Problem 4 - Bonds You recently inherited from your late uncle a US government bo

Question

Problem 4 - Bonds
You recently inherited from your late uncle a US government bond that matures December 31, 2025. The bond has a face value of 20,000 USD, which is equal to its redemption value. It pays an annual interest of 8%, payable semi-annually (i.e. as 4%) on June 30 and December 31 of each year. Answer the following question by performing your calculations both analytically and by using the relevant Excel functions.
a) If you wish to earn a 5% semi-annual return on your bond investment, what is the value of this bond to you on July 1, 2016?

b) If the bond trades for 17,988 USD in the market on July 1, 2016, would you sell it? Shortly explain why.

c) In reference to part (b) above, if there was a 3% transaction fee you have to pay to the tradinghouse, would you sell it, or buy more of the bond?

d) If bond yield rates (per semi-annum) in the market are currently around 4.78%, what market price does this predict for your bond on July 1, 2016?

e) If the bond trades for 17,988 USD in the market on July 1, 2016, what is the implied bond-yield rate?

Explanation / Answer

a.

To calculate the present value:

With the help of excel function calculate the present value.

PV (rate, nper, pmt, fv)

PV = (5%, 19, 800, 20000) = ($17,582.94)

Thus, the value of bond is $17,582.94

b.

If the bond trades for $17,988 then the bonds can be sold. The reason behind is the value of the bond is $17,582.9. This implies that the bonds are traded at premium.

c.

If the transaction fee of 3% is charged then the selling price would be

= $17,988 – ($17,988 × 3%) = $17,448.36

It is clear from the calculation that, the bond value is more than the traded value. Hence, the bond should not be sold off.

d.

If bond yield rate in the market are currently around 4.78% then the market value of the bond would be as under:

With the help of excel function calculate the present value.

PV (rate, nper, pmt, fv)

PV = (4.78%, 19, 800, 20000)

PV = ($18,080.43)

Therefore, if the bond yield rate is 4.78% then the market value of the bond would be $18,080.43.

e.

If the bond trades for 17,988 USD in the market on July 1, 2016, the implied bond-yield rate is:

Bond Yield rate = Coupon amount ÷ Market rate of bond

                        = $800 ÷ $17,988

           = 0.0447 or 4.45%

Therefore, the bond yield rate would be 4.45%.

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