Lecture Notes 6d PDF

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These lecture notes were written for the FINU 421 course taught by Professor Aaron Schmerbeck....

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Coupon Bonds •

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Yield to Maturity of a Coupon Bond: –

Coupon bonds have many cash flows, complicating the yield to maturity calculation

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The coupon payments are an annuity, so the yield to maturity is the interest rate y

Yield to Maturity of a Coupon Bond: –

Coupon bonds have many cash flows, complicating the yield to maturity calculation

–

The coupon payments are an annuity, so the yield to maturity is the interest rate y that solves the following equation:

Computing the Yield to Maturity of a Coupon Bond Problem: •

Consider the five-year, $1000 bond with a 2.2% coupon rate and semiannual coupons.

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If this bond is currently trading for a price of $963.11, what is the bond’s yield to maturity?

Solution: Plan: •

From the cash flow timeline, we can see that the bond consists of an annuity of 10 payments of $11, paid every 6 months, and one lump-sum payment of $1000 in 5 years (ten 6-month periods).

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We can use Eq. 6.3 to solve for the yield to maturity.

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However, we must use 6-month intervals consistently throughout the equation.

Execute: • •

Because the bond has ten remaining coupon payments, we compute its yield y by solving Eq. (6.3) for this bond We can solve it by trial-and-error, financial calculator, or a spreadsheet. To use a financial calculator, we enter the price we pay as a negative number for the PV (it is a cash outflow), the coupon payments as the PMT, and the bond’s par value as its FV. Finally, we enter the number of coupon payments remaining (10) as N.

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Therefore, y = 1.50%.

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Because the bond pays coupons semiannually, this yield is for a six-month period.

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We convert it to an APR by multiplying by the number of coupon payments per year.

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Thus, the bond has a yield to maturity equal to a 3.0% APR with semiannual compounding.

Evaluate:

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As the equation shows, the yield to maturity is the discount rate that equates the present value of the bond’s cash flows with its price.

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Note that the YTM is higher than the coupon rate and the price is lower than the par value. We will discuss why

Problem: •

Consider again the five-year, $1000 bond with a 2.2% coupon rate and semiannual coupons in Example 6.4. Suppose interest rates drop and the bond’s yield to maturity decreases to 2% (expressed as an APR with semiannual compounding). What price is the bond trading for now? And what is the effective annual yield on this bond?

Solution: Plan: •

Given the yield, we can compute the price using Eq.6.3. First, note that a 2.0% APR is equivalent to a semiannual rate of 1.0%. Also, recall that the cash flows of this bond are an annuity of 10 payments of $11, paid every 6 months, and one lump-sum cash flow of $1000 (the face value), paid in 5 years (ten 6-month periods). In Chapter 5 we learned how to compute an effective annual rate from an APR using Eq. 5.3. We do the same here to compute the effective annual yield from the bond’s yield to maturity expressed as an APR.

Execute: •

Using Eq. 6.3 and the 6-month yield of 1.0%, the bond price must be

Evaluate: •

The bond’s price has risen to $1009.47, lowering the return from investing in it from 1.5% to 1.0% per 6-month period. Interest rates have dropped, so the lower return brings the bond’s yield into line with the lower competitive rates being offered for similar risk and maturity elsewhere in the market.

Problem: •

Consider the nine-year, $1000 note with a 3% coupon rate and semiannual coupons described in Example 6.3a.

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If this bond is currently trading for a price of $1,038.32, what is the bond’s yield to maturity?

Solution: Plan: •

We worked out the bond’s cash flows in Example 6.3a.

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From the cash flow timeline, we can see that the bond consists of an annuity of 18 payments of $15, paid every 6 months, and one lump-sum payment of $1000 in 9 years (eighteen 6-month periods).

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We can use Eq. 6.3a to solve for the yield to maturity.

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However, we must use 6-month intervals consistently throughout the equation.

Execute: •

Because the bond has eighteen remaining coupon payments, we compute its yield y by solving Eq. (6.3) for this bond

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Therefore, y = 1.26%.

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Because the bond pays coupons semiannually, this yield is for a six-month period.

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We convert it to an APR by multiplying by the number of coupon payments per year.

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Thus, the bond has a yield to maturity equal to a 2.52% APR with semiannual compounding.

Evaluate: •

As the equation shows, the yield to maturity is the discount rate that equates the present value of the bond’s cash flows with its price....