Discounted Cash Flow Valuations: Sara Gandhi Is A 50-Year-Ol

Discounted Cash Flow Valuationsara Gandhi Is A 50 Year Old Entrepreneu

Discounted Cash Flow Valuation Sara Gandhi is a 50-year-old entrepreneur with a new computer software product idea. She owns an S corporation, which offers tax advantages and limited liability. Sara aims to expand her business internationally and wants to understand financial concepts such as the time value of money to support her growth strategy. She has read about how money today is worth more than the same amount in the future because it can be invested to generate returns. Sara seeks assistance in applying these concepts to personal and business financial decisions.

Paper For Above instruction

Introduction

Understanding the time value of money (TVM) is crucial for making informed financial decisions, especially for entrepreneurs like Sara Gandhi who are planning investments, savings, and expansion strategies. TVM emphasizes that a sum of money today is worth more than the same sum received in the future due to its potential to earn interest. This paper explores various core TVM concepts through a series of practical questions that Sara has posed, providing detailed calculations and explanations based on financial principles. The discussions include future value, present value, annuities, perpetuities, and the impact of different interest rates and compounding frequencies, offering Sara a comprehensive understanding to manage her finances effectively.

1. Future Value of Investment in Retirement Account

Sara plans to invest $150,000 in an IRA at an 8% annual interest rate for 15 years. Using the future value formula:

FV = PV × (1 + r)^n

Where PV = $150,000, r = 8% or 0.08, n = 15 years.

FV = 150,000 × (1 + 0.08)^15 ≈ 150,000 × 3.1722 ≈ $475,830

Therefore, Sara can expect her investment to grow to approximately $475,830 at the end of 15 years.

2. Present Value Needed for College Funding

Sara wants to ensure her daughter has $120,000 in 16 years. With an 8% annual return, the present value (PV) is calculated as:

PV = FV / (1 + r)^n

PV = 120,000 / (1 + 0.08)^16 ≈ 120,000 / 3.518 ≈ $34,095

Thus, she needs to invest about $34,095 today to reach her goal.

3. Growth of Money Market Investment

Sara invests $60,000 in a money market fund earning 8% interest compounded annually for 5 years. Using the future value formula:

FV = PV × (1 + r)^n

FV = 60,000 × (1 + 0.08)^5 ≈ 60,000 × 1.4693 ≈ $88,158

This investment will grow to approximately $88,158 after 5 years.

4. Present Value of Uneven Cash Flows

Sara expects to receive cash flows of $20,000, $30,000, and $40,000 over the next 3 years. At a discount rate of 7%, the present value (PV) is:

PV = ∑ (Cash Flow / (1 + r)^t)

PV = 20,000 / (1 + 0.07)^1 + 30,000 / (1 + 0.07)^2 + 40,000 / (1 + 0.07)^3

PV ≈ 20,000 / 1.07 + 30,000 / 1.1449 + 40,000 / 1.225043

PV ≈ 18,696 + 26,209 + 32,653 ≈ $77,558

The present value of these cash flows is approximately $77,558.

5. Valuation of Perpetuity

If Sara considers a perpetuity paying $100 annually with a 6% interest rate, its value is calculated by:

Perpetuity Value = Payment / Rate = 100 / 0.06 ≈ $1,666.67

The perpetuity is worth approximately $1,666.67.

6. Valuing Preferred Stock with Growing Dividends

The Gordon Growth Model evaluates the current price of preferred stock, with a dividend of $3, expected to grow at 6% annually, and a required rate of return of 11%:

Price = D1 / (r - g)

D1 = $3 × (1 + 0.06) = $3.18

Price = 3.18 / (0.11 - 0.06) = 3.18 / 0.05 = $63.60

The current stock price is approximately $63.60.

7. Investment Decision for Property Purchase

Sara's company plans to buy a property for $400,000 with a projected value of $480,000 in one year. Using the discounted cash flow approach at a 10% interest rate:

Present Value (PV) = Future Value / (1 + r) = 480,000 / 1.10 ≈ $436,364

Since $436,364 exceeds the purchase price, the investment has a positive net present value (NPV), indicating it is financially sound to buy at 10% interest rate.

8. Buy Decision at Higher Discount Rate

At a 25% rate:

PV = 480,000 / 1.25 ≈ $384,000

Because $384,000 is less than the purchase price of $400,000, the investment would not be favorable at this higher rate, suggesting the project is less financially attractive under increased cost of capital.

9. Effective Annual Rate (EAR) with Monthly Compounding

The formula for EAR when compounded monthly:

EAR = (1 + r/n)^n - 1, where r = 24% or 0.24, n = 12

EAR = (1 + 0.24/12)^12 - 1 ≈ (1 + 0.02)^12 - 1 ≈ 1.2682 - 1 = 0.2682 or 26.82%

The effective annual rate is approximately 26.82%.

10. EAR with Quarterly Compounding at 24% APR

Using the EAR formula:

EAR = (1 + 0.24/4)^4 - 1 ≈ (1 + 0.06)^4 - 1 ≈ 1.2625 - 1 = 0.2625 or 26.25%

The effective annual rate with quarterly compounding is approximately 26.25%.

Financial Concepts Summary and Conclusion

This exploration demonstrates the importance of understanding TVM for various financial decisions. The calculations show how different interest rates, compounding frequencies, and cash flow patterns influence the valuation of investments, savings, and financial planning. For Sara, grasping these concepts enables strategic decision-making—whether for retirement savings, education funding, investment appraisals, or capital budgeting. Applying these principles, she can better evaluate opportunities, optimize her financial outcomes, and support her entrepreneurial growth ambitions effectively.

References

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