Question 1179443: A Php 100,000, 10% bond, pays a dividend every quarter for 8 years. The bond is priced at par and is redeemable at 110% of the par value. Find the yield to maturity.
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! To calculate the yield to maturity (YTM) of the bond, we can use the following formula:
```
YTM = (C + (FV - PV) / N) / ((FV + PV) / 2)
```
Where:
* C = Annual coupon payment
* FV = Face value of the bond
* PV = Present value of the bond
* N = Number of years to maturity
In this case:
* C = 100,000 * 10% = 10,000 Php (annual coupon payment)
* FV = 100,000 Php (face value)
* PV = 100,000 Php (priced at par)
* N = 8 years (number of years to maturity)
However, since the bond is redeemable at 110% of the par value, we need to adjust the FV accordingly:
* FV = 100,000 * 110% = 110,000 Php (redeemable value)
Now, we can plug these values into the YTM formula:
```
YTM = (10,000 + (110,000 - 100,000) / 8) / ((110,000 + 100,000) / 2)
```
```
YTM = (10,000 + 1,250) / 105,000
```
```
YTM = 11,250 / 105,000
```
```
YTM ≈ 0.1071 or 10.71%
```
Therefore, the yield to maturity of the bond is approximately **10.71%**.
Note that this is just an approximate YTM, as it doesn't take into account the quarterly coupon payments. To get a more precise YTM, you would need to use a financial calculator or spreadsheet software that can handle the time value of money calculations with quarterly compounding.
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