| Course | MAT 444 Finance for Managers |
|---|---|
| Module | Module 2 |
| Paper type | Time value of money problem set |
| Length | About 1,052 words, 6 pages |
| Format | APA 7 student paper |
| School | Aspen University |
| Program | Business Administration |
| Updated | October 2026 |
Free sample paper for MAT 444 Module 2
Four Decisions, One Principle: Time Value of Money Problems From a Fabricator's In-Box
Student Name
Business Administration Program, Aspen University
MAT 444: Finance for Managers
Instructor Name
Month Day, Year
Four Decisions, One Principle: Time Value of Money Problems From a Fabricator's In-Box
Every item in the in-box of Haverstock Fabrication's controller this month turns on cash that moves on different dates. A dollar today can be invested or used to pay down a loan, so it is worth more than a dollar promised later, and comparing amounts at different dates requires moving them to the same date at an appropriate rate. This paper works four such decisions, showing the formula, the inputs and the answer for each, and then explains what each answer means. Haverstock and every amount are composites for teaching. Unless stated, the rate is 8% a year, Haverstock's approximate cost of borrowing on its bank line plus a margin for risk.
Why Intuition Is Not Enough
Frederick et al. (2002) reviewed several decades of studies that estimated how people discount future outcomes. The implied discount rates ranged from slightly negative to several thousand percent a year, varied with how the question was asked, and often contradicted each other for the same person. People also tended to discount the near future much more steeply than the far future, so preferences reversed as an event came closer. Thaler (1981) gave people choices between amounts now and later and found that implied annual rates were very high for short delays and small amounts and fell as the delay lengthened and the amount grew. If individuals cannot apply a consistent rate by feel, a company should not make large timing decisions that way. Graham and Harvey (2001) asked 392 finance chiefs which tools they relied on to judge projects. Net present value and internal rate of return led the list, each named as a regular tool by roughly three in four respondents, and both depend on discounting.
Problem 1: Lease or Buy the Laser Cell
The equipment vendor will sell the cutting cell for $2.4 million or lease it for $52,000 a month for sixty months, with payments due at the start of each month. Monthly rate: 8% divided by 12, or 0.6667%.
For a level stream paid at period end, PV = PMT × (1 minus v raised to n) / r, with v = 1 / (1 + r). With PMT = $52,000, r = 0.006667 and n = 60, the factor is 49.32, so PV = $2,564,640. Because each payment is made at the start of the month, the stream is an annuity due, worth the ordinary annuity value times (1 + r): $2,564,640 × 1.006667 = about $2,581,740.
Recommendation: buy, unless the lease includes service or upgrade terms worth more than the difference. The lease would break even only at a monthly rate near 1% a year higher than the bank loan, which Haverstock does not face.
| Option | Cash cost in today's dollars | Ownership at the end |
|---|---|---|
| Buy for cash or with a bank loan at 8% | 2,400,000 | Haverstock owns the cell |
| Lease, 60 payments of $52,000 in advance | about 2,581,700 | Returned to the vendor |
Problem 2: The Supplier's Early-Payment Discount
The steel supplier offers 2/10, net 60: Haverstock may take 2% off if it pays within ten days, or pay the full amount in sixty days. Skipping the discount means keeping $98 for fifty more days at a cost of $2, a periodic rate of 2/98 = 2.04%. There are 365/50 = 7.3 such periods in a year, so the effective annual cost is 1.0204 raised to 7.3, minus 1, or about 15.9%.
Recommendation: take the discount. Haverstock's revolving credit line charges about 8.5%, so drawing on the line to pay within ten days saves roughly 7.4 percentage points a year on the amount involved. On about $6 million of yearly steel purchases from this supplier, the discount is worth $120,000 a year.
Problem 3: The Retiring Shareholder's Buyout
One of the family shareholders, retiring to Arizona, has asked Haverstock to buy back her shares. The board has offered two forms of payment: $3 million at closing or ten yearly payments of $380,000, the first due one year after closing.
Present value of the payments at 8%: factor (1 minus 1/1.08 raised to 10) / 0.08 = 6.7101, so PV = $380,000 × 6.7101 = about $2,549,800.
For Haverstock, whose money costs about 8%, the payment plan is about $450,000 cheaper in today's dollars. For the shareholder, the two are equal only if she can earn about 4.55% on the lump sum. If her safe alternative earns less, she should prefer the payments; if she can earn more, she should prefer cash. The board should also weigh the risk to the shareholder, who becomes Haverstock's creditor for ten years and may ask for security.
| Discount rate | Present value of ten payments of $380,000 | Cheaper for Haverstock |
|---|---|---|
| 4% | 3,082,100 | Lump sum |
| 4.55% | about 3,000,000 | Equal |
| 8% | 2,549,800 | Payments |
| 10% | 2,334,900 | Payments |
Problem 4: Funding the Roof Replacement
The plant roof will need replacing in about four years at an estimated $600,000. Haverstock plans to deposit a fixed sum into an account earning 4.5% at each of the next four year-ends. Deposits made at period end grow to FV = PMT × ((1 + r) raised to n, minus 1) / r. The factor for four years at 4.5% is 4.2782, so PMT = $600,000 / 4.2782 = about $140,250 a year.
