Question

I do not understand how to go about trying to calculate this, if someone could help?

Exercise 5.2.3 - Price Sensitivity of Bonds (2) An, a student majoring in corporate finance, invested part of her wealth in stocks in order to be able to pay her studies and also because all her friends were doing the same. An got fed up with investing into stocks and decided to put her money into government bonds. She bought a government bond with a coupon rate of 6% and a face value equal to €1,000. The coupons on this bond are paid annually and the remaining time to maturity of the bond is equal to 10 years. At the time she bought the bond the yield to maturity was equal to 8%. As yields on other short-term bonds were then around 5%, An thought buying the 10-year bond was really a smart choice. Her reasoning was: what risk is there in buying government bonds anyway? Exactly one year later, An needs her savings to pay for her tuition. The government has not gone bankrupt, but unfortunately her bond's yield to maturity has increased to 10%. When An enters the local bank to ask them to sell the bond before maturity (remember the bond has still a remaining time to maturity of 9 years!!), a large part of her savings is gone! An needs the money back before the bond's maturity and thus needs to sell the bond before maturity. Calculate the capital loss she must realize on her savings.

Answer 1

Part 1:

Face Value of government bond (FV) = Euro 1,000

Coupon rate annual (PMT) = 6% = 1,000 x 6% = 60

Time to maturity (N) = 10 years

Yield to maturity (I/Y) = 8%

Using financial calculator, we get Present Value (PV) = Euro 865.79

Hence, based on above calculation, we can see that the bond is trading at discount. This is mainly because the yield to maturity on government bond is greater than the coupon rate. On the other hand, if she had bought short term bond with yield to maturity of 5% paying annual coupon of 6%, the bond would have been trading at a premium, as shown below:

Face Value of government bond (FV) = Euro 1,000

Coupon rate annual (PMT) = 6% = 1,000 x 6% = 60

Time to maturity (N) assumed to be assumed to be 5 years

Yield to maturity (I/Y) = 5%

Using financial calculator, we get Present Value (PV) = Euro 1,043.29

Hence, based on above, we can see that a bond with yield to maturity less than coupon rate, trades at premium.

Although government bonds are virtually free from any credit risk, still they suffer from opportunity risks i.e. there is a risk that you could have earned better money elsewhere. The risks lie in three areas: inflation, interest rate risk, and opportunity costs.

Interest Rate Risk : When interest rates rise, the market value of debt securities tends to drop. This makes it difficult for the bond investor to sell a T-bond without losing on the investment.

Opportunity Costs : All financial decisions, even government bond investments, carry opportunity costs i.e. investor could earn better returns elsewhere.

Inflation : Every economy experiences inflation from time to time, to some extent.government bonds have a low yield, or return on investment. A little bit of inflation can erase that return, and a little more can effectively wipe out the savings.

Hence, An's reasoning that government bonds are riskless is not correct.

Part 2:

After 1 year:

Face Value of government bond (FV) = Euro 1,000

Coupon rate annual (PMT) = 6% = 1,000 x 6% = 60

Time to maturity (N) = 9 years

Yield to maturity (I/Y) = 10%

Using financial calculator, we get Present Value (PV) = Euro 769.64

Based on above calculation, the bond is trading at Euro 769.64 at the end of first year. If An sells the bond now, assuming she bought the bond at Euro 1,000, her capital loss shall be as follow:

Capital Loss = Purchase Price - Current trading price of bond = 1,000 - 769.64 = Euro 230.36

Hence, she would lose Euro 230.36, if she sold the bond today i.e. at end of first year.