The purchace price would be ₹875.4, if the maturity period is 20 years.
Present Value of Dividends:
a. We need to know the maturity period of the bond to calculate the total number of dividends. Let's assume it's 20 years for this example.
b. Using the present value formula for an annuity:
PV = PMT * (1 - (1 + r)⁻ⁿ) / r
where:
- PV = Present Value
- PMT = Annual Payment (₹40)
- r = Discount Rate (Desired yield rate, 5%)
- n = Number of periods (20 years)
PV of dividends = ₹40 * (1 - (1 + 0.05)⁻²⁰) / 0.05
PV of dividends = ₹498.5
Present Value of Redemption Value:
a. Using the present value formula for a single sum:
PV = FV / (1 + r)ⁿ
where:
FV = Future Value (₹1000)
r = Discount Rate (5%)
n = Number of periods (20 years)
b. PV of redemption value = ₹1000 / (1 + 0.05)²⁰
c. PV of redemption value ≈ ₹376.9
Combining Present Values:
a. Purchase Price = PV of dividends + PV of redemption value
b. Purchase Price ≈₹498.5 + ₹376.9
c. Purchase Price ≈ ₹875.4
Therefore, the purchase price of the bond is approximately ₹875.4