| Course | MAT 444 Finance for Managers |
|---|---|
| Module | Module 3 |
| Paper type | Bond and stock valuation analysis |
| Length | About 1,076 words, 6 pages |
| Format | APA 7 student paper |
| School | Aspen University |
| Program | Business Administration |
| Updated | October 2026 |
Free sample paper for MAT 444 Module 3
What the Note Will Fetch and What the Shares Are Worth: Valuing Debt and Equity in a Private Fabricator
Student Name
Business Administration Program, Aspen University
MAT 444: Finance for Managers
Instructor Name
Month Day, Year
What the Note Will Fetch and What the Shares Are Worth: Valuing Debt and Equity in a Private Fabricator
Haverstock Fabrication faces two valuation questions this quarter. To fund the laser cutting cell discussed in Modules 1 and 2 and refinance an older equipment loan, the company plans to sell a $4 million seven-year note to an insurance company through a private placement. At the same time, the board has offered $3 million for the 25% stake of a retiring family shareholder, and her advisor has asked how the figure was reached. This paper prices the note, explains the yield investors require and values the equity to judge the offer. Haverstock and every figure are composites for teaching.
The Note's Cash Flows
The note will pay interest at 7.25% a year in two payments of $36.25 for every $1,000 of face value, and repay the $1,000 at the end of the seventh year. The placement agent reports that investors in comparable notes from mid-sized private manufacturers currently require a yield of 7.75%. Because both payments and the yield are semiannual, the calculation uses fourteen half-year periods at 3.875% each.
Pricing the Note
A bond is worth the present value of its coupons plus the present value of its face value. With a coupon of $36.25, a half-year rate of 3.875% and fourteen periods, the coupon factor is 10.6511 and the discount factor for the final payment is 0.587271.
At the market yield the note raises about $3.89 million, not $4 million. Haverstock could instead set the coupon at 7.75% so the note sells at face value; the cost of the money is the same either way, because investors are pricing the yield, not the coupon. The table also shows the risk investors take: if yields rose one point after purchase, each $1,000 note would lose about $50 of value.
| Yield to investors, yearly | Half-year rate | Value of coupons | Value of face amount | Price per $1,000 | Proceeds on $4 million |
|---|---|---|---|---|---|
| 6.75% | 3.375% | 399.21 | 628.32 | 1,027.53 | 4,110,100 |
| 7.75%, current market | 3.875% | 386.10 | 587.27 | 973.37 | 3,893,500 |
| 8.75% | 4.375% | 373.60 | 549.10 | 922.70 | 3,690,800 |
What the Spread Pays For
A seven-year Treasury note currently yields about 4.10%, so Haverstock's notes would pay roughly 3.65 percentage points more. It is tempting to read the whole difference as compensation for the chance that Haverstock defaults. Elton et al. (2001) tested that reading on corporate bond data and found it wrong. Losses investors could expect from default explained only a modest fraction of the spread. A large part reflected state income taxes, which investors owe on corporate coupons but not on Treasury coupons, and much of the remainder behaved like a premium for the same broad market risks that move stock returns.
Longstaff et al. (2005) took a different route, using the prices of credit default swaps, contracts that pay off when a company defaults, to measure the default part of each firm's spread directly. Default risk made up the majority of spreads, a larger share for lower-rated borrowers, but a meaningful part remained that was not related to default. That remainder moved with measures of how hard bonds were to trade. A private placement note from a company with no public rating is about as hard to trade as debt gets, which helps explain why Haverstock pays more than a rated public company with similar credit.
Valuing the Equity
Haverstock has no market price for its shares, so a model has to stand in for one. Gordon (1959) studied how share prices related to dividends and earnings and found strong support for valuing a share by its dividend and the growth investors expect in that dividend. In the constant-growth form, a share's value is the coming year's dividend over the gap between what investors require and the rate of growth.
Haverstock has paid about $1.4 million a year in dividends to its owners for the past five years, raising them roughly in line with inflation. The model assumes 3% growth, near the company's long-run sales growth after inflation, and a 14% required return, reflecting the risk of a small, undiversified, private manufacturer; Module 5 will test that rate.
Next year's dividend: $1.4 million × 1.03 = $1.442 million.
Equity value: $1.442 million / (0.14 minus 0.03) = about $13.11 million.
The retiring shareholder's 25% is worth about $3.28 million on that basis. A minority stake in a private company cannot be sold easily or used to control decisions, and appraisers commonly reduce the value of such stakes; a 15% discount for limited marketability brings her stake to about $2.79 million.
Testing the Equity Value
Across reasonable inputs, the undiscounted stake ranges from about $2.75 million to $4.04 million. After a 15% marketability discount, the middle case is about $2.79 million.
| Required return | Growth 2% | Growth 3% | Growth 4% |
|---|---|---|---|
| 13% | 3,245,000 | 3,605,000 | 4,044,000 |
| 14% | 2,975,000 | 3,277,000 | 3,640,000 |
| 15% | 2,746,000 | 3,004,000 | 3,309,000 |
Is the $3 Million Offer Fair?
