Calculating Value with Varying Compounding & Investing in Stocks & Bonds, Exams of Investment Management and Portfolio Theory

Download Calculating Value with Varying Compounding & Investing in Stocks & Bonds and more Exams Investment Management and Portfolio Theory in PDF only on Docsity! INVESTMENT THEORY PLEDGE: "On my honor, I have neither given nor received any unauthorized aid on this exam, nor am I aware of anyone giving or receiving any unauthorized aid on this exam." ________________________________________ Signature ________________________________________ Name (Print) 1. Assuming annual compounding, calculate the present value of $10,000 to be received in 16 years when a 9% rate of return can be earned on investment. Solution: The present value of a $10,000 investment to be received in 16 years when a 9% rate of return can be earned on investment can be easily calculated using the formula: PV = $10,000/(1.09)16 = $2,519. This value can also be approximated using the Rule of 72 formula. 2. Assuming annual compounding, use the Rule of 72 calculate the present value of $10,000 to be received in 16 years when a 9% rate of return can be earned on investment. Solution: According to the Rule of 72, money growing at 9% doubles in 8 years, where the number of years to double = 72/interest rate. Money growing at 9% will double twice over a 16 year period. When calculating the future value of a present sum, the Rule of 72 suggests that $10,000 will grow into $40,000 over a 16-year period. Therefore, according to the Rule of 72, $2,500= $10,000/$40,000 is the present value of a $10,000 investment to be received in 16 years when a 9% rate of return is assumed. 3. Show how the future value of a 10-year $100,000 investment growing at 12% differs when using annual versus continuous compounding. Explain any differences. Solution: The future value of a 10-year $100,000 investment earning 12% interest with annual compounding can be easily calculated using the formula: FV = $100,000 Η (1.12)10 = $310,585. docsity.com Using continuous compounding this value is FV = $100,000 Η e(0.12)(10) = $332,012. Continuous compounding yields a larger result given more Ainterest on interest.@ Use the following information to help answer questions 4-7 On February 24, 2003, the DJIA closed at 10566.37, down 43.25 points. The value of the DJIA divisor on that date was 0.135. 4. Calculate the average market price of DJIA component stocks on February 24, 2003. Solution: The DJIA = Σ Prices/Divisor, where Σ Prices is the sum of stock prices for all 30 component stocks, and the Divisor is a constant calculated by Dow Jones. On February 24, 2003, DJIA = 10566.37 = Σ Prices/0.135. Therefore, Σ Prices = 10566.37Η 0.135 = $1,426.46. The average price of a component stock on that date was $47.55 = $1,426.46/30. 5. How much would it cost to buy a round lot of all DJIA components on February 24, 2003? Solution: A round lot is 100 shares of stock. The cost of a round lot of 100 shares of each component stock in the DJIA on February 24, 2003 was $142,646 = $1,426.46 Η 100. 6. Calculate the average price change (in dollars) for DJIA components on February 24, 2003. Solution: Because the DJIA = Σ Prices/Divisor, ΔDJIA = ΔΣ Prices/Divisor. On February 24, 2003, ΔDJIA = 43.25 = ΔΣ Prices/Divisor. = ΔΣ Prices/0.135. Therefore, ΔΣ Prices = 43.25 Η 0.135 = $5.83875. The average price change for a component stock on that date was $5.83875/30 = $0.1946, or 19.464. 7. Calculate the effect on the DJIA of the $0.96 fall in 3M on February 24, 2003. Solution: Because the DJIA = Σ Prices/Divisor, ΔDJIA = ΔΣ Prices/Divisor. Following the $0.96 decline in 3M on February 24, 2003, ΔDJIA = 7.11 points = ΔPrice/Divisor. = $0.96/0.135. 8. EP has a bid of 6.99, a bid size of 83, an ask of 7.00, and an ask size of 114. How much money is represented on the sell of the market? Solution: Ask size is the number of round lots represented on the sell side of the market. A round lot is 100 shares, so an ask size of 114 at 7.00 for EP represents 11,400 shares worth $79,800. 9. An investor went long DIS at 21.55 using 50% margin. At what price would the investor face a 30% maintenance margin call? Solution: 15.39. Stock purchased with 50% initial margin triggers a 30% maintenance margin call following only a 28.6% decline in price. Note that the initial amount of margin debt is 50% of the initial purchase price, P0 of a given stock. In equation form, this means that Debt = 0.5P0. To docsity.com FIRST EXAM, FALL 2003, page 5. premium with the convertible=s higher income. Because the common stock in this instance pays no dividend, stockholders would earn no dividend income on a $1,200 investment in the stock. In contrast, a convertible bondholder would earn $40 (= 4% Η $1,000) of interest income on a similar $1,200 investment in one bond. On an annual basis, the convertible bondholder earns $40 in higher income. With a conversion premium of $400 = $1,200 - $800, it would take the convertible bondholder ten years to recoup the conversion premium. Breakeven time is 10 years (= $400/$40). 