Question

A 5 year government treasury bond is bought at $P a. Explain under what circumstances the purchase price be i. above face value ii. below face value iii. same as face value b. If the buyer wants to sell it after 2 years, will the buyer make a positive rate of return or negative rate of return? Explain. C. Assume that the bond pays 10% coupon rate, bought at $900, face value is $1000, and fetches a price of $850 next year, what is the rate of return?

Answer 1

a)

A Treasury bond may be trading at different prices at different times. These are issued by federal government.

(i) above face value - Premium

The bonds will be trading at Premium when they offer interest rate higher than the market rate prevailing in the economy.

(ii) below face value - Discount

The bonds will be trading at discount when they offer interest rate lower than the prevailing market interest rate

(iii) same as face value - at par

The bonds will be trading at face value when the interest rate offered by them and the market is same.

Note : The interest in rate is themainy factor in deciding the trading price of treasury bonds. There are also other factors like risk component, which we ignored here.

b)

If the buyer wants to sell after two years, he will generally have a positive rate of return as he receives the interest on such bonds during these two years.

Return = Interest during two hearsy + Difference between purchase price and selling price

(Time value of money ignored in this equation, for simple understanding)

The only case where he generates negative return is when the Purchase price of such bond is higher than the Sale price of bond by an amount more tham the interest receieved from such bond during 2 years

c)

Coupon rate - 10%, Time held - 1 year, Purchase price - 900, Sale price - 850, face value - 1000

Rate of return = [(coupon + sale value)/purchase value ] - 1

= [(10% x 1000 + 850)/900] - 1

= [1.05556] - 1

= 0.05556 or 5.56%

Note : Rate of Return is found ignoring time value of money (it we want to consider time value of money, we must know whether coupons are paid semi annually or annually)