MT480 Unit 2 Time Value of Money Problems Example

Timelines First, Formulas Second: An MT480 Unit 2 Time Value Problem Set for a Mushroom Grower

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Purdue University Global

MT480: Corporate Finance

Unit 2 Time Value Problem Set

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[Date]

Brandywine Hollow Mushrooms and every figure are composite; the sources cited are real.

Layout of the Six

Each of the six moves through the same steps: the question in plain words, a timeline marking when each cash flow occurs, the formula, the inputs and the answer with a sentence on what it means for Brandywine Hollow Mushrooms, a composite grower in southeastern Pennsylvania. The timeline comes first because most time value errors are timing errors: a payment placed at the wrong end of a period, or a deferred stream discounted one year too few. Ross et al. (2022) recommend drawing the timeline before choosing a formula for exactly this reason.

Problem 1: A Spawn License Now or Later

A spawn laboratory offers a license for a new brown mushroom strain for $1.20 million today or $1.46 million paid in three years. The grower's opportunity cost is 7 percent a year. The timeline has one payment at time zero for the first option and one at year three for the second. The present value of $1.46 million in three years is $1.46 million divided by 1.07 cubed, about $1,191,795. Paying later costs $8,205 less in today's money, so the grower should choose the deferred payment, provided it is confident the license terms will hold.

Problem 2: A Lease Paid in Advance

The grower leases a packing building for $312,000 a quarter for six years, 24 quarters, at 2 percent a quarter. Payments are due at the start of each quarter, so the first falls at time zero. As an annuity due, the lease's present value is about $6,019,168. If the same payments were made at the end of each quarter, an ordinary annuity, the present value would be about $5,901,145. Paying in advance costs $118,023 more in present value, because every payment moves one quarter earlier.

Problem 3: The Cost of Skipping a Discount

Brandywine's carton supplier invoices on 2/10 net 45: a 2 percent discount for paying within 10 days, or the full amount in 45. Skipping the discount means borrowing 98 cents for 35 extra days at a cost of 2 cents. The simple annual rate is about 21.28 percent; compounded over the 365/35 periods in a year, the effective annual cost is about 23.45 percent. The grower's bank line costs 8.25 percent, so it should borrow on the line and take every discount.

Skipping a 2 percent discount costs the grower nearly three times what its bank line charges.

Problem 4: Paying Off a Climate System Loan

A new climate control system was financed with a $4.35 million loan at 6.6 percent a year, compounded monthly. The system saves about $61,000 a month in energy, and the grower plans to put all of it toward the loan. Solving the annuity formula for the number of monthly payments gives about 90.78 months, roughly seven and a half years. The timeline helps here: the payments are fixed, and the unknown is how many of them it takes.

Problem 5: A Growing House Built Over Two Years

A second growing house would take two years to build and then produce about $5.2 million a year in cash flow for ten years, years three through twelve. At a 9 percent required return, the ten payments are first valued as of the end of year two, one period before the first arrives, about $33.37 million, and then discounted back two years to today, about $28,088,393. The common mistake is to discount the stream back to year three rather than year two; the annuity formula already values the payments one period before the first one arrives.

Problem 6: A Packing Line Loan With a Balloon

An automated packing line costs $2.8 million, financed over seven years at 7.2 percent a year, compounded monthly, with a $560,000 balloon payment due with the last installment. The balloon's present value is subtracted from the loan amount, and the remainder is spread over 84 monthly payments, giving about $37,387.03 a month. Without the balloon, the payment would be higher; with it, the grower pays less each month but must plan for a large final payment, which the timeline makes impossible to overlook.

What the Set Shows

The six problems share one lesson: the formula matters less than knowing when each dollar moves. Brealey et al. (2020) describe the present value rule as the foundation of every later topic in corporate finance, and these small decisions, a license, a lease, a discount, a loan, are where a grower meets it every month. Graham and Harvey (2001) found that most chief financial officers use present value and internal rate of return when they decide on investments, so the same discounting the grower applies to a lease will reappear, at larger scale, when the company evaluates a new growing house in Unit 8. Getting the timing right on small problems is the practice that keeps those larger decisions honest.

References

Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of corporate finance (13th ed.). McGraw-Hill Education.

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

Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2022). Fundamentals of corporate finance (13th ed.). McGraw Hill.