FNCE 3001 Week 5 Time Value of Money Set Example

Five Time Value of Money Problems From One Sporting Goods Chain's Finance Desk: A Cash Reserve, a Future Remodel, a Store Loan, Lease Savings and the True Rate on a Supplier's Late-Payment Charge

Student Name

Walden University

FNCE 3001: Financial Management

Instructor Name

Month Day, Year

Five Time Value of Money Problems From One Sporting Goods Chain's Finance Desk: A Cash Reserve, a Future Remodel, a Store Loan, Lease Savings and the True Rate on a Supplier's Late-Payment Charge

How Each Problem Is Laid Out

Each problem below comes from a decision facing Juniper Peak Sports, a composite retailer of ski, bike and camping gear. Every solution shows four parts: the inputs, listed with the rate and number of periods matched to the compounding frequency; the method, as a formula with values substituted; the answer, rounded to the cent; and a sentence reading the answer back in plain terms. The formulas follow Brigham and Houston (2022). A spreadsheet function is given beside each formula so the result can be checked.

Problem 1: Growing a Cash Reserve

Question. The company sets aside $500,000 in an account paying 4 percent a year, compounded annually. How much will it hold in three years?

Inputs. Present value = $500,000; rate = 4 percent per year; periods = 3 years; annual compounding.

Method. FV = PV x (1 + r)^n = 500,000 x (1.04)^3 = 500,000 x 1.124864. Spreadsheet: =FV(0.04, 3, 0, -500000).

Answer. $562,432.00.

Meaning. If the company leaves the reserve untouched, interest adds $62,432 over three years, close to what the company spends in a single day of spring operations. The reserve grows, but slowly; it is a cushion, not a source of funding.

Problem 2: Setting Aside Today for a Remodel

Question. The flagship Denver store will need a $1,200,000 remodel in four years. If the company can earn 6 percent a year, how much must it set aside today?

Inputs. Future value = $1,200,000; rate = 6 percent per year; periods = 4 years; annual compounding.

Method. PV = FV / (1 + r)^n = 1,200,000 / (1.06)^4 = 1,200,000 / 1.262477. Spreadsheet: =PV(0.06, 4, 0, -1200000).

Answer. $950,512.40.

Meaning. Setting aside about $950,500 now would fully fund the remodel, because four years of interest at 6 percent would supply the remaining $249,488.

Problem 3: Payment on a Store Loan

Question. To open a new store, the company borrows $2,000,000 at 7 percent annual interest, repaid in equal monthly payments over five years. Find the monthly payment and the total interest paid over the life of the loan.

Inputs. Present value = $2,000,000; rate = 7 percent / 12 = 0.58333 percent per month; periods = 5 x 12 = 60 months.

Method. PMT = PV x r / [1 − (1 + r)^-n] = 2,000,000 x 0.0058333 / [1 − (1.0058333)^-60]. Spreadsheet: =PMT(0.07/12, 60, -2000000).

Answer. $39,602.40 a month. Total payments are 60 x $39,602.40 = $2,376,143.82, so total interest is $376,143.82.

Meaning. The new store must generate about $39,600 a month in cash, after its own operating costs, just to service the loan, and borrowing adds about 19 percent to the cost of the money over five years.

Problem 4: Value of Lease Savings

Question. A renegotiated lease would save $48,000 a year for eight years, paid at the end of each year. At a 6 percent discount rate, what are those savings worth today?

Inputs. Payment = $48,000 per year; rate = 6 percent; periods = 8 years; ordinary annuity.

Method. PV = PMT x [1 − (1 + r)^-n] / r = 48,000 x [1 − (1.06)^-8] / 0.06 = 48,000 x 6.209794. Spreadsheet: =PV(0.06, 8, -48000).

Answer. $298,070.10.

Meaning. The landlord is asking for a one-time payment of $250,000 to agree to the new lease. Because the savings are worth about $298,000 today, paying $250,000 for them adds about $48,000 in value, so the deal is worth taking at a 6 percent rate.

Problem 5: The True Cost of a Late-Payment Charge

Question. One supplier adds 1.5 percent a month to any balance paid late. What is the effective annual rate?

Inputs. Periodic rate = 1.5 percent per month; periods per year = 12.

Method. EAR = (1 + r)^m − 1 = (1.015)^12 − 1 = 1.195618 − 1. Spreadsheet: =EFFECT(0.18, 12).

Answer. 19.56 percent a year.

Meaning. The supplier's charge is quoted as "18 percent a year" in simple terms, but compounding makes it cost almost 19.6 percent. That is far more than the 7 percent on the company's bank loan, so paying suppliers on time, even by drawing on the credit line, is cheaper than paying late (Ross et al., 2022). Comparing rates only after converting them to the same effective basis is the general rule (Brealey et al., 2020).

What the Set Shows Together

Each answer is a single figure, but each one only means something beside a decision: whether the reserve is large enough, how much to set aside for the remodel, whether a store can carry its loan, whether the lease payment is worth making and how to finance supplier bills. A correct number with no sentence after it leaves the decision unanswered.

References

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

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

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