a result Tiqui presently pays an average annual rate of

2 6.5% on its accounts in order to remain competitive. In addition, the bank incurs a service cost of.75% per account. Because of an established tradition for banks to put a ceiling on the amount of interest they pay on their accounts (dating back to the late 980s and now being revitalized by the Donde Bill) to some points below the treasury bill rate, the banking industry at large has been experiencing disintermediation a loss of clients to the open money market (Government paper such as Floating Rate Bonds, Treasury bills, etc), where interest rates are higher. Largely because of the interest rate situation (which shows no sign of improving), Tiqui s managing director has stipulated that for the branch project to be acceptable its entire cost of KSh.40 million will have to be raised by 90% debt and 0% equity. The bank s cost of equity capital is %. Tiqui s marginal tax rate is 48%. Market analysis indicates that the new branch may be expected to return net cash flows according to the following schedule: Year to infinite Net cash flow Ksh ,000,000,800 3,600 3,600 4,000 4,000 Required: (a) Determine the weighted average cost of capital to be used in evaluating the acceptability of opening the new branch. (0 marks) (b) On the basis of a suitable analysis advise on whether Tiqui should open the new branch. (0 marks) (Total: 0 marks) NUMBER THREE The following data have been developed for the VIT Company Limited: Year Market Returns Company Returns

3 The yield to maturity on Treasury Bills is and is expected to remain at this point for the foreseeable future. Required: (a) The equation of the Security Market Line. (4 marks) (b) The required return for the VIT Company Limited. (3 marks) (c) Is the Company correctly priced, underpriced or overpriced in the market? Explain. (3 marks) (Total: 0 marks) NUMBER FOUR Jung Cycles Ltd. wishes to design a new sports bicycle. The Company would have to invest Ksh.0,000 at the beginning of the first year for the design and model testing of the new bicycle. Jung s managers believe that there is a 60% probability that this phase will be successful and the project will continue. If phase is not successful the project will be abandoned with zero salvage value. The next phase, if undertaken would consist of making the molds and producing two prototype bicycles. This would cost Ksh.500,000 at the end of the first year. If the bicycles test well, Jung would go into production. If they do not, the molds and prototypes could be sold for Ksh.00,000. The managers estimate that the probability is 80 percent that the bikes will pass testing and that Phase 3 will be undertaken. Phase 3 consists of changing over one current production line to produce the new design. This would cost Ksh. million in Year. If the economy is strong at this point, the net value of sales would be Ksh.3 million, while if the economy is weak the net value would be Ksh..5 million. Both net values occur during Year 3, and the two states of the economy are equally likely. Jung s cost of capital is percent. Required: (a) Construct a decision tree and determine the project s expected NPV assuming that the project has average risk. ( marks)

4 (b) Calculate the project s standard deviation of NPV and coefficient of variation of NPV. (5 marks) (c) If Jung average project had a coefficient of variation of between.0 and.0, would this project be of high, low or average standalone risk? (3 marks) (Total: 0 marks) NUMBER FIVE (a) Explain the difference between private and public financial management. (0 marks) (b) Outline the benefits of capital budgeting in public sector. (0 marks) (Total: 0 marks)

5 NUMBER ONE ANSWERS (a) (i) We can minimize risk by setting the first derivate of expression for portfolio variance equal to as follows: d dw p = wσ σ wσ e σ σ 4we σ Solving for w (percentage of wealth to invest in security to obtain the minrisk): w = = r ² ² r = /3 or VAR(RP) = w² ² w² ² w wcov Substitute for known values: VAR(RP) =.0w² +.05(w)².0 x w(w) Simplify: VAR(RP) =.09w².w +.05 Differentiate = equate to zero and solve:.8w. = 0 w =..3 = /3 (ii) (RP) =.4 x 3% +.6 x 8% σ P =.4² x.0 +.6² x.05 (4)(.6)(.

6 =.064 =.8% (b) Pi R xi PiR xi R xi e(r x ) Pi(R xi E E(R x )= VAR (R x ) = Pi R yi PiR yi P i [R yi E(R y )]² E(R x )= 8.0 VAR (R x ) = 0.7 Pi[R xi E(R x )] Cov = 0.86 VAR(R P ) = w²var(r x ) + (w)²var(r y ) + w(w)cov(r x,r y ) = 4.3w² + (w)² x x w(w) = 0 =.075w² w = 0 w = = ² 4(.0753)(.007) (.075) Thus 5% of wealth should be invested in asset x so as to achieve zero variance. NUMBER THREE (a) Prob.(pi) Rci Pi*Rci Rci E(Rc) Rci E(Rc)ˆ Pi*(Rci E(Rc)ˆ Pi*[RciE(Rc)] E(M)] [Mi

7 % 5.00% 5.00% 0.00% 30.00% E(J) = 4.7% 0.83% 0.83%.50%.67% 5.00% 0.00% 5.00% 5.00% 0.00% 0.00% VAR(Rc) = S.D.(Rc) = % COV(RC,RM)= Prob.(pi) Security M % % % % % % E(M) = Pi*mi 4.50%.00% 0.50%.00% 0.50% 4.50%.00% (MiE(M) ˆ VAR(M)= S.D.(M) = Mi E(M) 0.00% 0.00% Pi*(Mi E(M) ˆ 0, % Beta = CC = The equation of the SML: Rj = 6.6% + 5.4% * Bj (b) The required return for VIT: Ru = 6.6% + 5.4% *.7 =.9% (c) The Company is overpriced in the market. Reason: expected return is less than required return implying that compensation for its level of risk is inadequate. NUMBER FOUR (a) It can be observed that the proposed branch constitutes an extension of Jung Ltd s existing business. This implies that the risk class of the new project is same as that of the existing business. Thus the appropriate discount rate to use in evaluating the project should be the bank s weighted average cost of capital.

