Suggested Answers to Sample Final Exam 1 1 FNCE10002 Principles of Finance Semester 2, 2021 Sample Final Exam 1 Questions 1 to 9 [9 × 4 = 36 marks] State whether the following statements are true or false and provide a brief explanation. Your answer must begin with True or False followed by your explanation. Note that your explanation cannot just be a restatement of the question statement. Q.1 Two sign reversals in a project’s cash flow stream is only a necessary condition for two internal rates of return to exist. Your answer must begin with True or False followed by your explanation. Q.2 If a firm accepts a zero net present value project then the value of the firm may increase or decrease depending on whether the project’s internal rate of return was relatively high or low, respectively. Your answer must begin with True or False followed by your explanation. Q.3 The payback period method of project evaluation discriminates against projects with long establishment periods and large cash flows later in their lives. Your answer must begin with True or False followed by your explanation. Q.4 Investors who purchase shares after the ex-dividend date are entitled to receive the dividend to be paid on the payment date. Your answer must begin with True or False followed by your explanation. Q.5 An investor wishes to hedge against the possibility of a significant fall in the price of QAF Ltd shares. If the investor currently owns these shares this risk can be hedged by selling call options on the shares. Your answer must begin with True or False followed by your explanation. Q.6 As the exercise price increases for an option, all else being the same, the value of a put option will decrease, and the value of a call option will increase. Your answer must begin with True or False followed by your explanation. Q.7 An investor who purchases a call option or sells a put option is expecting the price of the underlying shares to rise. Your answer must begin with True or False followed by your explanation. Q.8 The expected return of a zero beta security is zero. Your answer must begin with True or False followed by your explanation. Q.9 Short selling a risky security refers to the strategy of borrowing and selling that security when you expect the security’s price to rise in the future. Your answer must begin with True or False followed by your explanation. Suggested Answers to Sample Final Exam 1 2 Questions 10 and 11 consider the following information [10 + 4 = 14 marks] The annual report of WTC Ltd provides the following information about the firm. It has 20 million ordinary shares outstanding with a current market price of $1.50 per share. The beta of ordinary shares is 1.5, the market risk premium is 8% p.a. and the riskfree rate is 6% p.a. The firm’s debt consists of 100,000 bonds paying an annual coupon rate of 10% at the end of each year and maturing in 4 years’ time. Each bond has a face value of $100 and the current yield to maturity on these bonds is 8.0% p.a. The company tax rate is 30%. Q10. Calculate WTC’s after-tax weighted average cost of capital. Show all calculations. Q11. Outline the two circumstances in which the weighted average cost of capital cannot be used in analyzing the investment projects being considered by the firm. What is typically recommended that a firm do in such situations? Questions 12 and 13 consider the following information [6 + 8 = 14 marks] HVH Ltd is considering two mutually exclusive projects where project A has a life of 5 years while project B has a life of 7 years. The cash flows related to the two projects are as follows: Year Project A Project B 0 –$300,000 –$300,000 1 $100,000 $80,000 2 $100,000 $80,000 3 $100,000 $80,000 4 $100,000 $80,000 5 $100,000 $80,000 6 – $80,000 7 – $80,000 The discount rate appropriate for evaluating these projects is 10% p.a. 12. Calculate the NPV of each project. 13. Which project should the firm accept and why? Clearly state any assumption(s) required for your analysis. Question 14 [10 marks] KLC Ltd is evaluating an investment project with the following information: Project life 2 years Initial project cost $400,000 Real before-tax net operating cash flows $350,000 per annum Real after-tax salvage value in year 2 $14,000 Corporate tax rate 30 percent Nominal project discount rate 10.24% per annum Expected inflation rate 4.00% per annum Assuming end-of-year cash flows, calculate the NPV of this project. What decision should the firm make? Show all calculations. Suggested Answers to Sample Final Exam 1 3 Questions 15 and 16 consider the following information [7 + 2 = 9 marks] You are given the following information on two stocks and the market portfolio. Note that the diagonal terms are variances of returns and the off-diagonal terms are covariances of returns. Variances and Covariances Security/Portfolio Delta Ltd Omega Ltd Market Portfolio Delta Ltd 0.250 Omega Ltd 0.060 0.090 Market Portfolio 0.030 0.050 0.040 15. You have $50,000 available to invest and you form a portfolio by short selling $30,000 worth of Delta Ltd and investing all the available funds in Omega Ltd. Calculate the beta of this portfolio. Show all calculations. 