On September 1, 2021, Blue Co., issued $1,600,000 of its 10% bonds at 98 plus accrued interest. The bonds are dated June 1, 2021 and have an effective interest rate of 11%. Interest is payable semiannually on June 1 and December 1. At the time of issuance, Blue would receive cash of:

$1,536,768 (look at explanation)

Explanation:

the question is missing the options which would help to determine the clean price using accrued interests and the YTM formula, or it is missing the years to maturity. Since I cannot guess any options (they are infinite), but I can use a 10 year to maturity period to solve it as an example:

in order to determine the clean market price of the bonds we can use the approximate yield to maturity formula (for 1,600 bonds of $1,000):

0.055 = {50 + [(1,000 - MV)/20]} / [(1,000 + MV)/2]

0.055 x [(1,000 + MV)/2] = 50 + [(1,000 - MV)/20]

0.055 x (500 + 0.5MV) = 50 + 50 - 0.05MV

27.5 + 0.0275MV = 100 - 0.05MV

0.0775MV = 72.50

MV = 72.50 / 0.0775 = $935.48

since the bonds yield a higher rate than coupon rate, they were sold at a discount at approximately $935.48 each

accrued interest per bond = $1,000 x 10% x 3/12 = $25

dirty price per bond = $935.48 + $25 = $960.48

total cash received = $960.48 x 1,600 = $1,536,768

Blue would receive cash of $1,608,000.

Explanation:

The amount of cash Blue would receive is the addition of the of price of the bonds and interest from June 1, i.e. the bond date, to September 1, i.e. the issue date.

These can be calculated as follows:

Price of the bonds = $1,600,000 * 98% = $1,568,000

Interest = $1,600,000 * 10% * (3 months / 12 months) = $1,600,000 * 10% * 0.25 - $40,000

Amount received by Blue = Price of the bonds * Interest = $1,568,000 + $40,000 = $1,608,000

Therefore, Blue would receive cash of $1,608,000.

Note that the question reads Interest is payable semiannually on June 1 and December 1. This implies that the accrued interest is not payable yet on th September 1 but it will be paid on December. This is why the accrued interest is added to the cash received by Blue in order to hold it till December 1 when it will be paid.