A bond maturing in 2030 with a coupon rate of 4% and price €85 has exactly 10 years to maturity. What is its annual gross redemption yield?

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Prepare for the Qualified Financial Adviser Exam 2 with flashcards and multiple choice questions, complete with hints and explanations. Get exam-ready and increase your confidence with our comprehensive study materials!

Multiple Choice

A bond maturing in 2030 with a coupon rate of 4% and price €85 has exactly 10 years to maturity. What is its annual gross redemption yield?

Explanation:
The key idea is yield to maturity: the annual rate i that equates the present value of all future coupons plus the redemption at maturity to the current price. Assume a par value of 100, so the annual coupon is 4. Let i be the annual gross redemption yield. The price must satisfy: 85 = 4 × [ (1 − (1 + i)^(−10)) / i ] + 100 × (1 + i)^(−10) Solving this numerically (trying i = 6% gives PV ≈ 85.28; a tiny increase in i lowers the PV), we find i is about 6.0% (approximately 6.04%). Therefore, the annual gross redemption yield is about 6.0% per year. The result makes sense since the price is below par and the coupon rate is 4%, so the yield must exceed the coupon.

The key idea is yield to maturity: the annual rate i that equates the present value of all future coupons plus the redemption at maturity to the current price.

Assume a par value of 100, so the annual coupon is 4. Let i be the annual gross redemption yield. The price must satisfy:

85 = 4 × [ (1 − (1 + i)^(−10)) / i ] + 100 × (1 + i)^(−10)

Solving this numerically (trying i = 6% gives PV ≈ 85.28; a tiny increase in i lowers the PV), we find i is about 6.0% (approximately 6.04%).

Therefore, the annual gross redemption yield is about 6.0% per year. The result makes sense since the price is below par and the coupon rate is 4%, so the yield must exceed the coupon.

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