| Course | FIN-3210 Security Analysis and Portfolio Management |
|---|---|
| Module | Module 4 |
| Paper type | Written assignment 4: debt securities and security analysis |
| Length | About 599 words, 5 pages |
| Format | APA 7 student paper |
| School | Thomas Edison State University |
| Program | B.S.B.A. in Finance |
| Updated | October 2026 |
Free sample paper for FIN 3210 Module 4
What Rates and Growth Are Worth: Bond Duration and Stock Valuation for a Trenton Household
Student Name
B.S.B.A. in Finance, Thomas Edison State University
FIN-3210: Security Analysis and Portfolio Management
Mentor Name
Month Day, Year
What Rates and Growth Are Worth: Bond Duration and Stock Valuation for a Trenton Household
Problem 1: Pricing a Bond
The bond has a $1,000 face value, a 4.5 percent coupon paid semiannually and ten years to maturity. Comparable bonds yield 5.2 percent. The bond answers rely on duration as Macaulay (1938) defined it, and the stock answers on the constant-growth model associated with Gordon (1962).
Price = Σ $22.50 / (1.026)^t for t = 1 to 20, plus $1,000 / (1.026)^20 = $945.95.
Its coupon trails the market yield, so it trades under par. If the couple buys at $945.95 and holds to maturity, their yield to maturity is 5.2 percent, assuming coupons are reinvested at that rate. Bodie et al. (2017) stress that yield to maturity is the single discount rate that equates the bond's price with its promised cash flows, not a guaranteed return.
Problem 2: Duration
Macaulay duration averages the timing of the bond's payments, weighting each by its share of present value. For this bond it is about 8.10 years, shorter than its ten-year maturity because the coupons arrive earlier. Modified duration, Macaulay duration divided by (1 + y/2), is about 7.89.
Modified duration estimates the percentage price change for a change in yield: ΔP / P ≈ −7.89 × Δy. If yields rose by half a point to 5.7 percent, the predicted price change is −7.89 × 0.005 × $945.95 = −$37.34. The actual price at 5.7 percent is $909.48, a fall of $36.47. The duration estimate is a little too gloomy because prices curve against yields; this convexity helps holders, since a fall in yields lifts prices more than an equal rise cuts them.
Problem 3: Valuing a Stock
The couple is considering shares of a regional company that just paid a $2.40 annual dividend. It earns a 12.5 percent return on equity and pays out 60 percent of earnings, so it reinvests 40 percent. Its sustainable growth rate is the plowback ratio times return on equity: 0.40 × 12.5% = 5 percent. With a required return of 9 percent:
P₀ = D₁ / (k − g) = $2.40 × 1.05 / (0.09 − 0.05) = $2.52 / 0.04 = $63.00.
Problem 4: Growth Opportunities
Next year's earnings are expected to be $4.20 a share. If the company paid out all earnings and did not grow, its value would be E₁ / k = $4.20 / 0.09 = $46.67. The difference, $63.00 − $46.67 = $16.33, is the present value of growth opportunities. About a quarter of the stock's value comes from the market's belief that reinvested earnings will earn more than the 9 percent investors require. If the company's return on equity fell to 9 percent, equal to the required return, reinvestment would add nothing and the stock would be worth $46.67 regardless of how much it plowed back.
Problem 5: The P/E Ratio
The stock's forward P/E ratio is $63.00 / $4.20 = 15.0. A P/E above the no-growth level, 1 / k = 11.1, signals that investors expect profitable growth. Comparing this P/E with similar companies helps the couple judge whether the market's expectations are reasonable: if peers trade at 12 with similar returns on equity, this stock's price may assume too much.
What the Problems Show
Bonds and stocks are both valued by discounting expected cash flows. For the bond, the main risk is a change in interest rates, measured by duration. For the stock, the main question is whether growth will create value, which depends on whether the company earns more on reinvested capital than investors require.
References
Bodie, Z., Kane, A., & Marcus, A. J. (2017). Essentials of investments (10th ed.). McGraw-Hill Education.
Gordon, M. J. (1962). The investment, financing, and valuation of the corporation. Richard D. Irwin.
Macaulay, F. R. (1938). Some theoretical problems suggested by the movements of interest rates, bond yields and stock prices in the United States since 1856. National Bureau of Economic Research.
FIN 3210 Module 4 instructions, in plain terms
FIN-3210's Module 4 covers debt securities and security analysis and closes the material tested on the proctored midterm, a closed-book, two-hour exam on Modules 1 to 4 with forty multiple-choice questions, ten of them computational. Its written assignment, one of eight worth 40 percent together, typically asks for bond pricing and yields, duration and interest rate risk, and equity valuation with dividend discount models and ratios. Macaulay's original work on duration and Gordon's on the growth model are the classic sources behind these tools. The securities here are composites. Expect bond pricing, yield to maturity, duration and the dividend discount model in one set of problems.
How this FIN 3210 Module 4 example is built
Problem 1 prices the bond with the formula and figures shown, and explains what yield to maturity does and does not promise. Problem 2 computes Macaulay and modified duration, estimates a price change and compares it with the exact change to introduce convexity. Problem 3 derives the growth rate from return on equity and plowback before valuing the stock, Problem 4 splits the price into no-growth value and growth opportunities and Problem 5 interprets the P/E ratio against its no-growth level and peers. Duration is used to estimate the price change for a rate move and then compared with the exact repricing. The equity valuation shows how sensitive the price is to the growth assumption.
FIN 3210 Module 4 rubric: what earns full marks
Pricing with semiannual periods and next year's dividend is where this set's marks are won or lost. Mentors check correct bond pricing, duration computations and equity valuation, and look for interpretation: why the bond sells at a discount, why duration misstates the change, and how much of a stock's value depends on growth. Since the midterm tests the same material with a calculator and formula sheet, accuracy in setting up each formula matters as much as the final number. Answers that explain why duration estimates differ from exact price changes, through convexity, show understanding beyond the formula. Stating each input and its source supports the valuation. Answers that interpret duration as a price change for a one-point move in yield, and test it against the exact price, show understanding beyond the formula.
FIN 3210 Module 4 help from the desk
Marks slip when a semiannual bond is priced with annual periods, when the coupon rate replaces the yield as the discount rate or when a stock is valued on this year's dividend instead of next year's. Match periods and rates. Check whether the bond is at a premium or discount before computing. Use D₁, not D₀, in the dividend discount model. Separate no-growth value from growth opportunities to see what the price assumes. A free first sample of your own FIN-3210 Module 4 problems is available on request. Use semiannual periods for coupon bonds, and check the growth rate is below the required return before using the constant-growth model.
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FIN 3210 Module 4 questions, answered
Where can I find a free FIN 3210 Module 4 sample paper?
The Trenton household problem set above prices a bond, computes its duration and convexity effect and values a stock with the dividend discount model and growth opportunities.
What is modified duration?
Macaulay duration over one plus the yield per period, giving the rough percent price move for a yield change.
Why does a bond sell at a discount?
Its coupon pays less than the yield buyers now demand on comparable bonds.
What is the present value of growth opportunities?
The part of a stock's price that comes from expected profitable reinvestment, the price minus the value of current earnings as a perpetuity.
How is sustainable growth calculated?
As the plowback ratio, the share of earnings reinvested, times return on equity.