Karla M. Avilés

Yasmín Morales

Ibsen Granda

Prof. Juan J. Fret – FINA 503

Universidad Metropolitana

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Concepts, Formulas and

Applications

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1. Bonds

A bond is a long-term contract under which a borrower agrees to make payments of interest and principal, on specific dates, to the holders of the bond.

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1. Bond Value

Fundamental principle of bond valuation is that the bond's value is equal to the present value of its expected (future) cash flows.

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1. Bond Value – Price and

Yield

Bonds can be priced at: Par,

Premium, Discount

Par: It is the face value of a bond when first issued

Premium: Investors pay a premium for a bond if the investment will return an amount greater than existing interest rates.

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1. Bond Value – Price and

Yield

Bonds can be priced at:

Discount: the condition of the price of a bond that is lower than par and equals the difference between the price paid for a security and the security's par value.

For example, if a bond with a par value of

$1,000 is currently selling for $990 dollars, it is selling at a discount.

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1.1 Definition of Yield

Yield is the income return on an investment. This refers to the interest or dividend received from a security and is usually expressed annually as a percentage based on the investment's cost, its current market value or its face value

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1.2 Types of Yields

1.

2.

The coupon rate (also nominal rate) is the yearly total of coupons

(or interest) paid divided by the

Principal (Face) Value of the bond.

The current yield are those same payments divided by the bond's spot market price.

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1.2 Types of Yields

3.

4.

The yield to maturity is the IRR on the bond's cash flows: the purchase price, the coupons received and the principal at maturity.

The yield to call is the IRR on the bond's cash flows, assuming it is called at the first opportunity, instead of being held till maturity.

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1.3 Calculating the Bond

Value

Sum of the present values of all expected coupon payments plus the present value of the par value at maturity. Discounting the known future cash flows. Present value (PV) is based on the assumption that each payment is re-invested at some interest rate once it is received.

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1.3 Calculating the Bond

Value

For bond pricing, this interest rate is the required yield.

Here is the formula for calculating a bond's price, which uses the basic present value (PV) formula:

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1.4 Present Value (PV)

Amount to be invested today to generate a future cash flow.

PV dependents on the timing of the cash flow and the interest rate

(discount rate)

PV of ordinary annuity formula is mathematically equivalent to the summation of all the PVs of future cash flows 12

1.4 Present Value (PV)

The following diagram illustrates how present value is calculated for an ordinary annuity

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1.4 Present Value (PV)

Each full moneybag on the top right represents the fixed coupon payments

(future value) received in periods one, two and three.

Notice how the present value decreases for those coupon payments that are further into the future.

The farther into the future a payment is to be received, the less it is worth.

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1.4 Present Value (PV)

Sum of the cash flow equals the present value of the annuity formula

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1.4 Present Value (PV)

By incorporating the annuity model into the bond pricing formula (including the present value of the par value received at maturity), we arrive at the following formula: 16

1.5 Example: Value of a

Bond

Calculate the price of a bond with a par value of $1,000 to be paid in ten years, a coupon rate of 10%, and a required yield of 12%. We'll assume that coupon payments are made semi-annually to bond holders and that the next coupon payment is expected in six months. Here are the steps we have to take to calculate the price

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1.5 Example: Value of a

Bond

Here are the steps we have to take to calculate the price:

1.Determine the Number of Coupon

Payments: Because two coupon…