FIN HW CHAPTER 10

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William Rainey Harper College *

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Apr 3, 2024

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HOMEWORK CHAPTER 10 FIN 311 AZEEM 12/06/2023 BASIC PROBLEMS 1) Bond Price = Present Value of Future Cash Flows  Future Cash Flows: These include the annual interest payments (coupon payments) and the face value repayment at maturity.  Present Value: This considers the time value of money, meaning future cash flows are discounted to their current worth using the YTM as the discount rate. Calculations:  Annual Interest Payment: $1,000 par value * 10% annual interest rate = $100 per year  Number of Coupon Payments: 20 years (maturity) * 1 payment per year = 20 a) YTM = 6%:  Present Value of Coupon Payments: ($100 annual payment / 1.06 YTM) * [1 + (1.06 YTM)^20] / (1.06 YTM - 1) = $1,658.55  Present Value of Face Value: $1,000 face value / (1.06 YTM)^20 = $347.39  Bond Price = $1,658.55 + $347.39 = $2,005.94 b) YTM = 9%:  Present Value of Coupon Payments: ($100 annual payment / 1.09 YTM) * [1 + (1.09 YTM)^20] / (1.09 YTM - 1) = $1,305.20  Present Value of Face Value: $1,000 face value / (1.09 YTM)^20 = $256.72

 Bond Price = $1,305.20 + $256.72 = $1,561.92 c) YTM = 13%:  Present Value of Coupon Payments: ($100 annual payment / 1.13 YTM) * [1 + (1.13 YTM)^20] / (1.13 YTM - 1) = $852.61  Present Value of Face Value: $1,000 face value / (1.13 YTM)^20 = $175.50  Bond Price = $852.61 + $175.50 = $1,028.11 Therefore, the current price of the Lone Star Company bonds will be:  $2,005.94 if the YTM is 6%.  $1,561.92 if the YTM is 9%.  $1,028.11 if the YTM is 13%. As expected, the bond price decreases as the YTM increases, demonstrating the inverse relationship between bond price and YTM. 3) Current Price of Exodus Limousine Bonds Following the same approach as for Lone Star Company, we can compute the current price of Exodus Limousine's bonds for the given yield to maturity (YTM) scenarios: Bond Parameters:  Par Value: $1,000  Coupon Rate: 10%  Maturity: 50 years  Annual Coupon Payment: $1,000 * 10% = $100 Calculations: a) YTM = 5%:  Present Value of Coupon Payments: ($100 annual payment / 1.05 YTM) * [1 + (1.05 YTM)^50] / (1.05 YTM - 1) ≈ $3,307.72

 Present Value of Face Value: $1,000 face value / (1.05 YTM)^50 ≈ $149.10  Bond Price ≈ $3,307.72 + $149.10 ≈ $3,456.82 b) YTM = 15%:  Present Value of Coupon Payments: ($100 annual payment / 1.15 YTM) * [1 + (1.15 YTM)^50] / (1.15 YTM - 1) ≈ $380.73  Present Value of Face Value: $1,000 face value / (1.15 YTM)^50 ≈ $6.06  Bond Price ≈ $380.73 + $6.06 ≈ $386.79 Results:  At a 5% YTM, the bond price is significantly higher at $3,456.82 due to the lower discount rate applied to future cash flows.  At a 15% YTM, the bond price drops considerably to $386.79 as the higher discount rate significantly reduces the present value of future payments. 5) Essex Biochemical Bond Prices at Different Maturities Bond Parameters:  Par Value: $1,000  Coupon Rate: 15%  Annual Coupon Payment: $1,000 * 15% = $150  Yield to Maturity (YTM): 17% Formula: Bond Price = Present Value of Coupon Payments + Present Value of Face Value Present Value Calculations:

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 Present Value of Coupon Payments: We need to discount each future coupon payment back to its present value using the YTM as the discount rate. This can be done with a summation formula: Present Value of Coupon Payments = Σ (Coupon Payment / (1 + YTM)^Year)  Present Value of Face Value: This is simply the face value of the bond discounted back to the present date: Present Value of Face Value = Face Value / (1 + YTM)^Maturity Calculations: a) Maturity: 30 years  Present Value of Coupon Payments: o Σ (150 / (1 + 0.17)^Year) = $2,095.16  Present Value of Face Value: $1,000 / (1 + 0.17)^30 = $161.80  Bond Price = $2,095.16 + $161.80 = $2,256.96 b) Maturity: 20 years  Present Value of Coupon Payments: $2,095.16 (same as 30-year calculations)  Present Value of Face Value: $1,000 / (1 + 0.17)^20 = $301.45  Bond Price = $2,095.16 + $301.45 = $2,396.61 c) Maturity: 4 years  Present Value of Coupon Payments: $1,604.54  Present Value of Face Value: $1,000 / (1 + 0.17)^4 = $675.56  Bond Price = $1,604.54 + $675.56 = $2,280.10 Results:  As expected, the bond price decreases with shorter maturities due to the smaller present value of future cash flows.

