Assume That You Are Nearing Graduation Of Your MBA Program

Assume That You Are Nearing Graduation Of Your MBA Program And Have Ap

Assume that you are nearing graduation of your MBA program and have applied for a job with a local bank. As part of the bank's evaluation process, you have been asked to take an examination that covers several financial analysis techniques. The first section of the test addresses time value of money analysis. See how you would do by answering the following questions.

A customer of the bank, Raj Kami, wants to deposit $100,000 in a savings account that pays a nominal rate of 8%.

  1. If the bank compounds interest annually, how much will the customer have in his account 3 years from now?
  2. What would the balance be in 3 years from now if the bank used quarterly compounding rather than annual compounding?
  3. If Raj Kami deposited the $100,000 in 4 equal payments of $25,000 each at the end of years 1, 2, 3, and 4, how much would he have in the savings account at the end of year 4, based on 8% annual compounding?
  4. Raj Kami wants to know how long it will take his sum of money to double if the growth rate per year is 8%.
  5. Raj Kami wants to buy a car, and a local bank will lend him $20,000. The loan would be fully amortized over 5 years (60 months), and the nominal interest rate would be 12%, with interest paid monthly. What is the monthly loan payment? What is the loan’s effective (or equivalent) rate EFF?
  6. What is the present value of $100,000 to be received in 4 years if the appropriate interest rate is 5%?
  7. Jackson Corporation’s bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 9%. The bonds have a yield to maturity of 10%. What is the current market price of these bonds?
  8. Renfro Rentals has issued bonds that have a 10% coupon rate, payable semiannually. The bonds mature in 10 years, have a face value of $1,000, and a yield to maturity of 9%. What is the price of the bonds?
  9. Wilson Wonders’ bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 10%. The bonds sell at a price of $900. What is their yield to maturity?
  10. What is the present value of a perpetuity that pays $1,000 per year if the appropriate interest rate is 5%?

Paper For Above instruction

Financial analysis techniques, especially the time value of money (TVM), are fundamental in evaluating investment options, loans, bonds, and savings strategies. This paper addresses each of the questions posed in the examination, illustrating the application of core financial concepts such as compound interest, future value, present value, loan amortization, bond valuation, yield to maturity, and perpetuities.

1. Future Value with Annual Compounding

If the bank compounds interest annually at a nominal rate of 8%, the future value (FV) of the $100,000 deposit after 3 years can be calculated using the formula:

FV = PV × (1 + r)^n

where PV = $100,000, r = 8% or 0.08, and n = 3 years.

FV = $100,000 × (1 + 0.08)^3 = $100,000 × 1.259712 ≈ $125,971.20.

Thus, after three years, Raj Kami will have approximately $125,971.20 in his savings account.

2. Future Value with Quarterly Compounding

When interest compounds quarterly, the interest rate per quarter is r/4 = 0.08/4 = 0.02, and total compounding periods n × 4 = 12.

Future value formula becomes:

FV = PV × (1 + r/4)^(4×n)

FV = $100,000 × (1 + 0.02)^12 ≈ $100,000 × 1.2682418 ≈ $126,824.18.

Quarterly compounding yields a slightly higher balance after 3 years, approximately $126,824.18.

3. Future Value of Annuity (Multiple Deposits)

Depositing $25,000 at the end of each year for 4 years, with an 8% annual interest rate, the future value is calculated via the future value of an ordinary annuity:

FV = P × [(1 + r)^n – 1] / r

FV = $25,000 × [(1 + 0.08)^4 – 1] / 0.08 ≈ $25,000 × [1.360489 – 1] / 0.08 ≈ $25,000 × 4.5061 ≈ $112,652.50.

At the end of year 4, Raj would have approximately $112,652.50.

4. Time to Double Investment at 8%

The rule of 72 provides a quick estimate: dividing 72 by the annual growth rate (8%) gives:

72 / 8 = 9 years.

More precisely, solving for n in FV = PV × (1 + r)^n where FV/PV=2:

2 = (1 + 0.08)^n

n = log(2) / log(1.08) ≈ 0.6931 / 0.07696 ≈ 9 years.

Therefore, it takes approximately 9 years for the investment to double at 8% annually.

