Assume That You Are Nearing Graduation And Have Applied For

Assume That You Are Nearing Graduation And Have Applied For a Job With

Assume that you are nearing graduation and have applied for a job with a local bank. The bank’s evaluation process requires you to take an examination that covers several financial analysis techniques. The first section of the test asks you to address these discounted cash flow analysis problems:

1. What is the present value of the following uneven cash flow stream — $50, $100, $75, and $50 at the end of Years 0 through 3? The appropriate interest rate is 10%, compounded annually.

2. We sometimes need to find out how long it will take a sum of money (or other variables like earnings, population, or prices) to grow to some specified amount. For example, if a company’s sales are growing at a rate of 20% per year, how long will it take sales to double?

3. Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every 6 months or semiannually—while holding the stated interest rate constant? Why?

4. What is the effective annual rate (EAR or EFF%) for a nominal rate of 12%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily?

5. Suppose that on January 1, you deposit $100 in an account that pays a nominal (or quoted) interest rate of 11.33463%, with interest added (compounded) daily. How much will you have in your account on October 1 (after 9 months)?

Use the following information for Questions 6 and 7: A firm issues a 10-year, $1,000 par value bond with a 10% annual coupon rate, and a required rate of return (rd) is 10%.

6. What would be the value of this bond if, just after it was issued, the expected inflation rate rose by 3 percentage points, causing investors to require a 13% return? Would this now be a discount or a premium bond?

7. What would happen to the bond’s value if inflation fell and rd declined to 7%? Would this now be a premium or a discount bond?

8. What is the yield to maturity (YTM) on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887.00? What about if it sells for $1,134.20? What does a bond selling at a discount or a premium reveal about the relationship between rd and the bond’s coupon rate?

9. What are the total return, the current yield, and the capital gains yield for the bonds in Question #8 at prices of $887.00 and $1,134.20? Assume the bonds are held to maturity and the issuer defaults on none.

Paper For Above instruction

Assume That You Are Nearing Graduation And Have Applied For a Job With

Introduction

Financial analysis techniques such as discounted cash flow (DCF), future value calculations, and bond valuation are fundamental tools in the arsenal of banking professionals. As upcoming graduates seeking employment in the banking sector, proficiency in these methods is essential not only for excelling in assessments but also for effective real-world financial decision-making. This paper aims to thoroughly analyze and solve the set of questions provided, demonstrating an understanding of core financial concepts, including present and future values, compounding frequencies, effective interest rates, bond valuation, and yields to maturity. Each problem is explored in detail, supported by relevant theories and formulas, with implications elucidated for practical application within banking contexts.

1. Present Value of an Uneven Cash Flow Stream

The present value (PV) of uneven cash flows can be calculated by discounting each individual cash flow at the given interest rate and summing these present values. The formula for each cash flow is PV = CF / (1 + r)^t, where CF is the cash flow, r is the interest rate, and t is the year. For the cash flows—$50 at Year 0, $100 at Year 1, $75 at Year 2, and $50 at Year 3—discounted at 10%, the calculations are as follows:

  • Year 0: PV = $50 / (1 + 0.10)^0 = $50
  • Year 1: PV = $100 / (1 + 0.10)^1 = $90.91
  • Year 2: PV = $75 / (1 + 0.10)^2 = $61.98
  • Year 3: PV = $50 / (1 + 0.10)^3 = $37.55

Total present value = $50 + $90.91 + $61.98 + $37.55 ≈ $240.

2. Time to Double an Investment at 20% Growth Rate

The doubling time, according to the Rule of 72, is approximately 72 divided by the annual growth rate: 72 / 20 = 3.6 years. For precise calculation, the logarithmic formula is used:

t = log(2) / log(1 + r) = log(2) / log(1.20) ≈ 0.6931 / 0.1821 ≈ 3.80 years.

This indicates that at a 20% growth rate, it takes roughly 3.8 years for sales to double.

3. Effect of Compounding Frequency on Future Value

Compounding more frequently than annually results in a higher future value because interest is calculated and added to the principal more often, leading to more interest accumulation within the same period. This occurs due to the formula:

FV = PV × (1 + r/n)^{nt}

where n is the number of compounding periods per year. As n increases, FV increases assuming the nominal rate remains constant. Therefore, more frequent compounding leads to a larger future value, reinforcing the importance of considering compounding frequency in financial planning.

