Question

A newly issued U.S. Federal? T-Note matures in exactly 9 years. The coupon rate is 3.5?% per year and coupons are paid semiannually. The bond is priced at 104.26 ?(per $100 of face? value) and yields 2.96?%. The economy is slowing and many forecasters predict a recession. You expect that the monetary authorities will relax monetary policy which will cause interest rates to fall. You expect the yield on the 9?-year bond to fall to 2.46?%. The bond has a face value of? $1M. If you want to earn? $1M by investing in bonds to profit from the interest rate? change, how many bonds do you? buy???

In order to earn? $1M by investing in? bonds, you need to buy ____ bonds?(Round up to the nearest whole? number.)

Answer 1

Answer:

Face value of T-Note = $100

Coupon rate is 3.5% per year and coupons are paid semiannually

Term = 9 years = 18 periods (of half year)

Semi-annual rate = 3.5% / 2 = 1.75%

Semi-annual coupon amount = $100 * 1.75% = $1.75

The bond is priced at $104.26

The yield is expected to fall to 2.46%

Semi-annual yield = 2.46% /2 = 1.23%

We need to find the price when the yield = 2.46%

Present Value Interest Factors for a One-Dollar Annuity Discounted at 1.23% Percent for 18 Periods = 16.05861

Present Value Interest Factors for One Dollar Discounted at 1.23% Percent for 18 Periods = 0.802479

Present value of T Note =16.05861 * $1.75 + 0.802479 * $ 100 = $108.350477

Profit per note of $100 = $108.350477- $104.26 = $4.090477

In order to $1 million in profit number of bonds required to be bought = $1,000,000 / $4.09 = 244,470