 Even though the YTM is higher than the coupon rate, the bond still trades at a premium (above par value) because of the long maturities in scenarios (a) and (b). INTERMEDIATE PROBLEMS 18) Calculating the Yield to Maturity for Coleman Manufacturing Bonds Bond Parameters:  Par Value: $1,000  Current Price: $690  Time to Maturity: 10 years  Annual Coupon Payment: $130 (13% of par value) Bond Pricing Formula: Bond Price = Present Value of Coupon Payments + Present Value of Face Value Present Value Calculations:  Each future coupon payment needs to be discounted back to its present value using the unknown YTM as the discount rate.  The face value also needs to be discounted back to its present value using the YTM. Iteration Process: Assume an initial YTM: We can start with a reasonable guess, like 8%. Calculate the present values of the coupon payments and face value using the assumed YTM. Compare the calculated bond price with the actual price ($690). Solution:

Through iteration, we find that the YTM for Coleman Manufacturing's bonds is approximately 12.62%. This means that an investor buying the bond at the current price of $690 and holding it until maturity will earn a total return of 12.62% per year. 19) The yield to maturity (YTM) for Stilley Resources bonds: Bond Parameters:  Par Value: $1,000  Current Price: $841.51  Time to Maturity: 4 years  Annual Coupon Payment: $50 (5% of par value) o Present Value = Payment / (1 + YTM)^Year o Calculate present values for each of the four remaining coupon payments and the face value at maturity. 2. Sum the present values of all cash flows (coupon payments and face value). 3. Compare the calculated bond price with the actual price ($841.51). 4. If the calculated price is not equal to $841.51, adjust the YTM guess and repeat steps 2-4 until you find the YTM that makes the calculated price equal to the actual price. Finding the Solution: Through iteration, you'll find that the YTM for Stilley Resources bonds is approximately 6.81%. This means that an investor buying the bond at $841.51 and holding it until maturity will earn a total return of 6.81% per year. 21) Bond Parameters:

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 Par Value: $1,000  Quoted Annual Interest Rate: 11% (paid semiannually, so 5.5% per period)  Yield to Maturity (YTM): 14% annual (needs to be converted to semiannual)  Time to Maturity: 7 years (14 semiannual periods) Steps: 1. Convert the annual YTM to semiannual: Divide the annual YTM by 2 because interest is paid twice a year. o Semiannual YTM = 14% / 2 = 7% 2. Calculate the semiannual coupon payment: Multiply the par value by the semiannual interest rate. o Semiannual Coupon Payment = $1,000 * 5.5% = $55 3. Discount the future cash flows (coupon payments and face value) using the semiannual YTM: o Present Value = Payment / (1 + YTM)^Period Calculation:  Present Value of Coupon Payments: o Σ ($55 / (1 + 0.07)^Period) for 14 periods  Present Value of Face Value: o $1,000 / (1 + 0.07)^14  Bond Price = Present Value of Coupon Payments + Present Value of Face Value Solution: The calculated price of the Locklear Airlines bond based on semiannual analysis is approximately $868.82. 22) Olsen's Clothing Stores Bond Pricing:

A. 15 Years to Maturity: To calculate the price of Olsen's Clothing Stores bonds with 15 years to maturity: 1. Convert annual interest rate and YTM to semiannual:  Annual interest rate = 10%  Semiannual interest rate = 10% / 2 = 5%  Annual YTM = 10%  Semiannual YTM = 10% / 2 = 5% 2. Calculate Semiannual Coupon Payment:  $1,000 par value * 5% semiannual interest rate = $50 per period 3. Calculate Present Value of Coupon Payments and Face Value: Use the formula: Present Value = Payment / (1 + YTM)^Period  PV of Coupon Payments: Σ ($50 / (1 + 0.05)^Period) for 30 periods (15 years * 2)  PV of Face Value: $1,000 / (1 + 0.05)^30 4. Sum the Present Values to get the Bond Price: Bond Price = PV of Coupon Payments + PV of Face Value Solution: B. 10 Years to Maturity and Lower YTM: If the YTM drops to 8% with 10 years remaining: 1. Repeat steps 1 and 2 for the updated YTM:  Semiannual YTM = 8% / 2 = 4% 2. Calculate Present Value of Coupon Payments and Face Value with the new YTM:  PV of Coupon Payments: Σ ($50 / (1 + 0.04)^Period) for 20 periods (10 years * 2)  PV of Face Value: $1,000 / (1 + 0.04)^20 3. Sum the Present Values to get the new Bond Price: Bond Price = PV of Coupon Payments + PV of Face Value

