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
Face Value(F): The principal amount owed by the bond issuer.
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.
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
Duration(n): The amount of epochs left to be paid
Discount Rate(R): Discount rate is derived using market price of a bond, duration of the bond and expected payments of the bond.
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.
Current Price（P): P is the market price at which a bond is being traded at
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.
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%.
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