The board's $3 million offer sits between the discounted value of $2.79 million and the undiscounted value of $3.28 million in the middle case. That is a fair position for a buyback within the family: it gives the retiring shareholder part of the value a discount would remove while protecting the remaining owners. The offer would look low only if one believed growth would reach 4% or that 13% is the right required return, and the advisor should be shown this grid so the negotiation is over assumptions rather than over a single number. Module 2 showed that paying in installments lowers the cost to Haverstock; the board might offer slightly more in installments in exchange for that saving.
Limits of the Models
Both values rest on inputs that are estimates. The bond price depends on a market yield reported by one agent; a second quote would strengthen it. The equity value assumes dividends grow steadily forever and ignores the possibility of a sale of the whole company, which would usually bring a higher price per share than a minority buyback. Neither limit changes the conclusions, but both belong in the report to the board.
Conclusion
At today's market yield, Haverstock's 7.25% note would raise about $3.89 million, and the 3.65-point spread over Treasuries pays investors for default risk, taxes, market risk and the note's illiquidity, as Elton and colleagues and Longstaff and colleagues show. Gordon's dividend growth approach values the company's equity near $13.1 million and places the board's $3 million offer within a fair range.
References
Elton, E. J., Gruber, M. J., Agrawal, D., & Mann, C. (2001). Explaining the rate spread on corporate bonds. The Journal of Finance, 56(1), 247-277. https://doi.org/10.1111/0022-1082.00324
Gordon, M. J. (1959). Dividends, earnings, and stock prices. The Review of Economics and Statistics, 41(2), 99-105. https://doi.org/10.2307/1927792
Longstaff, F. A., Mithal, S., & Neis, E. (2005). Corporate yield spreads: Default risk or liquidity? New evidence from the credit default swap market. The Journal of Finance, 60(5), 2213-2253. https://doi.org/10.1111/j.1540-6261.2005.00797.x
Reading the MAT 444 Module 3 assignment instructions
The third module of MAT 444 deals with bond and stock valuation, and students are commonly asked to price a bond and value shares, then explain what drives each value. Defer to the Module 3 instructions in your own Aspen classroom; Haverstock and its securities are fictional. Identify the cash flows each security pays and the rate investors require. Price the bond, including at yields above and below the coupon. Explain what the yield spread compensates investors for. Value the equity with an appropriate model, state the assumptions behind growth and the required return and test how sensitive the value is. Cite your sources in APA 7 form.
How this MAT 444 Module 3 example is built
The note pays a 7.25% coupon twice a year for seven years, while investors in similar private placements require 7.75%, so each $1,000 of face value is worth about $973.37 and the issue would raise about $3.89 million. Prices at 6.75% and 8.75% show the inverse link between yield and price. The 3.65-point spread over a seven-year Treasury yield is read with Elton and colleagues (The Journal of Finance) and Longstaff and colleagues (The Journal of Finance). The equity section uses Haverstock's $1.4 million of yearly dividends, 3% expected growth and a 14% required return in the constant-growth model from Gordon (The Review of Economics and Statistics), valuing the company's equity near $13.1 million and the 25% stake near $3.28 million, or about $2.79 million after a 15% discount for limited marketability. A grid varies the required return and growth.
Where the marks sit in the MAT 444 Module 3 rubric
Valuation papers earn their marks through correct cash flows and rates, clean arithmetic and assumptions that are stated and tested. This one lists the note's coupon, frequency, term and yield before pricing it, converts both rates to half-year terms and shows the price at three yields, which demonstrates the inverse relationship instead of merely asserting it. The spread discussion uses two studies to explain what investors are paid for beyond default. The equity value comes from a model whose inputs are each justified, and the grid shows that the board's offer sits inside a reasonable range. Adjusting for the stake's limited marketability shows awareness that a private holding is not a listed share.
Common MAT 444 Module 3 mistakes, and how to avoid them
Bond problems often go wrong when an annual coupon rate and yield are used with semiannual payments; halve the rates and double the periods. Another error is reporting a price without saying whether it is above or below face value and why. In the equity section, a frequent slip is plugging in the dividend just paid where the formula wants the one expected a year from now. The model also fails when the required return is close to the growth rate, so show that the gap is reasonable. State where each input comes from. Finally, a private company's shares cannot be sold easily, so discuss whether the value should be adjusted before comparing it with an offer.
Write yours, or have the desk draft it
This paper is an original model document written by our desk, not a submitted student paper and not an official Aspen University document. Read it for the moves, then write your own to the instructions in your classroom. If you want one built to your exact prompt and rubric, the first custom sample is free and arrives in 24 to 48 hours.
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MAT 444 Module 3 questions, answered
What does MAT 444 Module 3 usually ask for?
Aspen's MAT 444 turns to bond and stock valuation in this module, so pricing a bond and valuing shares, with an explanation of what drives each, is typical. The task wording is in your classroom prompt.
Why does a bond's price fall when yields rise?
Its coupons are fixed, so when investors demand a higher yield the only way to give it to them is a lower price today.
What is the constant-growth dividend model?
Value is the dividend expected a year from now, divided by the required return less the growth rate; it assumes growth never stops or changes.
Where can I find a free MAT 444 Module 3 sample paper?
Right here. The paper prices a seven-year note at three yields and values a 25% stake in an invented fabricator with the dividend growth model.
Is a corporate bond's spread just default risk?
No. Elton and colleagues found expected default explains only part of it, and Longstaff and colleagues tied part of the rest to illiquidity.