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Difficulty: Very hardDebt Securities and Bond Structure

An investor purchases a portfolio of municipal bonds with a total par value of $50,000\$50,000. The bonds carry a nominal annual coupon rate of 4.50%4.50\% with interest payable semi-annually. If the current market price of the portfolio is quoted at 90.0090.00 (% of par), what is the annual current yield of this bond portfolio?

Answer: 5 %

Answer

The annual current yield of the bond portfolio is 5.00%.
The current yield of a bond or bond portfolio is calculated by dividing the annual dollar coupon payment by the current market price of the bond position. With a total par value of $50,000\$50,000 and a nominal coupon rate of 4.50%4.50\%, the annual coupon income is $2,250\$2,250. At a quoted price of 90.0090.00 (% of par), the market value of the position is $45,000\$45,000. Dividing $2,250\$2,250 by $45,000\$45,000 yields an annual current yield of 5.00%5.00\%.

Step-by-Step Solution

1
Determine the dollar market value of the bond portfolio.
Market Value = \$50,000 \times \(\frac{90.00}{100}\) = \$45,000.
Bond prices are quoted as a percentage of par value (100%100\% = $1,000\$1,000 per bond).
2
Determine the annual dollar coupon interest received.
Annual Interest = $50,000×4.50%=$2,250\$50,000 \times 4.50\% = \$2,250.
The nominal coupon rate is always based on par value regardless of market price fluctuations.
3
Calculate the current yield by dividing annual coupon income by market price.
Current Yield = $2,250$45,000=0.05=5.00%\frac{\$2,250}{\$45,000} = 0.05 = 5.00\%.
Current yield measures annual interest income relative to the bond's current secondary market price.

Key Concept

Current Yield Calculation and Bond Price/Yield Dynamics
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Topics

Debt Securities and Bond Structure

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