Exam 2 Answers

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Stock & Bonds Quiz Questions 1. Today, a bond has a coupon rate of 9.64%, par value of $1000, YTM of 9.40%, and semi- annual coupons with the next coupon due in 6 months. One year ago, the bond’s price was $983.42, and the bond had 15 years until maturity. What is the current yield of the bond today? Current yield today = annual coupons / bond value today Approach: 1) Find the annual coupons 2) Find the value of the bond today 3) Find the current yield today 1) Find the annual coupons Annual coupons = par × coupon rate = 1000 × 9.64% = $96.40 2) Find bond value today If the bond had 15 years until maturity from 1 year ago, then today it has 14 years until maturity, so N = 14 years × 2 coupons per year = 28 I% = YTM ÷ # coupons per year = 9.40 ÷ 2 = 4.70 FV = par = 1,000 PMT = par × coupon rate ÷ # coupons per year = 1000 × 9.64% ÷ 2 = 48.20 END mode Enter 28 4.70 48.20 1000 N I% PV PMT FV Solve for -1,018.48 Today, the price of the bond is $1,018.48 3) Find current yield today Current yield today = annual coupons / bond value today = 96.40 / 1,018.48 = .0947 = 9.47%

2. Bond A has a coupon rate of 17.80 percent, a yield-to-maturity of 15.60 percent, and a face value of $1,000; matures in 12 years; and pays coupons annually with the next coupon expected in 1 year. What is (X + Y + Z) if X is the present value of any coupon payments expected to be made in 5 years from today, Y is the present value of any coupon payments expected to be made in 10 years from today, and Z is the present value of any coupon payments expected to be made in 15 years from today? Approach: 1) Determine the coupon payments expected in 5, 10, and 15 years 2) Determine the appropriate period length and discount rate 3) Find the present values of any coupon payments expected in 5, 10, and 15 years 4) Add up the present values of any coupon payments expected in 5, 10, and 15 years 1) Determine the coupon payments expected in 5, 10, and 15 years The expected annual coupon for bond A = par × coupon rate ÷ # coupons per year = $1,000 × 17.80% ÷ 1 = $178.00 Since the bond matures in 12 years, a coupon of $178.00 is expected in 5 years and in 10 years, but not in 15 years. 2) Determine the appropriate period length and discount rate Since coupons are paid annually, the relevant period is a year Therefore: - The coupon of $178.00 expected in 5 years, which is in 5 periods - The coupon of $178.00 expected in 10 years, which is in 10 periods - There is no coupon expected in 15 years, which is in 15 periods The relevant discount rate per period for bond A = YTM ÷ # coupons per year = 15.60 percent ÷ 1 = 15.60 percent = .1560 per year 3) Find the present values of any coupon payments expected in 5, 10, and 15 years PV 0 = C t / (1+r) t X = the present value of the coupon of $178.00 expected in 5 years = $178.00 / 1.1560 5 = $86.22 Y = the present value of the coupon of $178.00 expected in 10 years = $178.00 / 1.1560 10 = $41.77 Z = $0, because no coupon is expected in 15 years 4) Add up the present values of any coupon payments expected in 5, 10, and 15 years X + Y +Z = $86.22 + $41.77 + $0.00 = $127.99

3. Dewey has one share of stock and one bond. The total value of the two securities is $1,050. The bond has a YTM of 18.60 percent, a coupon rate of 12.40 percent, and a face value of $1,000; pays semi-annual coupons with the next one expected in 6 months; and matures in 6 years. The stock pays annual dividends that are expected to grow by 1.73 percent per year forever. The next dividend is expected to be $18.10 and paid in one year. What is the expected return for the stock? Since the stock’s dividends are expected to grow at a constant rate forever, R = (D 1 /P 0 ) + g We know that g = .0173 and D 1 = $18.10 We don’t know what P 0 and R are, but we know that bond value + stock value (P 0 ) = $1,050 If we find the bond value, we can find the stock value, and we can find R from R = (D 1 /P 0 ) + g Finding the bond value N = 6 years × 2 coupons per year = 12 I% = YTM ÷ # coupons per year = 18.60 ÷ 2 = 9.3 FV = 1,000 = par PMT = par × coupon rate ÷ # coupons per year = 1000 × 12.40% ÷ 2 = 62 END mode Enter 12 9.3 62 1000 N I% PV PMT FV Solve for -781.33 Finding the stock value Since bond value + stock value = $1,050, stock value = $1,050 – $781.33 = $268.67 Finding the expected return Since P 0 = D 1 /(R – g), then R = (D 1 /P 0 ) + g = (18.10 / 268.67) + .0173 = .0847 = 8.47 percent