16. If the market portfolio’s return unexpectedly falls by 2 percent what, if anything, will happen to the portfolio’s return? Explain. Questions 17 to 20 consider the following information [6 + 6 + 3 + 2 = 17 marks] The CFO of the CSC Ltd is considering a recapitalization plan that would convert CSC from its current all-equity capital structure to one including substantial financial leverage. At present, CSC has 250,000 ordinary shares outstanding, which are selling for $60.00 each, and the recapitalization proposal is to issue $7,500,000 worth of long-term debt at an interest rate of 6.0 per cent and use the proceeds to repurchase 125,000 ordinary shares worth $7,500,000. CSC’s expected EBIT next year will be $2,000,000. Assume there are no market frictions such as corporate or personal income taxes. 17. Calculate the number of shares outstanding, the share price and the debt-to-equity ratio for CSC if the proposed recapitalization is adopted. Show all calculations. 18. Calculate the expected earnings per share and return on equity for CSC’s shareholders under the expected EBIT for both the current all-equity capitalization and the proposed mixed debt/equity capital structure. Show all calculations. 19. Calculate the breakeven level of EBIT where earnings per share for CSC’s shareholders are the same under the current and proposed capital structures. Show all calculations. 20. At what level of EBIT will CSC’s shareholders earn zero EPS under the current and the proposed capital structures? Show all calculations. Suggested Answers to Sample Final Exam 1 4 FNCE10002 Principles of Finance Semester 2, 2021 Suggested Answers to Sample Final Exam 1 Have you reviewed the lectures and tutorials and worked through the sample exam? If not, I would strongly advise you to do so before reading further! Note that the suggested answers are not meant to be exhaustive and should be supplemented with your understanding of the material covered in class and in your tutorials. If you do not follow any of the answers you should check with the Online Tutor or a tutor during their Zoom consult. Q.1 True. This is a necessary condition for multiple IRRs to exist, but it does not mean that there will be multiple IRRs, that is, it is not a sufficient condition. Q.2 False. Accepting a zero NPV project will have no effect on the firm’s value because the investment does not add any value to the firm’s overall value. Q.3 True. The payback period method is biased toward projects that recover their initial cash outlays quickly. The method does not consider cash flows after the recovery of the initial investment and does not consider the time value of money. So, mining and large infrastructure projects will typically be discriminated against by this method. Q.4 False. Investors who purchase shares after the ex-dividend date are not entitled to receive the dividend as this is received by the original shareholders. Q.5 False. Selling a call option imposes an obligation on the seller to sell the shares if the option is exercised against. The appropriate action would be buy put options which give the buyer the right, but not the obligation, to sell the shares at the exercise (or strike) price. This hedges the exposure of the owner of the shares against price drops. Q.6 False. All other things remaining the same, as the exercise price increases, the (intrinsic) value of a put option will increase. For example, take a put option with current stock price (S = $9.00) with an exercise price (X) of $11.00. The intrinsic value is X – S = $2.00. The value of a call option would decrease for the opposite reason. Q.7 True. A purchased call option will earn a profit if the underlying share price rises resulting in the option being in-the-money. A sold put option will be out-of-the-money so the seller of the put can keep the premium earned upfront. Q.8 False. A zero beta security is a riskfree security which is earn a riskfree rate of return according to the CAPM. Suggested Answers to Sample Final Exam 1 5 Q9 