18. What is the difference between modified duration and convexity? Solution: Modified duration measures the sensitivity of bond prices to changes in yield to maturity. Convexity measures the sensitivity of modified duration to changes in yield to maturity. If modified duration can be thought of as the Aspeed@ of bond price changes from yield changes, then convexity is the rate of Aacceleration@ in bond price changes tied to yield changes. 19. Calculate the percentage change in price for a bond featuring modified duration of 1.5 following a 10 basis point decline in interest rates. Solution: 0.15%. Bond yields are quoted in terms of basis points, where each basis point equals 1/100th of 1%. Thus, a 0.1% decline in rates translates into a 10 basis points decline in yield. Modified duration is a direct estimate of the percentage change in a bond=s market price for each percentage point change in market interest rates. Modified duration of 1.5 means that this bond=s price would rise roughly 0.15% = -1.5 Η (-0.1%) following a 0.1% decline in interest rates, or fall by 0.15% if prevailing rates rose by 0.1%. 20. Explain the PEG ratio and the PEG ratio rule-of-thumb. Solution: The PEG ratio is simply the P/E ratio divided by the expected EPS growth rate. If a company has a P/E of 20, and is expected to enjoy EPS growth of 20% per year, the company=s PEG ratio would be 1. Generally speaking, a stock is fully valued if it sports a PEG ratio of 1 or more. If the PEG ratio is less than 1, the stock as worthy of investment consideration. The PEG ratio rule of thumb goes something like this: If PEG #1, the stock may be worthy of investment attention and possible purchase; If PEG #0.5, the stock is definitely worthy of investment attention, and may represent a very attractive investment; If PEG #0.33, the stock is apt to represent an extraordinarily attractive investment opportunity. Needless to say, the investment merit of a stock increases with a decrease in the PEG ratio. Strict growth-at-a-reasonable-price investors seldom, if ever, buy growth stocks with PEG ratios greater than 1. docsity.com FIRST EXAM, FALL 2003, page 6. 21. A nondividend paying company has a share price of $20, P/B ratio of 5, and EPS of $1. Calculate the rate of growth made possible by internally generated funds. Solution: 25%. The rate of growth made possible by internally generated funds is determined by the retention rate and ROE. In this case, a price-book ratio of 4 implies book value per share of $4 = $20/5, and ROE = $1/$4 = 25%. If a company earns a 25% ROE and retains all earnings for future investment, the amount of book-value growth that could be funded internally is 25%. 22. According to the dividend discount or constant growth model, calculate the required rate of return for a stock with a current price of $36, a projected dividend of 544 per share, projected dividend growth of 8% Solution: 9.5%. According to the dividend discount or constant growth model, k = D1/P0 + g. In this case, k = 0.54/36 + 8% = 9.5%. 23. HON has a current price of 29, an expected dividend per share of $0.75, expected EPS of $1.75, expected EPS growth of 6.5% per year, and a typical P/E ratio of 16. According to the Discounted Present Value Model, what is the expected rate of return on HON over the next five years? Solution: 8.35%. According to the Discounted Present Value Model, the expected price for HON in five years is According to the Discounted Present Value Model, the expected price for HON in five years is P5 = (1 + g)5 Η EPS0 Η P/E = (1.065)5 Η $1.75 Η 16 = $38.36. With a present price of $29 and a price of $38.36 in five years, the rate of capital appreciation is g = (It/I0)1/t -1 = ($38.36/$29)1/5 - 1 = 1.0576 - 1 = 5.76%. With an expected dividend of $0.75, the expected dividend yield is 2.59% = $0.75/$29. Therefore, the expected total return is 8.35% = 5.76% + 2.59%. 24. HON has a current price of 29, an expected dividend per share of $0.75, expected EPS of $1.75, expected EPS growth of 6.5% per year, and a typical P/E ratio of 16. According to the Discounted Present Value Model, is HON overvalued if investors have a risk-adjusted required return of 10% per year? Explain your answer. Solution: Yes. HON is overvalued if investors have a risk-adjusted required return of 10%. Recall from above that according to the Discounted Present Value Model, the expected total expected return on HON is 8.35%. When the expected total return is less than the required return, a stock is overvalued. 25. HON has a current price of 29, an expected dividend per share of $0.75, expected EPS of $1.75, expected EPS growth of 6.5% per year, and a typical P/E ratio of 16. According to the dividend discount model, calculate the maximum price an investor would pay for HON if docsity.com FIRST EXAM, FALL 2003, page 7. that investor has a required rate of return of 10% per year. Solution: $21.42. According to the Dividend Discount Model, P0 = D1/(k-g) = $0.75/(0.1 - 0.065) = $21.42. docsity.com