Question

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. a) What is the market price of the bond at beginning of year 1? And year 2? b) 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

• Annual bond coupon = $1000 x 5% = $50
• Bond price = PV of future coupon + PV of face value
• It's assumed that the bond matures at end of year 2.

(a)

Bond price at beginning of year 1 (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 (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 (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

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

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