Suppose that a corporation issues a bond having face value ₹ 1,000 redeemable at premium of 10% at the end of 3 years. If the discount rate is 12% and coupon rate is 8%, then calculate the value of this bond. Moreover, would you buy this bond if the market price of the bond is ₹ 1,050 or ₹ 800? Calculate the yield to maturity from the following information. Coupon rate = 7%, face value = ₹ 500, price of bond = ₹ 350, maturity period = 10 years.

Part A: Valuation of Bond

Given:

• Face Value (FV) = ₹1,000
• Coupon Rate = 8% → Annual Coupon = 8% of ₹1,000 = ₹80
• Redemption Value = ₹1,000 + 10% premium = ₹1,100
• Time to maturity = 3 years
• Discount Rate (r) = 12%

Formula for Present Value of Bond:

Bond Value = Present Value of Coupons + Present Value of Redemption Value

Step-by-step Calculation:

We calculate each component using present value formula:

1. Present Value of Coupons (Annuity):

PV of Coupons = ₹80 × [1 – (1 + r)^-n] / r
= ₹80 × [1 – (1 + 0.12)^-3] / 0.12
= ₹80 × [1 – (1 / 1.4049)] / 0.12
= ₹80 × [1 – 0.7118] / 0.12
= ₹80 × 2.402
≈ ₹192.16

2. Present Value of Redemption Value:

PV = ₹1,100 / (1 + 0.12)³
= ₹1,100 / 1.4049
≈ ₹782.89

3. Total Bond Value:

Total Value ≈ ₹192.16 + ₹782.89 = ₹975.05

Conclusion on Purchase Decision:

• If market price is ₹1,050 → Overpriced → Do not buy.
• If market price is ₹800 → Undervalued → Buy the bond.

Part B: Calculate Yield to Maturity (YTM)

Given:

• Coupon Rate = 7%
• Annual Coupon = 7% of ₹500 = ₹35
• Face Value = ₹500
• Current Price = ₹350
• Time to maturity = 10 years

YTM is the rate (r) that satisfies the equation:

₹350 = ₹35 × [1 – (1 + r)^-10] / r + ₹500 / (1 + r)¹⁰

Trial and Error Approach:

At r = 10%

PV of Coupons = ₹35 × 6.1446 ≈ ₹215.06
PV of Face Value = ₹500 / (1.10)¹⁰ = ₹500 / 2.5937 ≈ ₹192.72
Total = ₹215.06 + ₹192.72 = ₹407.78 (> ₹350)

At r = 14%

PV of Coupons = ₹35 × 5.2161 = ₹182.56
PV of Face Value = ₹500 / (1.14)¹⁰ = ₹500 / 3.707 ≈ ₹134.87
Total = ₹182.56 + ₹134.87 = ₹317.43 (< ₹350)

At r = 12%

PV of Coupons = ₹35 × 5.6502 = ₹197.76
PV of Face Value = ₹500 / 3.106 = ₹160.96
Total ≈ ₹358.72 (≈ ₹350)

Approximate YTM = 12%

Conclusion

For the first bond, the computed fair value is ₹975.05. If the bond is priced at ₹1,050, it is overpriced and should be avoided. But if available at ₹800, it is undervalued and worth buying.

For the second bond, the Yield to Maturity is approximately 12%, which is higher than the coupon rate of 7%, indicating that the bond is trading at a discount and is attractive for investors.