Question 1181668: Determine the return for the buyer of a 7-year, 3% bond of PhP 500,000 face value if on the date it is issued it is purchased from its original owner for PhP 450,000.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the return for the buyer of the bond:
**1. Calculate the Annual Interest Payment:**
* Annual interest = Face value * Coupon rate
* Annual interest = PhP 500,000 * 0.03 = PhP 15,000
**2. Calculate the Total Interest Received Over the Bond's Life:**
* Total interest = Annual interest * Number of years
* Total interest = PhP 15,000 * 7 = PhP 105,000
**3. Calculate the Capital Gain:**
* Capital gain = Face value - Purchase price
* Capital gain = PhP 500,000 - PhP 450,000 = PhP 50,000
**4. Calculate the Total Return:**
* Total return = Total interest + Capital gain
* Total return = PhP 105,000 + PhP 50,000 = PhP 155,000
**5. Calculate the Return on Investment (ROI) or Yield to Maturity (YTM):**
There are two ways to express the return:
* **Total ROI:** (Total return / Purchase price) * 100
* Total ROI = (PhP 155,000 / PhP 450,000) * 100 ≈ 34.44% This is the total return over the 7-year life of the bond.
* **Annualized ROI (YTM):** This is more complex to calculate precisely and often requires iterative methods or financial calculators. It's the discount rate that equates the present value of all future cash flows (interest payments and face value) to the current purchase price. A rough estimate can be obtained by dividing the total return by the number of years:
* Annualized ROI ≈ (Total ROI) / Number of Years
* Annualized ROI ≈ 34.44% / 7 ≈ 4.92% This is a simplified YTM calculation.
**Therefore:**
* The total return the buyer receives over the 7-year life of the bond is PhP 155,000.
* The total return expressed as a percentage is approximately 34.44%.
* The annualized return (or approximate YTM) is approximately 4.92%. For a more precise YTM, a financial calculator or software is recommended.
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