A company XYZ Ltd. has issued a bond having a face value of Rs 10,000 paying annual dividend at 8.5% p.a. The bond will be redeemed at par at the end of 10 years. Find the purchase value of this bond, if the investor wishes a yield rate of 8%. [Given : ]
A company XYZ Ltd. has issued a bond having a face value of Rs 10,000 paying annual dividend at 8.5% p.a. The bond will be redeemed at par at the end of 10 years. Find the purchase value of this bond, if the investor wishes a yield rate of 8%. [Given : ]
The purchase value is the present value of all future coupons plus the present value of the redemption amount.
Given data:
- Face value F = Rs 10,000; coupon rate = 8.5%, so annual coupon C = Rs 850.
- Redemption at par = Rs 10,000 after years.
- Yield rate ; .
Present value of coupons (annuity):
- = = Rs 5,703.57.
Present value of redemption:
- = Rs 4,631.93.
Purchase value:
- = Rs 10,335.50 (approximately).
Marking Scheme
- 10.5 mark: annual coupon C = Rs 850 identified.
- 21.5 marks: present value of coupon annuity = = Rs 5,703.57.
- 31 mark: present value of redemption = Rs 4,631.93 and total purchase value = Rs 10,335.50 (accept Rs 10,335 to Rs 10,336).
Hint
Coupon = 8.5% of 10,000 = Rs 850. Discount the coupon annuity and the Rs 10,000 redemption at 8%, then add them.
Quick Oral Answer
I discount the Rs 850 annual coupons and the Rs 10,000 redemption at the 8% yield; the coupon annuity is Rs 5,703.57 and the redemption present value is Rs 4,631.93, so the purchase value is about Rs 10,335.50, a premium since the coupon rate exceeds the yield.
Analysis & Explanation
Bond valuation is a straight present-value exercise: the fair price today equals the discounted value of every future cash flow at the investor's required yield.
Concept:
- A bond pays a fixed annual coupon (here 8.5% of face value = Rs 850) for its life and returns the face value at redemption. Discounting these two streams at the desired yield of 8% gives the maximum price the investor should pay.
Why price exceeds face value:
- The coupon rate (8.5%) is higher than the yield rate (8%), so the bond pays more than the market demands. Such a bond trades at a premium, which is why the purchase value Rs 10,335.50 is above the Rs 10,000 face value.
Exam trap:
- Confusing coupon rate with yield rate when computing either the annual coupon or the discount factor. The coupon uses 8.5%, the discounting uses 8%.
Real-world link:
- This is exactly how government securities and corporate bonds are priced on exchanges; when market yields fall below the coupon, bond prices rise above par, and vice versa.
Common Mistakes
- 1Using the yield rate 8% to compute the coupon instead of the coupon rate 8.5%.
- 2Forgetting to add the present value of the redemption (face) value to the coupon annuity.
- 3Discounting the coupons at 8.5% instead of the required yield rate 8%.
Interesting Facts
A bond selling above its face value, like this one, is called a premium bond, and it happens whenever the coupon rate exceeds the market yield.
The relationship 'yield up, price down' from this present-value formula is why central-bank rate changes instantly move bond markets worth trillions worldwide.
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Frequently Asked Questions
Why is the purchase value more than the Rs 10,000 face value?
The bond's coupon rate (8.5%) is higher than the investor's required yield (8%). Because the bond pays more than the market demands, it is worth a premium over par, so its fair price of Rs 10,335.50 is above the Rs 10,000 face value.
Which rate do I use for the coupon and which for discounting?
Use the coupon rate 8.5% to find the annual interest payment (Rs 850). Use the required yield rate 8% to discount both the coupon annuity and the redemption amount to present value. Swapping these rates is the most common mistake.