8 Cost of debt:: before tax 6.5% +.75% = 9% After tax 9%(.48) = 4.68% Cost of equity: as given = % Weighted average cost of capital: (b) Capital component Debt Equity Computation of NPV: Component cost % Weight % 90 0 Weighted cost % Year to infinite Net cash flow Sh. 000 (40,000),000,800 3,600 3,600 4,000 4,000/0.5 = 80,000 PVIF(5%,t) PV of CF Sh. 000 (40,000),904.6, ,09.68,96.7 3,34 NPV = 34,39.6 The new branch should be opened since the NPV is positive. SV=0 SOS 00 SMAP 3, ES 0.4 BPT SMAP ES SOS (0) I 0.6 (500) 0.8 (000) PBB BPT PND I

9 PPB PND JOINT PPOB NPV KSH. Ksh (0) (40) 0. ( ) (45.) 0.4 (85.95) (44.63) 0.4 (88.78) (.6) Key I Invest I = Do not invest SOS PPB PND SMAP Stage one successful Produce prototype bicycles Produce new design Sale molds and prototypes ES Economy strong Workings for NPV 00, ,000. 0,000.. = 376,709,500,000,000, , ,000.².. = 85,95 3,000,000,000, , , = 88,78 Projects Standard deviation of NPV Pi NPB i E(NPV) NPVENPV P i (NPV ENPV)² 0.40 (0,000) (4,000) (7,779) 6,530,989,36

10 (376,709) (85,95) 00,78 (45,05) (44,68),6 (494,488) (303,73) 763,939 9,34,05,000,40,604,000 40,064,670,000 σ = 445,060 (c) CV = σ m 445,060 7,779 = 3.78 The project has high stand alone risk since its CV far much exceeds the firm s of between.0 and.0. NUMBER FIVE (a) Private Versus Public Financial Management Financial management in government departments is different from financial management in an industrial or commercial company for some fairly obvious reasons. (i) Government departments do not operate to make a profit and the objectives of a department or of a programme of spending cannot be expressed in terms of maximizing the return n capital employed. Government services are provided without the commercial pressure of competition. There are no competitive reasons for controlling costs, being efficient or, when services are charged for (such as medical prescriptions), keeping prices down. Government departments have fulltime professional civil servants and their managers, but decisions are also taken by politicians. (iv) The government gets its money for spending from taxes, other sources of income and borrowing (such as issuing gilts) and the nature of its fundraising differs substantially from fundraising by companies. The financial markets regard the government as a totally secure borrower, and so the government can usually borrow whatever it likes, provided it is prepared to pay a suitable rate of interest.

11 Central government borrowing is coordinated centrally by the Treasury and the Central Bank. Individual departments of government do not have to borrow funds themselves. Local governments raise some taxes locally and can do some borrowing in the financial markets, but they also rely for some of their funds on central government. Companies rely heavily on retained profits as a source of funds. Government departments cannot rely on any such source, because they do not make profits. Some government services must be paid for by customers, for example health and educational services, although the price that is charged might not cover the costs in full. Since managing government is different from managing a company, a different framework is needed for planning and control. This is achieved by: setting objectives for each department; careful planning of public expenditure proposals; emphasis on getting value for money. (b) The Capital Budgeting Process A number of terms are used interchangeably to refer to capital budgeting in public sector, e.g. public work planning, capital improvement planning, capital facility planning or capital outlay planning. Capital Budget in public sector refer to the legislative plan for proposed capital outlay and the means of financing them for the coming fiscal period. The capital planning and programming role of the chief executive guides the capital budgeting and programming process and makes recommendations to the legislature. The guidelines for preparing and submitting the capital plan are determined by parliament which establishes the time frame for the program, project or activities, the extent of the citizen participation and the administrative responsibilities for the capital planning process. The authority to analyse the financial implication and impact of the capital program on the operating budget and to make recommendation on the financing approaches to assign to the department (Ministry of Finance) where a planning commission exists. Benefits of Capital Budgeting in Public Sector

12 A number of important results flow from an effective plan and executed capital improvement program. These include: It forces communities to examine their goals and needs capabilities It promotes greater efficiency in the use of tax resources. It provides an important guide in and the growth and development of the community. It encourages government for public organizations to improve their administrative systems. It is an important means for promoting Regional Corporation it facilitates and promotes sound financial management. It offers an effective way to replace or repair capital facilities. It enhances the government or the organisation s opportunity to participate because of the many programs that the government maintain to aid in the planning and construction of infrastructure.

Cost of Capital (represents risk)

Cost of Capital (represents risk) Cost of Equity Capital - From the shareholders perspective, the expected return is the cost of equity capital E(R i ) is the return needed to make the investment = the