Question

A $1,000 par value bond, has an annual coupon rate of 6 percent, an annual yield to maturity of 7.5 percent, and 10 years until maturity. Assuming semi-annual coupon payments:

d.         If the bond were selling for $929, what would the effective yield-to-maturity if you reinvest coupon payments at 9 percent?

***please show the work or what is entered in calculator***

Answer 1

For an investor who buys the bonds today, the cash flows are as below :

Time 0 = -$929 (price of bond)

0.6 years = $1000 * 6% / 2 = $30 (semiannual coupon payment = par value * coupon rate / 2)

1.0 years = $30

1.5 years = $30

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.

.

.

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and so on, until

10.0 years = $1030 (cash flow after 10 years = par value + semiannual coupon payment)

Now, we enter these cash flows into Excel, and use the MIRR function to calculate the effective YTM

values = array of cells containing the cash flows

finance rate = semiannual YTM = 7.5% / 2 = 3.75%

reinvest rate = reinvestment rate of coupons (semiannual) = 9%/2 = 4.5%

MIRR is calculated to be 3.75%. This is the effective semiannual YTM. To compute the effective annual YTM, we multiply this by 2. Effective annual YTM = 7.51%