How to calculate the value of a $bDUET

Before we calculate the value of a bond, we need to understand the basics of a bond

1. Face Value(F): The principal amount owed by the bond issuer.

2. Epoch: The time interval between every payment, Duet defines an Epoch to be 1-month equivalent amount of blocks, depending on different block times of different blockchains. All pending payments of all bonds are claimable on the same block every month.

3. Coupon Rate(r): The Coupon interest rate is used to calculate interest payments each epoch, for example, a bond with face value of 100 Duet and a coupon rate of 10% per epoch will be paid 10%*100=10 Duet tokens each epoch as interest payments

4. Duration(n): The amount of epochs left to be paid

5. Discount Rate(R): Discount rate is derived using market price of a bond, duration of the bond and expected payments of the bond.

6. Net Present Value(NPV): The NPV is arrived by discounting all expected payments of a bond with respective discount rates, NPV is the fair value of a bond.

7. Current Price（P): P is the market price at which a bond is being traded at

8. Yield to Maturity(YTM): YTM is annualized return on principal of a bond

Now Consider a simplest bond, a bond with a face value of 100, coupon rate of 10% and duration of 1 epoch.

Coupon payments=F*r=100*10%=10 Duet

Principal Payment= F =100

The bond holder is expected to receive 110 Duets in 1 epoch time. On the date of issuance, coupon rate is always equal to discount rate, which is 10%.

NPV=Payment/(1+R)n=110/(1+10%)1=100 Duets

When a bond’s current price is equal to its face value, the bond is trading at par, when it is trading above the face value, it is trading at a premium and when it is trading at lower than the face value, it is trading at a discount.

Now consider after the issuance of the bond, discount rate drops to 5%, the value of the bond would be

NPV=Payment/(1+R)n=110/(1+5%)1=104.76 Duets

This example shows how the value of a bond can appreciate when its coupon rate is higher than the discount rate (which is typically coupon rate of a newly issued bond)

Now back to the more complicated bond that is mentioned in the overview, a bond with face value of 100 Duets, coupon rate of 10% and a duration of 6 epochs. The payment structure of the bond is shown below

Month 1	10
Month 2	10
Month 3	10
Month 4	10
Month 5	10
Month 6	110

The above payment structure can be replicated with 6 bonds like follows

Bond No.	Face Value	Coupon Rate	Duration
1	10	0%	1
2	10	0%	2
3	10	0%	3
4	10	0%	4
5	10	0%	5
6	110	0%	6

Calculating the NPV of the bond now is just as easy as adding NPVs of these 6 bonds.

$$NPV=Payment/(1+r)^1+Payment2/(1+r)^2+....+Payment6/(1+r)^6$$

Assuming the discount rate is as follows such that it increases as durations lengthen, the NPVs are calculated as

Bond No.	Face Value	Coupon Rate	Duration	Discount Rate	NPV
1	10	0%	1	1%	9.90099
2	10	0%	2	2%	9.61169
3	10	0%	3	3%	9.15147
4	10	0%	4	4%	8.54804
5	10	0%	5	5%	7.83526
6	110	0%	6	6%	77.5457
Total	160		null		122.59

The bond’s fair value or NPV is 122.59 Duets, thus the bond is trading at a premium, selling immediately will amount to a return of 22.59 Duets. This is the result from a lower coupon rate after the issuance of the original bond. However, by selling the bond now, the holder will have to accept a discount of 1-(122.59/160)=23.38%.