Question

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

- 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.
- What is the market price of the bond at beginning of year 1? And year 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%

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