Solution: With the lower YTM, the new bond price will be approximately $1,135.90. This increase in price reflects the higher present value of future cash flows due to the lower discount rate. Therefore, a decrease in YTM leads to a higher bond price for Olsen's Clothing Stores bonds because the present value of future cash flows increases. 23) The preferred stock of Denver Savings and Loan can be valued using the dividend discount model, which considers the present value of its future dividend payments. 1. Identify the relevant information:  Annual Dividend: $8.10  Required Rate of Return (RRR): 9% 2. Apply the dividend discount model formula: Present Value of Stock = Annual Dividend / Required Rate of Return 3. Substitute the values and calculate the price: Present Value of Stock = $8.10 / 0.09 = $90.00 Therefore, the price of the preferred stock of Denver Savings and Loan is $90.00.  In this case, the market is willing to pay $90 for the preferred stock as long as it receives the expected annual dividend of $8.10 and meets the 9% RRR. 27) Since Stagnant Iron and Steel expects to maintain a constant dividend of $12.25 per year and future growth is not anticipated, we can use the constant growth dividend discount model (CGDDM) to determine the stock price. Formula: Price = D0 / (Ke - g)

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where:  D0 is the current annual dividend ($12.25)  Ke is the required rate of return by common stockholders (18%)  g is the expected growth rate of dividends (0% in this case) Calculation:  Price = $12.25 / (0.18 - 0%) = $12.25 / 0.18 ≈ $68.06 Therefore, the price of Stagnant Iron and Steel's common stock is approximately $68.06. Reasoning:  The CGDDM assumes a constant dividend in perpetuity, hence the expected growth rate (g) is 0%.  As the required rate of return (Ke) is higher than the growth rate (g), the price of the stock is solely determined by the current dividend and Ke.  A higher Ke translates to a lower stock price because investors require a higher return on their investment. 30) Ecology Labs Inc. Stock Valuation: Given:  D = $6.40 (next 12 months dividend) ₁  Ke = 14% (required rate of return)  g = 5% (constant growth rate) a. Compute Po: Po = D / (Ke - g) ₁ Po = $6.40 / (0.14 - 0.05) = $6.40 / 0.09 ≈ $71.11 Therefore, the current price of Ecology Labs' stock is approximately $71.11. b. New Po with Ke = 18%:

If the required rate of return increases to 18%, the new price will be: Po = $6.40 / (0.18 - 0.05) = $6.40 / 0.13 ≈ $49.23 The higher Ke leads to a lower stock price because investors require a higher return for their investment. c. New Po with g = 9%: If the growth rate increases to 9%, the new price becomes: Po = $6.40 / (0.14 - 0.09) = $6.40 / 0.05 ≈ $128.00 The higher growth rate indicates faster future dividend growth, leading to a higher stock price. d. New Po with D = $7: ₁ If the next dividend increases to $7 with Ke and g back to their original values: Po = $7 / (0.14 - 0.05) = $7 / 0.09 ≈ $77.78 The higher dividend directly translates to a higher stock price. 32) a) Project earnings and dividends for 20X6: 1. Calculate the growth rate: o Growth Rate = (20X5 EPS / 20X4 EPS) - 1 = (6.32 / 5.96) - 1 ≈ 0.061 or 6.1% 2. Project earnings for 20X6: o 20X6 EPS = 20X5 EPS * (1 + Growth Rate) o 20X6 EPS = $6.32 * (1 + 0.061) ≈ $6.70 3. Project dividends for 20X6: o Dividends = 40% * 20X6 EPS o Dividends = $6.70 * 0.40 = $2.68 Part b) Anticipated stock price (Po) at the beginning of 20X6: Stock price:

Po = D / (Ke - g) ₁ where:  D = Expected dividend for the next year (20X6) = $2.68 ₁  Ke = Required rate of return = 13%  g = Growth rate = 6.1% Plugging in the values: Po = $2.68 / (0.13 - 0.061) ≈ $27.53 Therefore, the anticipated stock price (Po) at the beginning of 20X6 is approximately $27.53.

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