Question

Assume a $1,000 face value bond has a coupon rate of 7.6 percent paid semiannually and has an eight-year life.

What is the value of the bond if investors wanted an 7.1-percent rate of return? (Round factor value calculations to 5 decimal places, e.g. 0.52755. Round other intermediate calculations to 2 decimal places, e.g. 52.75. Round final answer to nearest dollar amount.)

Answer 1

Here value of bond means present value of all cash flow from the bond.

Value of bond = present value of interest payments and maturity value.

Here interest payments are semi annually and recurring in nature. so, here we use present value of annuity concept used.

And maturity payment is one time activity so we use present value concept used.

Value of bond = semi annually coupon payment * PVIFA ( 7.1%/2 , 8*2) + maturity value * PVF (7.1%/2,8*2)

= 38 *{ [ 1 - (1 +0.0355)^-16] / 0.0355 } + 1000 * 1/(1 + 0.0355)^​​16

Value of bond = $ 38 *12.04883 + 1000 * 0.57227

= 457.86 + 572.27

Value of bond = $ 1030.13

Value of bond =$ 1030

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