Question

plz show all calculations and don't use excel or financial calculator or table.

5. Suppose there are only 2 investment alternatives: a bank deposit that pays 4% per year and a 2-year coupon bond with 5% annual coupon rate and face value of $1,000. Assume the bank deposit and coupon bond are perfect substitutes.
   1. What is the market price of the bond at beginning of year 1? And year 2?
   2. Assume now that at the beginning of year 2, the deposit interest rate unexpectedly increases to 6% annual. What is the market price of the bond at the beginning of year 2? What is the yearly return on the bond in each year?

Answer 1

Working notes:

• Annual bond coupon interest = $1000 x 5% = $50
• Bond price = Present Value of future coupon payments + Present Value of face value
• Bond is assumed to mature at end of year 2.

(a)

Bond price at beginning of year 1 (at end of year 0) ($) = 50 x P/A(4%, 2) + 1000 x P/F(4%, 2)

= 50 x 1.8861 + 1000 x 0.9246

= 94.31 + 924.6

= 1018.91

Bond price at beginning of year 2 (at end of year 1) ($) = 50 x P/A(4%, 1) + 1000 x P/F(4%, 1)

= 50 x 0.9651 + 1000 x 0.9651

= 48.26 + 965.1

= 1013.36

(b)

Bond price at beginning of year 2 (at end of year 1) ($) = 50 x P/A(6%, 1) + 1000 x P/F(6%, 1)

= 50 x 0.9434 + 1000 x 0.9434

= 47.17 + 943.4

= 990.57

Annual return in year 1 = ($990.57 / $1018.91) - 1 = 0.9722 - 1 = - 0.0278 = - 2.78%

Annual return in year 2 = ($1000 / $990.57) - 1 = 1.0095 - 1 = 0.0095 = 0.95%