Part 1 (20 marks) – Time Value of Money

Q1. Stanley plans to invest $10,000 at the end of each year for 7 years on a project. This project will pay him a rate of return of 10% per annum. How much money will John have at the end of year 7? (5 marks)

Q2. You want to purchase a house. The house costs $500,000. You have $50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price.

(a) The ABC bank offers a 30-year mortgage that requires annual payments and has an interest rate of 6% per year. What will your annual payment be if you sign up for this mortgage? (4 marks)

(b)  Suppose you take the 30-year mortgage in part (a), how much will you still owe on the mortgage after 10 years? (3 marks)

(c)  Assume now you are at the end of year 10, and you have just made your annual payment. You have decided to refinance your mortgage with a monthly payment of $3,000 with an interest rate of 5% p.a.. With this plan, how much earlier will it take for you to pay off the mortgage? (5 marks)

(d)  Assume there is another bank: BetterDeal Bank offer you another refinance option. It is still a monthly payment at $3,000 per month but with the interest rate compounding quarterly. Would you prefer this deal or the deal with ABC bank in part (c)? Explain, while calculation is not compulsory. (3 marks)

Part 2 (20 marks) - Portfolio Analysis

You have information on several possible investments as laid out in the table below. A, B, and C are individual risky securities. For now, assume these are the only 3 risky investments that comprise the market. M is the market portfolio. Assume the risk-free rate it 3%. All returns are annual returns.

Answer the following questions with respect to this investment information: (a) Calculate the risk for assets A, B and C. (3 marks)

(b) Assume that you want to form a portfolio that consists of a long position of $18,000 in asset C and a short position of $6,000 in asset A. What is the expected return and risk of this portfolio? (5 marks)

(c) You have $100,000 to invest. You would like to use a combination of the market portfolio and risk-free rate to obtain a standard deviation of4% on your overall portfolio. How much (in dollars) do you invest in F if you choose the most efficient portfolio possible? What is the return of this portfolio?  (5 marks)

(d) Compare the portfolio you constructed in (a) and (b), which one would a rational investor prefer to hold, explain why. (2 marks)

(e) You have $100,000 to invest. What is the maximum Sharp ratio you can obtain on a portfolio? Show the calculation.  (2 marks)

(f)  You realize that asset C has the same return as the market portfolio. What does that tell you? Explain your findings. (3 marks)

Part 3 (35 marks) - Project Evaluation

ABC Ltd. plans to introduce a new flavour of the ice cream to the market. The marketing team has completed a $10,000 feasibility study to assess the demand for the new ice cream. To carry out this project, the company requires to purchase a new machine at the cost of $150,000 today. It will be depreciated on a straight-line basis over 10 years, after which it has no salvage value.

You expect that the new machine will produce an incremental sales revenue of $50,000 per year for the next 5 years, with the cost of goods sold to be $20,000 per year. It is expected that the new ice cream will cannibalize the demand for the existing products at an amount of $3,000 per year. Assume that you can sell the machine after 5 years for $90,000. The company requires a 10% net working capital as the next year’s sales at the commencement of the project. This is assumed to be fully recoverable at the end of the project. The company’s tax rate is 45%.

(a) Estimate the after-tax cash flows for the project using the accounting flow and the cash flow table. IMPORTANT: You must show each input in your table as a separate row. DO NOT group inputs together. (12 marks)

(b) In your capital budgeting analysis, you would have to adjust the depreciation in both accounting flow table  and cash  flow table. Discuss the logic  and the purpose of the adjustment of depreciation. (5 marks)

(c) Using NPV analysis, should ABC Ltd. go ahead with the project? Assume its cost of capital is 10%.  (3 marks)

(d) You have also calculated the IRR for this project to be 6.35%. Is the IRR rule give you the same conclusion as NPV rule? Explain. (3 marks)

(e) Determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged and interpret. (2 marks)

(f)  To make your existing ice cream more attractive, the company plan to provide free sprinkle toppings for free. There are two types of sprinkle equipment that is available on the market. The SP1 cost $400 to buy, and it will last for three years. The SP2 costs $550 to buy, and it will last for four years. The company expects to keep this free topping service in the future, and they would replace the equipment at the end of its life. Which equipment should the company buy, assume the cost of capital is 10%. (5 marks)

(g)  The 10% cost of capital in the questions above assumes that the project would share the same systematic risks and financing with the same capital structure as ABC Ltd. Discuss what may be the potential issue with this assumption on the discount rate. (5 marks)