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Instructions This Assignment Must Be Submitted On Blackboard Word F

This Assignment Must Be Submitted On Blackboard Word F

Instructions: · This Assignment must be submitted on Blackboard ( WORD format only ) via the allocated folder. · Email submission will not be accepted. · You are advised to make your work clear and well-presented; marks may be reduced for poor presentation. This includes filling your information on the cover page. · Assignment will be evaluated through BB Safe Assign tool. · Late submission will result in ZERO marks being awarded. · The work should be your own, copying from students or other resources will result in ZERO marks. · Use Times New Roman font 12 for all your answers.

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Suppose Abdulrahman plans to borrow a loan of SAR 120,000 now and will repay it in 10 equal annual installments. If the bank charges 10% interest, what will be the amount of the annual installment?

To determine the annual installment for Abdulrahman's loan, we consider the loan as an amortized loan with fixed payments. The principal amount is SAR 120,000, the interest rate is 10%, and the repayment period is 10 years.

The formula for calculating the annual payment (PMT) for an amortized loan is:

PMT = (r * P) / (1 - (1 + r)^-n)

Where:

  • r = interest rate per period (10% or 0.1)
  • P = principal amount SAR 120,000
  • n = number of payments (10)

Applying the values:

PMT = (0.1 * 120,000) / (1 - (1 + 0.1)^-10)

PMT = 12,000 / (1 - (1.1)^-10)

Calculating (1.1)^-10 ≈ 0.3855

Denominator: 1 - 0.3855 = 0.6145

Thus, the annual installment:

PMT ≈ 12,000 / 0.6145 ≈ SAR 19,529.44

Therefore, Abdulrahman’s annual payment will be approximately SAR 19,529.44.

Regarding the Time Value of Money (TVM) concept: The TVM states that money available now is worth more than the same amount in the future due to its potential earning capacity. This principle is rooted in the idea that money can earn interest or returns over time, making present money more valuable than future money. Factors such as inflation reduce the purchasing power of money over time, further emphasizing the importance of TVM in financial decision-making.

In practice, TVM allows investors and borrowers to compare cash flows occurring at different times by converting future cash flows to their present value or vice versa. This is crucial for investment appraisal, loan amortization, and capital budgeting, where understanding the value of future cash inflows and outflows enables better decision-making.

In the context of bonds, investors assess the present value of future coupon payments and the face value to determine the bond’s fair price relative to prevailing market yields. This process exemplifies the core idea of TVM — that money’s value changes over time and needs to be adjusted accordingly for accurate evaluations.

Ahmed’s bond evaluation: The bond issued at $800 with a coupon rate of 7%, paid semiannually, and a market yield of 10% requires calculating its fair price. The bond’s semiannual coupon payment is:

Coupon rate per period: 7% annual / 2 = 3.5% per period

Coupon payment: 3.5% of $800 = $28 per period

Number of periods: 10 years x 2 = 20 periods

Market yield per period: 10% / 2 = 5% = 0.05

Using the present value formula for bond pricing:

Bond Price = (C * [1 - (1 + r)^-n]) / r + FV / (1 + r)^n

Where:

  • C = $28
  • r = 0.05
  • n = 20
  • FV = $800

Calculating the present value of coupons:

PV of coupons = 28 [1 - (1 + 0.05)^-20] / 0.05 ≈ 28 13.1597 ≈ $368.27

Present value of face value:

PV of FV = 800 / (1 + 0.05)^20 ≈ 800 / 2.6533 ≈ $301.29

Therefore, the fair price of the bond is:

Price ≈ $368.27 + $301.29 ≈ $669.56

Since this price is less than the offered price of $800, the bond appears overvalued at the market yield of 10%. Hence, Ahmed should not buy the bond at the offered price.

Regarding the bond with a 6% coupon purchased at $760 with a promised yield of 8%, which was sold after one year at $798.8, the realized yield can be calculated considering the income received and sale price:

Initial purchase price: $760

Coupon received after 1 year: 6% of $1,000 = $60 (assuming face value $1,000)

Sale price: $798.8

Total earnings: $60 + $798.8 = $858.8

Effective return over the year:

Realized yield = (Total earnings / Initial investment) ^ (1 / number of years) - 1

Realized yield = ($858.8 / $760) ^ 1 - 1 ≈ 1.13 - 1 = 0.13 or 13%

This indicates the investor achieved a 13% return, outperforming the initial promised yield of 8%, mainly due to the bond’s price increase in the secondary market.

In conclusion, understanding the time value of money, bond valuation techniques, and yields is essential for making informed investment decisions. Proper application of these principles ensures that investors can evaluate the true worth of securities relative to prevailing market conditions and their individual investment goals.

References

  • Brigham, E. F., & Houston, J. F. (2019). Fundamentals of Financial Management (15th ed.). Cengage Learning.
  • Fabozzi, F. J. (2016). Bond Markets, Analysis, and Strategies (9th ed.). Pearson.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (3rd ed.). Wiley.
  • Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2018). Essentials of Corporate Finance (10th ed.). McGraw-Hill Education.
  • Trimble, D. (2017). Time Value of Money: Concepts and Applications. Journal of Finance Education, 23, 45-55.
  • Gürsel, V., & Erdem, E. (2020). Bond Pricing and Yield Analysis. Journal of Economics and Finance, 25(3), 150-165.
  • Mishkin, F. S., & Eakins, S. G. (2018). Financial Markets and Institutions (9th ed.). Pearson.
  • Hull, J. C. (2018). Risk Management and Financial Institutions (5th ed.). Wiley.
  • Investopedia. (2023). Time Value of Money (TVM). Retrieved from https://www.investopedia.com/terms/t/timevalueofmoney.asp
  • Morningstar. (2023). Bond Valuation and Yields. Retrieved from https://www.morningstar.com/bonds/valuation

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