5. Loan Payment Calculation

The loan is $20,000, amortized over 60 months, at an annual nominal rate of 12%, compounded monthly. The monthly interest rate r = 12% / 12 = 1% or 0.01.

The monthly payment P is given by:

P = [r × PV] / [1 – (1 + r)^–n]

P = [0.01 × 20,000] / [1 – (1 + 0.01)^–60] ≈ $200 / [1 – 0.547] ≈ $200 / 0.453 ≈ $441.52.

The effective annual rate (EFF) considers compounding:

EFF = (1 + r)^12 – 1 = (1 + 0.01)^12 – 1 ≈ 1.1268 – 1 ≈ 12.68%.

6. Present Value of a Future Sum

The present value of $100,000 to be received in 4 years at 5% interest rate:

PV = FV / (1 + r)^n = $100,000 / (1.05)^4 ≈ $100,000 / 1.215506 ≈ $82,270.42.

Thus, the present value is approximately $82,270.42.

7. Bond Valuation

For Jackson Corporation’s bonds, with 10 years remaining, coupon rate of 9%, yield of 10%, face value of $1,000, interest paid annually:

The bond price is the present value of future cash flows: annual coupon payments plus face value at maturity, discounted at YTM.

Coupon payment = $1,000 × 0.09 = $90.

Price = [C × (1 – (1 + YTM)^–n) / YTM] + [FV / (1 + YTM)^n]

= [$90 × (1 – (1 + 0.10)^–10) / 0.10] + [$1,000 / (1 + 0.10)^10] ≈ $90 × 6.1446 + $385.54 ≈ $553.01 + $385.54 ≈ $938.55.

The current market price of the bonds is approximately $938.55.

8. Bond Price with Semiannual Payments

Bond details: 10 years to maturity, face value $1,000, coupon 10% payable semiannually, YTM 9% semiannual:

Coupon payment = $1,000 × 10% / 2 = $50.

Number of periods = 10 × 2 = 20.

Periodic YTM = 9% / 2 = 4.5% or 0.045.

Price = [C × (1 – (1 + r)^–n) / r] + [FV / (1 + r)^n]

= [$50 × (1 – (1 + 0.045)^–20) / 0.045] + [$1,000 / (1 + 0.045)^20] ≈ $50 × 13.269 + $442.18 ≈ $663.45 + $442.18 ≈ $1,105.63.

The estimated price of the bonds is about $1,105.63.

9. Yield to Maturity Calculation

For Wilson Wonders’ bonds, with 10 years remaining, face value $1,000, coupon rate 10%, selling at $900:

The yield to maturity (YTM) is the interest rate that equates the present value of cash flows to price:

PV = C × (1 – (1 + YTM)^–n) / YTM + FV / (1 + YTM)^n

Trial-and-error or financial calculator methods estimate YTM ≈ 11.36%.

Hence, the approximate YTM is around 11.36%.

10. Present Value of a Perpetuity

A perpetuity paying $1,000 annually, with 5% interest rate:

PV = Payment / interest rate = $1,000 / 0.05 = $20,000.

The present value of the perpetuity is $20,000.

Conclusion

This analysis demonstrates the application of various core financial calculations, essential for banking professionals, financial analysts, and investors. Understanding these calculations enables better decision-making regarding investments, loans, and bond valuations and illustrates the importance of the time value of money in financial planning and analysis.

References

  • Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  • Fabozzi, F. J. (2017). Bond Markets, Analysis and Strategies. Pearson.
  • Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2021). Fundamentals of Corporate Finance (12th ed.). McGraw-Hill Education.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
  • Hord, S. M., & Rhoda, E. (2018). Financial Management: Theory & Practice. Cengage Learning.
  • Investopedia. (2023). Time Value of Money (TVM). https://www.investopedia.com/terms/t/timevalueofmoney.asp
  • Morningstar. (2023). Bond Valuation. https://www.morningstar.com/articles/124567/bond-valuation
  • Kaplan, S., & Nelson, H. (2019). Corporate Finance: Tools for Analysis. Routledge.
  • Graham, B., & Dodd, D. (2008). Security Analysis: Sixth Edition. McGraw-Hill.
  • Harris, L. (2020). Financial Institutions and Markets. South-Western College Pub.

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