Question 1184249: A certain bond pays coupons of Php 5,000 every six months for:
Given:
Semi-annual coupons = 1,000
Face value = 120,000
Time to maturity = 8 years
Market rate = 6%
The bondholder receives 16 payments of Php 5,000 each, and Php 120,000 at t = 8
Find:
Bond price =
Present value of Interest Payment =
Number of periods =
Present Value of Lumpsum =
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! There seems to be a discrepancy in the given information. You state that the bond pays coupons of Php 5,000 every six months, but then give "Semi-annual coupons = 1,000". I will assume the semi-annual coupon payment is Php 5,000, as this aligns with the total payments received. The Php 1,000 figure will be disregarded.
Here's the corrected calculation:
**1. Number of Periods (n):**
* Time to maturity = 8 years
* Semi-annual payments: 8 years * 2 periods/year = 16 periods
**2. Semi-Annual Coupon Payment (C):**
* C = Php 5,000
**3. Semi-Annual Market Rate (r):**
* Annual market rate = 6%
* Semi-annual market rate = 6% / 2 = 3% or 0.03
**4. Present Value of Interest Payments (PV of Annuity):**
PV of Interest = C * [1 - (1 + r)^-n] / r
PV of Interest = 5000 * [1 - (1 + 0.03)^-16] / 0.03
PV of Interest = 5000 * [1 - (1.03)^-16] / 0.03
PV of Interest = 5000 * [1 - 0.623167] / 0.03
PV of Interest = 5000 * [0.376833] / 0.03
PV of Interest = 5000 * 12.5611
PV of Interest ≈ Php 62,805.50
**5. Present Value of Lump Sum (PV of Face Value):**
PV of Lump Sum = FV / (1 + r)^n
PV of Lump Sum = 120,000 / (1.03)^16
PV of Lump Sum = 120,000 / 1.604701
PV of Lump Sum ≈ Php 74,772.10
**6. Bond Price:**
Bond Price = PV of Interest + PV of Lump Sum
Bond Price = 62,805.50 + 74,772.10
Bond Price ≈ Php 137,577.60
**Summary:**
* **Bond Price:** Approximately Php 137,577.60
* **Present Value of Interest Payments:** Approximately Php 62,805.50
* **Number of Periods:** 16
* **Present Value of Lump Sum:** Approximately Php 74,772.10
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