Mid-term exam 2022.pdf

Mid-term exam for IS4228 (Sem I 2022-2023) Instructions: 1. This paper contains SIX (6) questions and comprises EIGHT (8) printed pages (including this page). Each question is on a separate page. 2. Please answer each question on its own page. (A blank page is given...

Mid-term exam for IS4228 (Sem I 2022-2023) Instructions: 1. This paper contains SIX (6) questions and comprises EIGHT (8) printed pages (including this page). Each question is on a separate page. 2. Please answer each question on its own page. (A blank page is given between question 5 and 6. You can use this page for question 5, if needed.) 3. Please print your name and student number on this page. 4. The exam time is 90 min, from 18:30 to 20:00. 5. This is a semi-closed book exam (a 2-sided hard copy A4 cheat sheet is allowed). 6. A calculator is allowed. 7. Workings MUST be provided clearly. Marks will not be awarded if working shown does not match the final answer or when there is no working. Name: Student Number: 1 Question 1(5 pts): Given the following information from a risk-free bond yield curve: Maturity(years) Coupon rate (annual YTM payments) 1 0 3% 2 10% 5% Calculate: the price of a two-year, $1000 face value risk-free bond with a 20% coupon rate and annual coupons. 2 Question 2(5 pts): Company A has just paid an annual dividend of $1.50. Analysts are predicting dividends to grow by $0.15 per year over the next two years. After then, Company A’s earnings are expected to grow 6% per year, and its dividend payout rate will remain constant. The risk-free interest rate is 2%. Company A’s equity cost of capital is 8% per year. a. What price does the dividend-discount model predict A’s stock should sell for today? b. The Fed raises the risk-free interest rate from 2% to 4%. Assume that the risk premium investors demand for Company A’s stock does not change. What price does the dividend-discount model predict A’s stock should sell for today? 3 Question 3(5 pts): You are thinking of purchasing a house. The house costs $300,000. You have $20,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 5% per year. Instead of a constant amount of payment over the life of the loan, you only need to pay $10,000 per year in the first 5 years. Then you need to pay a constant amount over the last 25 years. a. How much you need to pay each year in the last 25 years? b. You take this mortgage with the house being the collateral. Right before you need to make the first payment with the raised rate, i.e., the payment at the end of the 6th year, you are considering whether you still want to make this payment. What is the minimum value of the house at that time such that you still want to make the payment? (Hint: you want to make the payment only when the value of the collateral is higher than the value of the cash flow you still need to pay.) 4 Question 4 (5 pts): You hold a portfolio with a 30% volatility. You consider short selling a small amount of stock with a 40% volatility and use the proceeds to invest more in your portfolio. If this transaction reduces the risk of your portfolio, what is the minimum possible correlation between the stock you shorted and your original portfolio? 5 Question 5 (7 pts): You are currently only invested in the Natasha Fund (aside from risk-free securities). It has an expected return of 14% with a volatility of 20%. Currently, the risk-free rate of interest is 3.8%. Your broker suggests that you add Hannah Corporation to your portfolio. Hannah Corporation has an expected return of 20%, a volatility of 60%, and a correlation of 0 with the Natasha Fund. a. Is your broker right? Why? b. You follow your broker’s advice and make a substantial investment in Hannah stock so that, considering only your risky investments, 60% is in the Natasha Fund and 40% is in Hannah stock. When you tell your finance professor about your investment, he says that you made a mistake and should reduce your investment in Hannah. Is your finance professor right? Why? 6 7 Question 6 (8 pts): Suppose you group all the stocks in the world into two mutually exclusive portfolios (each stock is in only one portfolio): growth stocks and value stocks. Suppose the two portfolios have equal size (in terms of total value), a correlation of 0.5, and the following characteristics: Expected return Volatility Value stocks 13% 12% Growth stocks 17% 25% The risk-free rate is 2%. From the information given above, can you determine whether CAPM holds in this economy? If so, does CAPM hold and why? If not, why? 8