Calculate YTM

This action is found only on the budget transactions, produces a Yield to Maturity rate based on what has been entered on the Schedule. The rate is calculated to a large amount of precision (up to 20 decimal places) so that rounding is minimized, however the system only displays up to four decimal places. The action first validates all necessary information is present, issuing an error and stopping if something is missing.

If all information is present, then it goes on to do one of the following calculations based on the Schedule Type:

Principal in Last Payment w/Compound Interest

Unlike later formulas, this one is solved in one pass whereas the others are recursive so that the action keeps trying different rates.

Y = ((FV / P)^1/N) - 1

Where:

Y = Yield to Maturity

N (Number of Payments) = Number of compounding periods plus final payment

FV (Face Value) = Denomination * Number of Bonds Issued

P = Purchase Price based on Major Type of Bond:

Zero Coupon then FV = Principal* - Total Interest - Discount (Other Amount 1)

Capital Appreciation or Convertible Capital Appreciation then FV = Principal* - Total Interest

*Principal is from the Schedule and not the Debt Instrument

Principal in Last Payment w/Rate Interest or w/Fixed Interest

Solving the following is a recursive effort so that a Y is obtained so that the right side equals P.

P = (CPN * (1 / Y) * (1 - (1 / (1+Y)^N)) + FV / (1+Y)^N

Where:

Y = Yield to Maturity

N (Number of Payments) = Count of Regular Payment Schedule Details

FV (Face Value) = Principal

P (Purchase Price) = FV -- Discount (Other Amount 1) + Premium (Other Amount 2)

R = Interest Rate Per Period

CPN = Coupon Payment based on Schedule Type:

Principal In Last Payment w/Rate Interest then CPN = FV * R

Principal In Last Payment w/Fixed Interest then CPN = Fixed Interest Payment Amount

Amortized Payment

Solving the following is a recursive effort so that a Y is obtained so that the right side equals P.

P = (Coupon 1/(1+Y^1)) + (Coupon 2/(1+Y^2)) + (Coupon N/(1+Y^N))

Where:

Y = Yield to Maturity

N (Number of Payments) = Count of Regular Payment Schedule Details

Coupon # = Principal + Interest of Each Individual Schedule Detail

P (Purchase Price) = FV -- Discount (Other Amount 1) + Premium (Other Amount 2)