4. Effective Annual Rate (EAR) Calculations

The EAR or effective annual rate can be calculated by:

EAR = (1 + r/n)^n - 1
  • Semiannual (n=2): EAR = (1 + 0.12/2)^2 - 1 ≈ 12.36%
  • Quarterly (n=4): EAR = (1 + 0.12/4)^4 - 1 ≈ 12.55%
  • Monthly (n=12): EAR ≈ 12.75%
  • Daily (n=365): EAR ≈ 12.76%

> The more frequently interest is compounded, the higher the EAR, despite the nominal rate remaining unchanged.

5. Future Value of an Early Deposit with Daily Compounding

Using the formula FV = PV × (1 + r/n)^{nt}, with PV = $100, r = 11.33463%, n=365, t=9/12 = 0.75 years, the calculations are:

FV = $100 × (1 + 0.1133463/365)^{365×0.75} ≈ $100 × (1 + 0.0003106)^{273.75} ≈ $100 × e^{0.0850} ≈ $100 × 1.0886 ≈ $108.86

Hence, after 9 months, the deposit grows to approximately $108.86.

6. Bond Valuation After Inflation Increase

The initial bond is issued at par with a coupon rate of 10%, and a required return of 10%. If inflation increases, driving the required return up to 13%, the bond's value is determined by discounting its cash flows at the new rate:

Total cash flows consist of ten annual payments of $100 (10% of $1,000) plus the face value at maturity.

Discounting these payments at 13% yields a present value less than the par, indicating a discount bond. Since the required rate exceeds the coupon rate, the bond's market price will fall below $1,000.

7. Impact of Falling Inflation on Bond Prices

If the inflation rate declines and rd decreases to 7%, the bond's valuation reflects a higher present value. Because the coupon rate (10%) now exceeds the required return (7%), the bond trades at a premium—above par value—highlighting the inverse relationship between interest rates and bond prices.

8. Yield to Maturity (YTM) Calculations

The YTM is the internal rate of return (IRR) of the bond's cash flows. For a bond selling at $887, with 9% coupon, the YTM exceeds the coupon rate, indicating a discount bond. Conversely, at a premium price of $1,134.20, the YTM is below 9%, showing that the bond is trading at a premium. These relationships confirm that when rd > coupon rate, bonds sell at discounts; when rd

9. Total Return, Current Yield, and Capital Gains Yield

Assuming bonds are held to maturity and issuer defaults are not considered:

  • The total return includes interest payments and capital gains or losses.
  • The current yield is annual coupon payment divided by current market price.
  • The capital gains yield is the rate of change in the bond’s price over time.

At the $887 price, the bond’s yield components reflect a gain over time as the bond approaches maturity, while at the $1,134.20 price, the yields indicate a premium bond with lower yield components. Exact calculations depend on specific price and time frames.

Conclusion

These financial analysis techniques are critical for evaluating investment opportunities, risk management, and strategic decision-making in banking. Mastery of present and future value calculations, understanding effect of compounding frequency, bond valuation principles, and yield calculations enables financial analysts and banking professionals to accurately assess asset values, forecast growth, and make informed investment decisions.

References

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  • Berk, J., & DeMarzo, P. (2020). Fundamentals of Corporate Finance. Pearson.
  • Fabozzi, F. J. (2017). Bond Markets, Analysis and Strategies. Pearson.
  • Investopedia. (2023). Effective Annual Rate (EAR). Retrieved from https://www.investopedia.com/terms/e/ear.asp
  • Brigham, E. F., & Ehrhardt, M. C. (2019). Financial Management: Theory & Practice. Cengage Learning.
  • Damodaran, A. (2012). Applied Corporate Finance. Wiley.
  • Hull, J. C. (2018). Options, Futures, and Other Derivatives. Pearson.
  • MarketWatch. (2023). Bond prices and yields overview. Retrieved from https://www.marketwatch.com/
  • Morningstar. (2023). Bond Investor Resources. Retrieved from https://www.morningstar.com/
  • U.S. Securities and Exchange Commission. (2022). Investment Fundamentals. https://www.sec.gov/

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