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On March 31st, 2020, you take delivery of a $100,000 T-bond that matures on October 31st,...

On March 31st, 2020, you take delivery of a $100,000 T-bond that matures on October 31st, 2030. The coupon rate on the T-bond is 4.20% and the current yield to maturity on the bond is 3.80%. The last coupon payment occurred on October 31st, 2019 and the next coupon payment occurs on April 30th, 2020. Calculate the clean and dirty prices of this transaction.

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Expert Solution

In the given question following information is given:

  1. T-bond amount is $100,000
  2. Coupon rate on T-bond is 4.20% paid semi-annually
  3. Current yield to maturity on bond is 3.80%
  4. Date of maturity is October 31st, 2030

Now let us first understand the meaning of clean and dirty prices. Dirty price of the transaction is the present value of all future cash flows including accrued interest in the near future and clean price of the transaction is the present value of all future cash flows that does not include any accrued interest in the near future. Accrued interest is the interest outstanding to be received from the bond at the coupon rate.

Now, the present values of future cash flows would be calculated using semi-annual yield to maturity rate i.e. 1.90% for 21 semiannual periods from April 30th, 2020 to October 31st, 2030 with semiannual interest of $2,100 calculated as below:

Semiannual interest = Interest * 6/12

Semiannual interest = ($100,000 * 4.20%) * 6/12

Semiannual interest = $4,200 * 6/12

Semiannual interest = $2,100

Statement showing Present Value of Bond

Semi annualy period Particulars Amount (A) Discounted Factor @ 1.90% (B)

Present Value (A * B)
1 Semi annual interest              2,100 0.9814               2,061
2 to 21 Semi annual interest              2,100 16.2025             34,025
21 Maturity amout of Bond          100,000 0.6735             67,350
Total Present Value of Bond          103,436

Hence,

Clean price of the bond will be the present value of bond i.e. $103,436

Dirty price of the bond = Present value of bond + Interest accrued for one month

Dirty price of the bond = $103,436 + ($100,000 * 4.20% * 1/12)

Dirty price of the bond = $103,436 + $350

Dirty price of the bond = $103,786

jeff jeffy answered 3 months ago
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