4. Two years ago, the price of a bond was $955.72, and one year ago, the price of the bond was $942.21. Over the past year, the bond paid a total of $88.43 in coupon payments, which were just paid. If the bond is currently priced at $991.52 then what was the rate of return for the bond over the past year (from 1 year ago to today)? The par value of the bond is $1,000. Percentage return = (cash flows from investment + ending value – initial value) / initial value Percentage return over the past year (from 1 year ago to today) = (cash flows from investment over past year + bond price today – bond price 1 year ago) / bond price 1 year ago Cash flows from investment over past year The bond (just) made a total of $88.43 in coupon payments over the past year Initial value = bond price 1 year ago One year ago, the bond had a price of $942.21 Ending value = bond price today The bond is currently priced at $991.52 Percentage return over past year = (cash flows from investment + ending value – initial value) / initial value = (cash flows from investment over past year + bond price today – bond price 1 year ago) / bond price 1 year ago = (88.43 + 991.52 – 942.21) / 942.21 = (88.43 + 49.31) / 942.21 = 137.74 / 942.21 = .1462 = 14.62% 5. Labrador has issued bonds, common stock, and preferred stock. The YTM for the bonds is 14% and the expected annual return for the preferred stock is 19%. Which of the following assertions about the expected annual return for the common stock issued by Labrador is most likely to be true? A. The expected annual return for the common stock is 9% B. The expected annual return for the common stock is 14% C. The expected annual return for the common stock is 16% D. The expected annual return for the common stock is 19% E. The expected annual return for the common stock is 21%

Answer: E. The expected annual return for the common stock is 21% Labrador common stock is most likely to be the riskiest, Labrador bonds are most likely to be the least risky, and Labrador preferred stock is most likely to be in the middle. Therefore, Labrador common stock should have the highest expected return, Labrador bonds should have the lowest expected return as measured by YTM, and Labrador preferred stock should have an expected return between the expected return of common stock and the YTM of bonds. Since Labrador’s preferred stock has an expected return of 19%, its common stock should have a return greater than 19%, and 21% is the only alternative that is greater than 19%. 6. Branford has one share of stock and one bond. The total value of the two securities is $1,200. The bond has a YTM of 10.2 percent, a coupon rate of 9.2 percent, and a face value of $1,000; pays semi-annual coupons with the next one expected in 6 months; and matures in 8 years. The stock pays annual dividends and the next dividend is expected to be $24.87 and paid in one year. The expected return for the stock is 15.2 percent. What is the price of the stock expected to be in 1 year? P 0 = (D 1 + P 1 ) / (1 + R) Since we know that D 1 = $24.87 and R = 15.2 percent, we can find P 1 if we know P 0 If we find the bond value, we can find the stock value (P 0 ), and we can find P 1 Finding the bond value N = 8 years × 2 coupons per year = 16 I% = YTM ÷ # coupons per year = 10.2 ÷ 2 = 5.1 FV = 1,000 = par

PMT = par × coupon rate ÷ # coupons per year = 1000 × 9.2% ÷ 2 = 46 END mode Enter 16 5.1 46 1000 N I% PV PMT FV Solve for -946.19 Finding the current stock price Since bond value + stock value = $1,200, stock value = $1,200 – $946.19 = $253.81 Finding the expected price in one year P 0 = (D 1 + P 1 ) / (1 + R) 253.81 = (24.87 + P 1 ) / 1.152  P 1 = (253.81 × 1.152) – 24.87 = $267.52 7. If 1) the expected return for Mindy’s Mending stock is 14.30 percent; 2) the dividend is expected to be $0 in one year, $4.53 in two years, $0 in three years, $5.68 in four years, and $6.44 in five years; and 3) after the dividend is paid in five years, the dividend is expected to grow by 2.40 percent per year forever, then what is the current price of the stock? Time 0 1 2 3 4 5 6 7 … Exp Div 0 0 4.53 0 5.68 6.44 6.44 × (1.0240) 6.44 × (1.0240) 2 … Mindy’s Mending dividends are expected to grow at a variable rate before growing at constant rate after 5 years from today The stock of a company that pays a dividend that does not grow at its long-term constant rate during the next N+1 years, before growing forever at that constant rate after N+1 years can be valued as

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