If construction costs rise 4% a year, the roof will cost closer to $702,000 in four years, and the yearly deposit should rise to about $164,100. Building the inflation estimate in now avoids a shortfall in the final year.
Sensitivity to the Rate
| Problem | Answer at 8% | Answer at 6% | Answer at 10% | Decision changes? |
|---|---|---|---|---|
| Lease vs. buy, PV of lease | 2,581,700 | 2,700,500 | 2,467,000 | Buy in every case |
| Buyout payments, PV | 2,549,800 | 2,796,800 | 2,334,900 | Payments in every case |
| Supplier discount | Take it at any borrowing rate below 15.9% | No |
Conclusion
Each of the four decisions turned on moving cash flows to a common date. Buying the laser cell is cheaper than leasing it, taking the supplier's discount earns a high return, the buyout payments cost Haverstock less than the lump sum and an inflation-adjusted deposit fills the roof fund. Frederick and colleagues and Thaler show why such questions should not be settled by feel, and Graham and Harvey show that discounting is how finance leaders actually decide.
References
Frederick, S., Loewenstein, G., & O'Donoghue, T. (2002). Time discounting and time preference: A critical review. Journal of Economic Literature, 40(2), 351-401. https://doi.org/10.1257/002205102320161311
Graham, J. R., & Harvey, C. R. (2001). The theory and practice of corporate finance: Evidence from the field. Journal of Financial Economics, 60(2-3), 187-243. https://doi.org/10.1016/S0304-405X(01)00044-7
Thaler, R. (1981). Some empirical evidence on dynamic inconsistency. Economics Letters, 8(3), 201-207. https://doi.org/10.1016/0165-1765(81)90067-7
MAT 444 Module 2 instructions, in plain terms
Module 2 of MAT 444 usually takes up the time value of money, and the assignment often pairs calculations with interpretation of what each result means for a decision. Follow your Aspen classroom's Module 2 directions where they differ; the company and amounts here are made up. State each problem, the cash flows and the rate used. Show the formula and the inputs, not only the answer. Distinguish present from future values and ordinary annuities from annuities due. Say what each number implies the company should do, and test whether that changes at another rate. Support the discussion of why calculation beats intuition with research, cited in APA 7 form.
How the MAT 444 Module 2 example is put together
The four problems come from Haverstock's controller. A $2.4 million laser cell can be bought or leased for sixty monthly payments of $52,000, each due on the first of the month. A steel supplier offers terms of 2/10, net 60. A retiring family shareholder may take $3 million now or $380,000 a year for ten years. And the plant roof needs replacing in four years at about $600,000. At an 8% rate, the lease is worth about $2.58 million today, more than the price; skipping the discount costs about 15.9% a year; the ten-year payments are worth about $2.55 million; and a deposit of about $140,250 a year at 4.5% fills the roof fund. Frederick and colleagues (Journal of Economic Literature), Thaler (Economics Letters) and Graham and Harvey (Journal of Financial Economics) explain why these questions must be calculated.
MAT 444 Module 2 rubric: what earns full marks
Problem sets in this course are graded on accurate calculations and on whether each answer is interpreted as a decision. This example sets out every input, writes the formula before the numbers, and labels which streams are annuities due, a detail that changes the lease answer. Each problem ends with a recommendation and a break-even rate or sensitivity, which shows understanding beyond the mechanics. The research section explains why the problems cannot be settled by feel, using Frederick and colleagues and Thaler on how inconsistently people weigh time, and Graham and Harvey to show the methods are standard practice. Tables keep the arithmetic easy to follow and check.
MAT 444 Module 2 help: mistakes that cost marks
Time value papers lose points for answers with no visible work, so show the formula, the rate per period and the number of periods. A frequent slip is mixing annual rates with monthly payments; convert the rate to match the payment period. Another is valuing a stream paid in advance as if each payment came at the end, which understates it. Students also forget to interpret: a present value is not a decision until it is compared with the alternative. Choose the discount rate deliberately and explain it, then show how the answer changes at a higher or lower rate. Round only at the end to avoid drift in multi-step problems.
Write yours, or have the desk draft it
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MAT 444 Module 2 questions, answered
What does MAT 444 Module 2 usually ask for?
Aspen's MAT 444 covers the time value of money in this module, so worked present value, future value and annuity problems with interpretation are typical. Use your classroom prompt for the exact problems.
What is the difference between an ordinary annuity and an annuity due?
Payments of an ordinary annuity come at the end of each period; payments of an annuity due come at the start, so each is discounted one period less and the stream is worth more.
How do I calculate the cost of skipping an early-payment discount?
For 2/10, net 60, the cost is (1 + 2/98) raised to 365/50, minus 1, about 15.9% a year.
Where can I find a free MAT 444 Module 2 sample paper?
The example above, at no cost, works four time value of money problems for an invented fabricator with every formula and input shown.
Why not decide timing questions by intuition?
Frederick, Loewenstein and O'Donoghue found that intuitive discount rates vary widely and inconsistently, so the same person can make contradictory choices.