Question

3. Suppose you buy a 3-year treasury note for $1,000 with a coupon rate of 2%. (a) If the risk-free rate remains at 2% for all treasury securities, how much could you sell this bond for after (i) 1 year, (ii) 2 years, (iii) 3 years? (b) If after 2 years you decide to sell this bond, how much would it be worth if the prevailing interest rate is (i) 1.5%, (ii) 3%? (c) Suppose after 1 year the interest rate rises to 3% and is expected to stay that way for several years. Someone offers to trade your bond for a $1,000 two-year bond that pays 3% after 1 year and 1% plus the principle after the second year. Would you take this trade? What if it paid 1% after 1 year and 3% plus the principle after the second year? Hint: Federal notes pay a simple interest rate structure, but you can always compound your earnings by buying another bond!

Answer 1

3. a)

If the risk free rate remains constant at 2% for all treasury securities, you would be able to sell the bond at $1000 1) after 1 year 2) after 2 year and 3) at $0 after 3 year as the maturity if the bond is 3 year. (Here discounting factor and coupon rate is equal)

b)

i) At 1.5% interest rate after 2 year:

Future Cash Flow and their timings:

Year	Cash Flow	Discounted Present Value @1.5%
1	1000	985.2216749
1	20	19.7044335
	Total	1004.926108

Hence, you would be able to sell the bond at $1004.92

ii)

Year	Cash Flow	Discounted Present Value @3%
1	1000	970.8737864
1	20	19.41747573
	Total	990.2912621

Hence, you would be able to sell the bond at $990.29

c) Below are the expected payoff of treasury after 1 year:

Year	Cash Flow	Discounted Present Value @3%
1	20	19.41747573
2	20	18.85191818
2	1000	942.5959091
	Total	980.865303

Hence, actual value of bond is 980.86 after year 1 @3%

For the offered bond:

Year	Cash Flow	Discounted Present Value @3%
1	30	29.12621359
2	10	9.425959091
2	1000	942.5959091
	Total	981.1480818

As the offered bond is more valuable, you should take the offer.

For the second scenario:

Year	Cash Flow	Discounted Present Value @3%
1	10	9.708737864
2	30	9.425959091
2	1000	942.5959091
	Total	961.7306061

Here, the bond is less valuable than the bond your are holding. Hence, you should not take the offer.