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Yield to Maturity The Approximation Approach

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**1. **Yield to Maturity The Approximation Approach Business 2039

**2. **Yield to Maturity – What is it? The yield to maturity is that discount rate that equates the current bond price with the discounted value of all future cash flows.
Usually you can observe the current market price of a bond (if it is publicly traded)…and since the coupon rate is a fixed percentage of the face value…and the face value is always $1,000, the only thing that we don’t know is the YTM.

**3. **The Bond Pricing Equation (Assuming payment of the coupon interest semi-annually)

**4. **The Bond Pricing Equation (Assuming payment of the coupon interest semi-annually)

**5. **Yield to Maturity – Ex ante YTM is an ex ante calculation – it is a forecast of the rate of return you might earn on a bond investment.
In order to make such a forecast – assumptions must be made.
To learn more about the assumption please check the other slide set on this website addressing the reinvestment rate assumption.

**6. **Yield to Maturity – methods of solution There are four different ways you can try to solve for the Yield to Maturity:
Iterative approach – keep substituting different discount rates until the sum of the present value of all future cash flows equals the bonds current price.
IRR function in MS Excel – there is a built-in financial function in all spreadsheet programs that will calculate the IRR for a series of cash flows – remember that the price should have a negative sign
Financial Calculator – financial calculators have built-in algorithms that will solve for the YTM – you just specify the current bond price, the future cash flows
The Approximation Formula – read on through this slide set to see how to use it.

**7. **The Approximation Formula F = Face Value = Par Value = $1,000
P = Bond Price
C = the semi annual coupon interest
N = number of semi-annual periods left to maturity

**8. **Example Find the yield-to-maturity of a 5 year 6% coupon bond that is currently priced at $850. (Always assume the coupon interest is paid semi-annually.)
Therefore there is coupon interest of $30 paid semi-annually
There are 10 semi-annual periods left until maturity

**9. **Example – with solution Find the yield-to-maturity of a 5 year 6% coupon bond that is currently priced at $850. (Always assume the coupon interest is paid semi-annually.)

**10. **The logic of the equation The numerator simply represents the average semi-annual returns on the investment…it is made up of two components:
The first component is the average capital gain (if it is a discount bond) or capital loss (if it is a premium priced bond) per semi-annual period.
The second component is the semi-annual coupon interest received.
The denominator represents the average price of the bond.
Therefore the formula is basically, average semi-annual return on average investment.
Of course, we annualize the semi-annual return so that we can compare this return to other returns on other investments for comparison purposes.