Calculating the Flat Price, Accrued Interest, and the Full Price

Assume you are a portfolio manager who was shut out of a new bond offering in which the issuer was a popular wearable fitness device company. You would still like to buy the bond in the secondary market, but you decide to wait because you are forecasting that market interest rates will increase over the next few months and would like to buy the bond at a discount. Six months later, you buy a bond with an 8% annual coupon that matures in four and a half years. The bond's yield to maturity is 9.5%. The bond's accrued interest is calculated on a 30/360 day count. What is the full price you will pay for the $100 par bond?

Great Job! $$\displaystyle {98.62 \approx \left[ \frac{8}{(1+0.095)^{1}} + \frac{8}{(1+0.095)^{2}} +...+ \frac{108}{(1+0.095)^{5}} \right] \times (1+0.095)^\frac{180}{360}}$$ The first part of the formula can be solved with your financial calculator as follows: [[calc: 5 n 9.5 iy 8 pmt 100 fv cpt pv , 5 n 9.5 i 8 pmt 100 fv pv]]

You will end up paying $98.62 for the bond, which includes the accrued interest that is owed to the seller of the bond. What is the dollar amount of accrued interest owed to the seller?

Incorrect. There are five coupon payments remaining.

Incorrect. Accrued interest does not take into account the time value of money.

It is important to note that the accrued interest calculation does not take into account the time value of money. In theory, accrued interest should be discounted to the present value, but in actual bond trading, time value of money of accrued interest is ignored due to accounting and financial reporting purposes. What would be the quoted price of the bond?

Incorrect. Accrued interest must be calculated separately from the full price formula.

Incorrect. The PV of cash flows does not take into consideration the impact of accrued interest.

Correct. The flat price is the quoted price in the market. It is calculated by subtracting the accrued interest from the full price.

Incorrect. The flat or clean price is the quoted price. Bonds trade at the full or dirty price.

In summary: [[summary]]

The full price of a bond that is being purchased includes the accrued interest that must be paid on the settlement date. $$\displaystyle PV_{\text{Full Price}} = PV_{\text{Flat Price}} + \text{Accrued Interest} $$ You can use the following formula to calculate the full price of a bond: Full Price = $$\displaystyle \left[ \frac{PMT}{(1+r)^{1}} + \frac{PMT}{(1+r)^{2}} +...+ \frac{PMT + PAR}{(1+r)^{n}} \right] \times (1+r)^{\frac{\text{days since last payment}}{\text{days in period}}} $$ The first part of the formula is simply the formula to discount cash flows and can easily be solved by using your financial calculator.

Correct. The accrued interest represents half a year’s worth of the coupon payment on a 30/360 day count. $$\displaystyle \$ 4 = \$ 8 \times \frac{180}{360} $$

No. That's the price of the bond without accrued interest.

$94.24

$98.62

$99.61

$3.82

$4.00

$4.64

$94.24

$94.62

$98.62

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