Assignment Questions: Abdulrahman Plans To Borrow

Assignment Questionsq1 Suppose Abdulrahman Plan To Borrow A Loan Of S

Q1. 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?

Q2. Briefly discuss the Time Value of Money concept?

Q3. Ahmed has been offered a 10-year bond issued by Homer, Inc., at a price of $800. The bond has a coupon rate of 7 percent and pays the coupon semiannually. Similar bonds in the market will yield 10 percent today.

• a. What should be the price of this bond?
• b. Should Ahmed buy the bonds at the offered price?

Q4. Suppose a 3-year bond with a 6% coupon rate was purchased for $760 and had a promised yield of 8%. Suppose that interest rates increased and the price of the bond declined. Displeased, you sold the bond for $798.8 after owning it for 1 year. What should be the realized yield?

Paper For Above instruction

The financial decisions individuals and corporations make are deeply rooted in the principles of the Time Value of Money (TVM). This fundamental concept states that a sum of money today is worth more than the same sum in the future due to its potential earning capacity. This core notion underpins virtually all financial calculations, such as loan amortizations, bond pricing, and investment appraisals, emphasizing that money's value is time-dependent. Understanding TVM is crucial for effective financial planning and resource allocation, as it influences how individuals assess the value of investments, loans, and savings over time.

In the context of Abdulrahman’s loan repayment, the calculation of equal annual installments involves using the annuity formula, which accounts for the present value of a series of future payments. If Abdulrahman borrows SAR 120,000 at an interest rate of 10%, the task is to determine the fixed installment payment necessary to amortize the loan over 10 years. This can be calculated using the standard annuity payment formula:

Payment = PV × [i / (1 - (1 + i)^-n)]

where PV is the present value or loan amount, i is the annual interest rate, and n is the number of periods. Plugging in the values:

Payment = 120,000 × [0.10 / (1 - (1 + 0.10)^-10)]

This results in an annual installment of approximately SAR 19,163.54. This payment includes both interest and principal components, systematically reducing the outstanding loan balance.

Transitioning to the concept of the Time Value of Money, it is vital to comprehend that money has a potential earning capacity. This means that a dollar today is worth more than a dollar tomorrow because the money received today can be invested to generate earnings. This principle underlies the valuation of investments, where future cash flows are discounted to their present value using an appropriate discount rate. The TVM concept is essential for evaluating loans, bonds, and other financial instruments, helping investors and borrowers make informed decisions based on the worth of money across different time periods.

In the case of the bond offered to Ahmed by Homer, Inc., the valuation involves calculating the bond’s fair present value based on the current market yield. The bond pays semiannual coupons of 7%, with a face value typically assumed to be $1,000 for standardization, but in this scenario, the market value is given as $800. The bond's coupon payments are semiannual, meaning a coupon of 35 dollars every six months. The market yield is 10% annually, which translates into a semiannual yield of 5%.

The bond valuation formula considers the present value of future coupon payments and the face value repayment at maturity:

Price = (C × [1 - (1 + r)^-n]) / r + Face value / (1 + r)^n

where C is the semiannual coupon payment, r is the semiannual market yield, and n is the total number of periods (20 semiannual periods for 10 years). Calculating with C = $35, r = 0.05, n = 20, and face value = $1,000, the bond's fair price can be determined.

Calculations indicate that the bond should be priced approximately at $734.50, which is less than the offered $800. The discrepancy suggests that the bond is priced above its theoretical fair value, mainly due to market factors or differences in credit risk perception. Consequently, whether Ahmed should buy the bond depends on his investment goals and whether he assesses the bond's yield to match his required rate of return. Since the bond's yield based on its price would be below the market yield, it may be a less attractive investment at the current price.

Regarding the third question, the bond’s price dynamics and the realized yield are directly influenced by interest rate movements. A bond purchased at $760, with a coupon rate of 6%, and a promised yield of 8%, after a year, is affected by changing market interest rates. When rates increase, bond prices fall, and vice versa. Being dissatisfied with the decline in market value, the investor sold the bond for $798.8 after holding it for a year. To compute the actual realized yield, the initial investment, coupon income received, and sale price are considered.

The total return includes the coupon payment and the capital gain or loss. Specifically, the investor received a coupon of 6% of face value (for simplicity, assuming a $1,000 face value, the coupon is $60). The sale generated $798.8, which implies a capital gain of $38.8 ($798.8 - $760). The total income over the year was $98.8, combining the coupon and capital gain. The realized yield is calculated as:

Realized yield = (Coupon + Sale price - Purchase price) / Purchase price

which equals approximately 13.05%, indicating the total compounded return achieved during the holding period, influenced by market fluctuations and interest rate changes.

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