Bonds, for a federal treasury bill, were issued with a face value of $250,000 and a...

Bonds, for a federal treasury bill, were issued with a face value of $250,000 and a coupon rate of 0.20% per quarter, and payments are quarterly. This bond is bought in the bond market before maturation, and there are only 16 payments remaining. The next payment is due after three months (one quarter), which you collect if you buy this bond now. How much are you ready to pay for this bond today if the next interest payment is due today? As an investor, you wish to earn 1.6% compounded daily.

Hints: Find quarterly effective interest rate for this investor.

Coupon rate can be used to calculate recurrent revenues from this bond which will be coupon rate x face value.

Solutions

Expert Solution

Face Value = $250,000

Coupon rate = .20% Quarterly and payments are made quarterly i.e. 250000*.20% = $500

There are 16 payment periods remaining before the bond matures if the bond is purchased a month before the next due interest payment.

It would imply that if the interest payment is due today, the remaining periods would be 15 as the price would be ex-interest.

The required rate of return of the investor = 1.6% compounded daily

The required rate of return should be converted into a quarterly rate in order to discount the future cash flows which

would in turn help in determine the current price of the bond.

Therefore, Required rate of return effective quarterly = ([1 + (1.6% / 90 days)]^90)-1 = 1.612%

Calculation of the price of the bond:

Discounted Coupon Payments = Coupon Interest * Present Value Annuity Factor of 1.612% for 15 periods

where,

Coupon interest is the quarterly interest amount

Therefore, Discounted Coupon Payments = $500 * 13.23 = $6615 (Approx.)

Face value of the bond that is to be paid on maturity will also be discounted to determine the current price.

Discounted face value of the bond = $250000 * ( 1/1.01612 )^15 = $196682 (Approx)

Current Price of the bond that an investor would be willing to pay requiring a return of 1.6% compounded daily

will be summation of discounted coupon payments for the remaining period and discounted face value of

the bond to be paid on maturity i.e. 6615+ 196682 = $203297

ekkarill92 answered 7 months ago

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