Bond Valuations

Please feel free to use my code to compute the bond value, cash flows till the maturity, current yield and approximated yield to maturity of the bond.

User guide

Firstly, run the Bond valuation.py which will install all necessary packages, import them and will create the class BondValuation in memory.

1. Bond value and cash flows

Example

A bond XYZ is issued on "2021-12-25" with the maturity date "2026-12-24" for a face value of £100,000 and coupon rate of 7% per annum to be paid semi-annually. If the current risk free return (discount rate) available in the market is 6.5% per annum, then what would be the value of the bond?

bc = BondCalculations(
    principal_amount = 100000,
    coupon_rate = 0.07,
    bond_issue_date = '2021-12-25',
    bond_maturity_date = '2026-12-24',
    discount_rate = 0.065,
    coupon_payment_frequency = 'semi-annually')

cash_flow, value_of_bond = bc.bond_value()

print(cash_flow)

   receivable_date  receivable_amount  present_value
1       2022-06-25             3500.0    3390.127555
2       2022-12-25             3500.0    3283.128822
3       2023-06-25             3500.0    3180.064424
4       2023-12-25             3500.0    3079.695674
5       2024-06-24             3500.0    2983.017476
6       2024-12-24             3500.0    2888.867895
7       2025-06-24             3500.0    2798.180186
8       2025-12-24             3500.0    2709.864413
9       2026-06-24             3500.0    2624.796005
10      2026-12-24           103500.0   75169.168548

print(value_of_bond)
102107.0

Since the tenure of the bond is 5 years and the interest amount paid is semi-annually, the cash flow table shows that the buyer will receive an amount of £3500 semi-annually. On the maturity or expiry date, in addition to the coupon amount of £3500, the face value value of the bond £100,000 will also be received.

The value of the bond is the sum of present values of all futures payments which came to £102,107. Since, the face value is £100,000 it will be therefore a bargain if you buy the bond.

Points to note

• if bond value > market price of the bond, the bond is at a premium price
• if bond value < market price of the bond, the bond is at a discount price
• if bond value = market price of the bond, the bond is at a par value

2. Current yield and Yield to maturity

Example

Considering the same example above, if the market price for the bond is £110,000, then what is the current yield and yield to maturity of the bond?

Current yield is the return earned if the bond is held for one year. Yield to maturity is the return earned if the bond is held till maturity.

current_yield, ytm = bc.yield_calculations(current_bond_price = 110000)

print(current_yield)
0.06364

print(ytm)
0.04762

The current yield is 0.06364 or 6.36% and the yield to maturity is 0.04762 or 4.76%.
Even though the coupon rate is 7%, the current yield and yield to maturity are lower because the bond is available at a premium (£110,000 instead of £100,000).

Example

Considering the same example above, if the market price for the bond is £90,000, then what is the current yield and yield to maturity of the bond?

current_yield, ytm = bc.yield_calculations(current_bond_price = 90000)

print(current_yield)
0.07778

print(ytm)
0.09474

The current yield is 0.07778 or 7.78% and the yield to maturity is 0.09474 or 9.47%.
Even though the coupon rate is 7%, the current yield and yield to maturity are higher because the bond is available at a discounted rate (£90,000 instead of £100,000).

Points to note

• if bond coupon rate > YTM, the bond is at a premium price
• if bond coupon rate < YTM, the bond is at a discount price
• if bond coupon rate = YTM, the bond is at a par value

Notes

• When comparing two bonds, choose the one with higher yield to maturity which indicates the higher profitability of the bond.
• Note that all my calculations assume that the coupon payments are reinvested as they are received.
• Also, the present value calculation relies on the start date:
  • if the bond was already issued, then the current date will be taken into account.
  • if the bond will be issued in the near future, then the issue date will be taken into account.
  • Therefore, if you repeat my examples above, the output will be different since your current date is different from mine.

Code execution via the terminal

Below is a demonstration of executing the code from a command line interface.