FIN 370 Week 2 Time Value of Money Example

Four Money Decisions for a Food Truck Owner: A Loan Payment, Leasing Versus Buying a Second Truck, Saving for a Commissary Kitchen and the Real Cost of a Merchant Cash Advance

[Student Name]

University of Phoenix

FIN/370: Finance for Business

Week 2 Assignment

[Instructor Name]

[Date]

The food truck business and all figures are composites written for a model paper; methods and research findings come from the sources listed.

A composite owner runs a food truck selling tacos and rice bowls at office parks and breweries and earns about $140,000 a year before her own pay. Demand exceeds what one truck can serve, and she plans to add a second truck this year and a small commissary kitchen within four years. Every step involves money paid or received at different times. A dollar next year and a dollar today are different amounts of money, and every one of her decisions depends on knowing by how much. This paper works through four decisions.

Decision One: The Equipment Loan

A lender offers $85,000 to buy and outfit a second truck at 9% annual interest for five years, with monthly payments at the end of each month. The monthly rate is 0.75% and there are 60 payments. The payment on an ordinary annuity is the loan amount times the rate divided by one minus the discount factor for 60 periods, which gives about $1,764 a month (Brigham & Houston, 2022). Over five years she would pay about $105,800, of which about $20,800 is interest. In the first month, $637.50 of the payment is interest and about $1,127 reduces principal; by the last year most of each payment is principal.

Decision Two: Lease or Buy

A leasing company offers the same outfitted truck for $1,650 a month for five years, paid at the beginning of each month, with no down payment, after which she could buy it for $15,000. If she buys with the loan, she owns the truck after five years and expects it to be worth about $22,000.

To compare, she discounts both at her borrowing rate of 9%. The loan option costs the present value of the loan payments, which equals the $85,000 borrowed, less the present value of the $22,000 resale value in five years, about $14,000, for a net cost of about $71,000. The lease payments are an annuity due; their present value is about $80,100. If she exercised the $15,000 purchase option to keep the truck, its present value of about $9,600 would add to the lease cost, while she would still own a truck worth $22,000, so the comparison favors buying by a wide margin. Buying is cheaper in present value terms by roughly $9,000 or more, depending on the resale value.

Decision Three: Saving for the Kitchen

She wants $60,000 in four years for commissary equipment and a lease deposit. A high-yield business savings account pays 4.2% compounded monthly. The monthly deposit that grows to $60,000 in 48 months is the future value annuity payment: $60,000 times the monthly rate divided by the growth factor minus one, about $1,150 a month. If she can deposit only $900 a month, she would have about $47,000 after four years and would need to wait about a year longer or finance the rest.

Decision Four: The Merchant Cash Advance

A company offers $30,000 now in exchange for $39,000 collected by taking 15% of her daily card sales until paid, which it expects to take about eight months. The offer is quoted as a factor of 1.30, which sounds like 30%. But the $9,000 cost is paid over about eight months, with the balance falling daily. Treated as a series of equal payments over 240 days, the implied monthly rate is roughly 6 to 7%, an effective annual rate above 100%. Compared with the 9% equipment loan, the advance is extraordinarily expensive and would only make sense for a short emergency she could not finance any other way.

What Compounding Means

Compounding explains why the advance is so costly and why the savings plan works. Interest earned or charged on prior interest grows over time; at 4.2% compounded monthly, the effective annual rate is about 4.28%, slightly more than the stated rate, while the advance's short repayment period multiplies its cost many times over. The Truth in Lending rules that require annual percentage rates on consumer loans exist because stated factors and fees hide these differences, but business financing like merchant cash advances is often not covered by those disclosure rules, so business owners must compute the effective rate themselves.

Taxes and Cash Flow

The comparison above ignores taxes to keep the focus on timing. In practice, interest on the loan and depreciation on the owned truck are deductible, while lease payments on an operating lease are deductible as rent. Because her business is profitable, both options produce tax savings of similar size, and the after-tax comparison still favors buying. Cash flow matters too: the loan payment is about $114 higher each month than the lease payment, which she must be able to cover in slow winter months.

Sensitivity

The lease versus buy answer depends on the resale value. If the truck were worth only $12,000 after five years, the loan's net cost would rise to about $77,200, still below the lease. The savings plan depends on the account rate; at 3% the deposit needed rises to about $1,180.

Putting the Answers Together

The owner should finance the second truck with the equipment loan rather than the lease, since buying is cheaper in present value terms and she keeps a valuable asset. She should decline the merchant cash advance. Petersen and Rajan (1994) found that small firms with close banking relationships obtained more credit and relied less on expensive alternatives, which argues for building her relationship with the equipment lender's bank now, before she needs short-term credit. She should begin a monthly transfer of about $1,150 to the savings account for the kitchen, or accept a later opening date if cash flow is tight while the loan is being paid. Graham and Harvey (2001) found that small firms more often rely on simple rules such as payback, but each of her choices turns on discounting, which a simple rule would miss.

Conclusion

Four decisions, a loan payment of about $1,764 a month, a lease that costs about $9,000 more than buying in present value, a savings plan of about $1,150 a month and an advance with an effective annual rate above 100%, all came from the same principle: money received or paid at different times must be brought to the same point before it can be compared.

References

Brigham, E. F., & Houston, J. F. (2022). Fundamentals of financial management (16th ed.). Cengage.

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

Petersen, M. A., & Rajan, R. G. (1994). The benefits of lending relationships: Evidence from small business data. The Journal of Finance, 49(1), 3-37. https://doi.org/10.1111/j.1540-6261.1994.tb04418.x