Question

Suppose that the term structure is currently flat so that bonds of all maturities have yields to maturity of 10%. Currently a 5-year coupon bond with annual coupons (with the first one due in 1 year) and face value of S1,000 is selling at par (a) What is the current price of the 5-year bond? What are the annual coupons in dollar terms? (b) A year from now interest rates will depend on the stance of monetary policy. If monetary policy is "tight" the yields to maturity on all bonds will be 12%. If monetary policy is "loose" the yields to maturity on all bonds will be 8%. If you sell the bond a year from now when monetary policy is tight what will be the return to your investment over the year? If you sell the bond a year from now when monetary policy is loose what will be the return to your investment over the year?

Answer 1

Step-by-step explanation:

a) PV=$1000

As price is equal to face value then the Coupon rate will be equal to its YTM, 10%.

Annual Coupons = 10% * 1000 = $100

b.) We have purchased the bond for $1000, so our investment is $1000

At the end of the year 1, we get a coupon of $100 and the selling price.

1st CASE - When monetary policy is tight.

New YTM = 12%

Time left to maturity (n) = 4 years

Coupon payment = $100

Price = Coupon payment X PVAF(YTM, n) + Face Value X PVF(YTM, n)

[USE TABLES or Financial calculator]

Price = 100 X PVAF(12%, 4) + 1000 X PVF(12%, 4) = 100 X 3.307 + 1000 X .636 = 303.7 + 636 = $939.7

If we sell the bond, Return = (Coupon Received + Selling price - Purchase price ) \div Purchase price

= (100 + 939.7 - 1000) \div 1000 = .0397 or 3.97%

Scenario 2 - When monetory policy is loose

New YTM = 8%

Time left to maturity (n) = 4 years

Coupon payment = $100

Therefore, Price = Coupon payment X PVAF(YTM, n) + Face Value X PVF(YTM, n)

Price = 100 X PVAF(8%, 4) + 1000 X PVF(8%, 4) = 100 X 3.312 + 1000 X .735 = 331.2 + 735 = $1066.2

If we sell the bond, Return = (Coupon Received + Selling price - Purchase price ) \div Purchase price

= (100 + 1066.2 - 1000) \div 1000 = .1662 or 16.62%