False. Short selling a risky security refers to the strategy where you borrow and sell a risky security in the expectation that its price will fall so you can buy it back and return it to the original owner and make a profit on the trade. Questions 10 and 11 10. The calculations for ordinary shares (equity) are as follows. Market value of equity, E = 20000000 × $1.50 = $30.0 million. Cost of equity, rE = rf + [E(rm) – rf)]βE = 0.06 + (0.08)1.5 = 18.0%. The calculations for debt (corporate bonds) are as follows. Price of a bond, ( )0 4 4 10 1 1001 $106.62 0.08 (1 0.08)1 0.08 P   = − + =    ++  . Total market value of debt, D = 100000 × $106.62 = $10.662 million. Cost of debt, rD (given) = 8.0%. After-tax cost of debt, rD = 0.08(1 – 0.3) = 5.6%. Market value of firm, V = 30.0 + 10.662 = $40.662 million. The calculations for the after-tax weighted average cost of capital are as follows. After-tax 10.662 30.0000.08(1 0.3) 0.18 14.7% 40.662 40.662 WACC    = − + =        . Q11. The two circumstances in which the weighted average cost of capital cannot be used in analyzing investment projects is if the projects alter the business and/or financial risk of the firm. A firm would need to use a project-specific hurdle (or discount) rate to evaluate such projects. Questions 12 and 13 12. The net present values of the two projects are as follows. ( )5 100000 11 300000 . 0.10 1 0.1 $79,079 0A NPV   = − − =     +  ( )7 80000 11 300000 0.10 1 0.1 $89,4 4 0 7 .BNPV   = − − =     +  13. Using the assumption that the projects will be replaced with themselves forever, we get the net present values using: 0 (1 ) (1 ) 1 N N rNPV NPV r∞ + = + − . Suggested Answers to Sample Final Exam 1 6 5 5 (1 0.10) 79079 $208,608. (1 0.10) 1 ANPV ∞  + = = + −  7 7 (1 0.10)89474 $183,784. (1 0.10) 1 BNPV ∞  + = = + −  So, the firm should select project A as it has a higher net present value. (Note that one could have used the lowest common duration assumption as well but this would have meant calculating the net present values for seven investments in project A and five investments in project B for a common duration of 35 years, resulting in a large number of calculations!) Question 14 Using real cash flows and the real discount rate, we have: Real discount rate = 1.1024/1.04 – 1 = 6.0%. Real after-tax operating cash flows = 350000(1 – 0.30) = $245,000. Real after-tax salvage value = $14,000 (given). NPV = 245000/(1.06)1 + 245000/(1.06)2 + 14000/(1.06)2 – 400000. NPV = $61,641. Using nominal cash flows and the nominal discount rate, we have: Real after-tax operating cash flows = 350000(1 – 0.30) = $245,000. Alternatively, using nominal cash flows and the nominal discount rate, we have: Nominal after-tax operating cash flows: C1 = 245000(1 + 0.04)1 = $254,800. C2 = 245000(1 + 0.04)2 = $264,992. Nominal after-tax salvage value = 14000(1 + 0.04)2 = $15,142. NPV = 254000/(1.1024)1 + 264992/(1.1024)2 + 15142/(1.1024)2 – 400000. NPV = $61,641. The project should be accepted as it is a positive NPV project. Questions 15 and 16 15. Beta of Delta = 0.03/0.04 = 0.75. Beta of Omega = 0.05/0.04 = 1.25. Suggested Answers to Sample Final Exam 1 7 Weight in Delta = –30000/50000 = –0.6. Weight in Omega = 1 – (–0.6) = 1.6 or 80000/50000 = 1.6. Beta of portfolio = (–0.6)0.75 + (1.6)1.25 = 1.55. 16. One would expect that the portfolio’s return would fall by around 3.1% (= 1.55 × 2%). Questions 17, 18, 19 and 20 17. If CSC issues $7,500,000 worth of debt and repurchases 125,000 shares worth $7,500,000, this implies that the shares will be repurchased at a price of $60 each ($7,500,000 ÷ 125,000 shares). After this transaction, 125,000 shares will remain outstanding, each worth $60, for a total equity value of $7,500,000. The debt-to-equity ratio will therefore be 1.0 ($7,500,000 debt ÷ $7,500,000 equity). 18. The analysis for the two capital structures is as follows. All Equity Financing 50% Debt: 50% Equity EBIT $2,000,000 $2,000,000 Interest (6.0%) $0 $450,000 Net Income $2,000,000 $1,550,000 Shares outstanding 250,000 125,000 Earnings per share $8.00 $12.40 Return on equity 13.33% 20.67% 19 The breakeven level of EBIT (EBIT*) occurs where the two capital structures result in the same EPS. EPS (no debt) = (EBIT* – 0)/250000 = (EBIT* – 450000)/125000 = EPS (with debt). So, (EBIT* – 0) = (EBIT* – 450000)250000/125000. EBIT* = (EBIT* – 450000)2. So, EBIT* = $900,000. 20 Under the current all-equity capitalization, shareholders will earn positive EPS for any EBIT above zero, so EBIT = $0 is where EPS = $0. Under the proposed capital structure, EPS = $0 where EBIT = Interest payments = $450,000.