Model Answer
0 min readIntroduction
Bonds are a crucial component of the financial markets, representing debt instruments issued by corporations or governments to raise capital. The price of a bond is inversely related to prevailing interest rates; when interest rates rise, bond prices fall, and vice versa. Bond valuation involves determining the present value of all future cash flows (coupon payments and face value) that an investor will receive. This calculation requires discounting these future cash flows using an appropriate discount rate, reflecting the risk associated with the bond. This question requires us to calculate the present value of a bond given its characteristics and the prevailing discount rate.
Bond Valuation: A Detailed Calculation
The value of a bond is the present value of its future cash flows. These cash flows consist of periodic coupon payments and the face value (par value) received at maturity. The formula for bond valuation is:
Bond Value = PV of Coupon Payments + PV of Face Value
1. Identifying the Components
- Face Value (FV): ₹100
- Coupon Rate: 8% per annum
- Coupon Payment (PMT): 8% of ₹100 = ₹8 per year. Since interest is payable quarterly, the quarterly coupon payment is ₹8 / 4 = ₹2.
- Maturity Period: 5 years
- Number of Quarters (n): 5 years * 4 quarters/year = 20 quarters
- Discount Rate: 12% per annum. The quarterly discount rate is 12% / 4 = 3% or 0.03.
2. Calculating the Present Value of Coupon Payments
The present value of an annuity (coupon payments) can be calculated using the following formula:
PV of Coupon Payments = PMT * [1 - (1 + r)^-n] / r
Where:
- PMT = Quarterly coupon payment = ₹2
- r = Quarterly discount rate = 0.03
- n = Number of quarters = 20
PV of Coupon Payments = ₹2 * [1 - (1 + 0.03)^-20] / 0.03
PV of Coupon Payments = ₹2 * [1 - (1.03)^-20] / 0.03
PV of Coupon Payments = ₹2 * [1 - 0.55367575] / 0.03
PV of Coupon Payments = ₹2 * 0.44632425 / 0.03
PV of Coupon Payments = ₹2 * 14.877475
PV of Coupon Payments = ₹29.75495
3. Calculating the Present Value of the Face Value
The present value of the face value can be calculated using the following formula:
PV of Face Value = FV / (1 + r)^n
Where:
- FV = Face Value = ₹100
- r = Quarterly discount rate = 0.03
- n = Number of quarters = 20
PV of Face Value = ₹100 / (1 + 0.03)^20
PV of Face Value = ₹100 / (1.03)^20
PV of Face Value = ₹100 / 1.80611123
PV of Face Value = ₹55.367575
4. Calculating the Bond Value
Bond Value = PV of Coupon Payments + PV of Face Value
Bond Value = ₹29.75495 + ₹55.367575
Bond Value = ₹85.122525
Therefore, the value of the bond is approximately ₹85.12.
Conclusion
In conclusion, the value of the 5-year bond with an 8% coupon rate and a 12% discount rate is approximately ₹85.12. This calculation demonstrates the inverse relationship between bond prices and discount rates. A higher discount rate results in a lower bond value, as future cash flows are discounted more heavily. Understanding bond valuation is crucial for investors and financial professionals in making informed investment decisions. The market constantly re-evaluates bond prices based on changing interest rate expectations.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.