BA 6005 Financial Management Midterm Review Part 1

Chapter 5: SUMMARY OF Key Equations

Equation Summary

Equations and Descriptions: 5.1 Future Value of an n-period Investment:

• Formula: FV = PV X (1 + i)^n

• Definition: Calculates the future value of an investment based on a fixed interest rate compounded over a number of periods.

5.2 Future Value with More Frequent Compounding:

• Formula: FV = PV X (1 + i/m)^(m*n)

• Definition: Adjusts for investments compounded more frequently than annually.

5.3 Continuous Compounding:

• Formula: FV = PV X e^(i*n)

• Definition: Computes the future value of an investment that is continuously compounded.

5.4 Present Value of an n-period Investment:

• Formula: PV = FV / (1 + i)^n

• Definition: Finds the present value based on expected future earnings discounted at a specific interest rate.

5.5 Rule of 72:

• Formula: TDM = 72 / i

• Definition: A quick way to estimate the years required to double the investment at a fixed annual rate of return.

5.6 Future Value with General Growth Rate:

• Formula: FV = PV X (1 + g)^n

• Definition: Calculates the future value of an investment considering a general growth rate over time.

Practical Applications

Example Scenarios

Mike's Investment for Home Purchase:

• Amount Invested: $12,000

• Interest Rate: 6.25% compounded monthly

• Duration: 10 years

• Calculation:FV = 12,000 * (1 + 0.0625/12)^(12*10)

• Final Amount: $22,383 (Answer: B)

Noah's Investment and Interest-on-Interest:

• Invested Amount: $5,000

• Interest Rate: 6.75%

• Duration: 3 years

• Simple Interest:SI = Principal * Rate * TimeSI = 5,000 * 0.0675 * 3 = $1,012.50

• Future Value with Compound Interest:FV = 5,000 * (1 + 0.0675)^3 ≈ $6,082.38

• Interest-on-Interest:Interest-on-Interest = FV - (Principal + Simple Interest)Interest-on-Interest = $6,082.38 - ($5,000 + $1,012.50) ≈ $69.88 (Answer: D)

Jamie's Investment for Future Goal:

• Target Amount: $25,000

• Interest Rate: 6.5%

• Duration: 7 years

• Present Value Calculation:PV = 25,000 / (1 + 0.065)^7 ≈ $16,088 (Answer: D)

Julie’s Loan Decision:

• Loan Amount: $6,000

• Bank Interest Rate: 7.25% compounded annually.

• Firm Payback: $8,130.93 in 4 years.

• Calculated Firm Interest Rate:Interest Rate = (Payback / Loan)^(1/n) – 1= (8,130.93 / 6,000)^(1/4) – 1 ≈ 8%.

• Cheaper Option: Choose the bank loan (Answer: C).

Joe’s Investment in Sister's Spa:

• Initial Investment: $25,000

• Future Value: $75,000 after 6 years.

• Calculated Rate of Return:Using the formula:FV = PV * (1 + r)^nRearranging gives:r = (FV/PV)^(1/n) - 1r = (75,000 / 25,000)^(1/6) - 1 ≈ 20% (Answer: B).

Expected Growth Rate for Traps Inc.:

• Current Sale: $325,000

• Future Sale in 5 years: $500,000

• Calculated Growth Rate:Growth Rate = (Future Sale / Current Sale)^(1/n) - 1= (500,000 / 325,000)^(1/5) - 1 ≈ 9% (Answer: A).

Ryan's Investment Query:

• Initial Deposit: $4,500

• Target Amount: $10,000

• Interest Rate: 8.25% annually.

• Calculation Method: Use the future value formula to calculate the number of years: FV = PV * (1 + r)^nRearranging for n gives: n = log(FV / PV) / log(1 + r) n = log(10,000 / 4,500) / log(1 + 0.0825) ≈ 10 years.

Chapter 6: SUMMARY OF Key Equations

Equation Summary

6.1 Present Value of an Ordinary Annuity:

• Formula: PVA₁ = CF/i * (1 - (1 + i)^-n) 6.2 Future Value of an Ordinary Annuity:

• Formula: FVA₁ = CF * [(1 + i)^(n) -1] / i 6.3 Present Value of a Perpetuity:

• Formula: PVP = CF/i 6.4 Value of an Annuity Due:

• Formula: Annuity due value = Ordinary annuity value X (1 + i) 6.5 Present Value of a Growing Annuity:

• Formula: PVA = CF * [((1 + g)^n - (1 + g) * CF)/ (i - g)] 6.6 Present Value of a Growing Perpetuity:

• Formula: PVP = CF₁/g 6.7 Effective Annual Interest Rate:

• Formula: EAR = (1 + (quoted interest rate / m))^m - 1

Application Demos

Matt's Future Value Calculation

• Future Cash Flows Received: $6,200, $6,450, $7,225, $7,500 over 4 years.

• Opportunity Cost: 10%.

• Future Value Calculation: $31,504 (Answer: D).

Firm Cash Flows and Present Values

• Cash Flows from Fin Corp.: $79,000, $112,000, $164,000, $84,000, $242,000 with an opportunity cost of 15%.

• Calculated Present Value: $429,560 (Answer: A).

Jackie’s Lottery Cash Flow Stream Decision

• Cash Flow: $25,000 for 30 years.

• Return Rate: 10%.

• Minimum Lump-Sum Value Determination: $235,700 (Answer: D).

Loan Payment Calculation Overview

• Loan Amount: $150,000 with annual payments of $35,000 for 6 years.

• Determined Interest Rate: 10.55%.

• Arthur’s Future Savings: Investing $5,000 annually at 10% for 45 years will yield $3,594,524 (Answer: B).

Conclusion

These formulas and examples illustrate important concepts in finance regarding investments, returns, and present values, providing a strong foundation for study and application in practical situations.