# Help

### How the Fair Value of a Sovereign Gold Bond is calculated?

To find the most valuable Sovereign Gold Bond in the secondary market, you need to calculate the fair value of each bond. Since the future gold price at maturity is unknown, the fair value provides a means for relative comparison across different Sovereign Gold Bonds.

#### Calculating Fair Value

The fair value calculation assumes a constant gold price for the entire duration, allowing for a relative comparison regardless of the actual gold price used. Sovereign Gold Bonds provide two types of income:

- Periodic interest income on the face/nominal value
- Value equal to the gold price difference between the purchase and maturity dates

The interest income is fixed for a given bond and does not fluctuate with gold price changes. For example, a 2.5% interest on an INR 6000 face value would yield INR 150 in two equal installments per year until maturity.

To account for the time value of money, the present value of all future interest cash flows is calculated using a formula like the PV function in Microsoft Excel. This ensures a fair comparison across bonds with different maturities.

The accrued interest, which is the interest earned but not yet paid, must be subtracted from the fair value calculation. The seller adds the accrued interest to the price, and the buyer effectively pays this interest when purchasing the bond.

#### Fair Value Formula

The fair value of a Sovereign Gold Bond is calculated as follows:

**Fair Value = Current Gold Spot Price + Present Value of all future interest cash flows - Accrued Interest**

The fair value represents the guaranteed value of a Sovereign Gold Bond if the gold price remains constant. It allows for a relative comparison of value across different Sovereign Gold Bonds to identify the most valuable option in the secondary market.

#### Discount to Fair Value

The discount to fair value is a measure of the value of the SGB relative to the current market price. It is calculated by dividing the current market price of the SGB by the fair value. A higher discount to fair value indicates a higher value for the SGB relative to the current market price.

### What is Effective Interest Rate and Effective Cash Flow Rate?

Effective Interest Rate and Effective Cash Flow Rate are important metrics used in evaluating the performance and returns of a Sovereign Gold Bond (SGB).

#### 1. Effective Interest Rate

The effective interest rate represents the actual rate of return an investor can expect to earn on their SGB investment, taking into account the current market price of the bond. It is different from the stated or coupon interest rate, which is based on the bond's face value at the time of issuance.

The effective interest rate is calculated by dividing the annual interest payment by the current market price of the SGB. It provides a more accurate representation of the bond's yield, as it considers the premium or discount at which the bond is trading relative to its face value.

For example, if an SGB with a face value of ₹4,000 and a coupon rate of 2.5% is currently trading at ₹4,200, the effective interest rate would be lower than the stated 2.5% because the investor is paying a premium over the face value.

#### 2. Effective Cash Flow Rate

The effective cash flow rate is a measure of the actual cash flow an investor can expect to receive from their SGB investment, expressed as a percentage of the current market price. It is calculated by dividing the effective interest payment (interest adjusted for any premium or discount) by the current market price of the SGB.

Example:

```
ibjaPrice = 4400
faceValue = 4000
currentValue = 4200
interestRate = 2.5
pendingInterestYears = 2
premium = currentValue - ibjaPrice ==> -200
interestPerYear = faceValue * (interestRate / 100) ==> 100
totalPendingInterest = interestPerYear * pendingInterestYears ==> 200
effectivePendingInterest = totalPendingInterest - premium ==> 400
effectiveInterestPerYear = effectivePendingInterest / pendingInterestYears ==> 200
effectiveInterestRate = (interestPerYear / currentValue) * 100 ==> 2.38%
effectiveCashFlow = (effectiveInterestPerYear / currentValue) * 100 ==> 4.76%
```

Both the effective interest rate and the effective cash flow rate are important metrics for investors to evaluate the potential returns and risks associated with an SGB investment. They help investors make informed decisions by providing a more accurate representation of the bond's performance based on current market conditions.