ANNUITIES & DISCOUNTED CASH FLOW RATE OF RETURN. ANNUITY EQUATIONS ARE USED TO EVALUATE DIFFERENT OPTIONS FOR FINANCING PROJECTS THE BASE PROJECT.

ANNUITIES & DISCOUNTED CASH

FLOW RATE OF RETURN

ANNUITY EQUATIONS

ARE USED TO EVALUATE DIFFERENT OPTIONS FOR FINANCING PROJECTS

THE BASE PROJECT FOR THIS CLASS ASSUMES THAT THE PROJECT IS 100% FUNDED BY THE COMPANY FROM AVAILABLE FUNDS. 100% EQUITY

DEBT FUNDING - MORE TYPICAL FUNDING IS ON THE ORDER OF 20% - 40% EQUITY WITH THE REMAINDER AS DEBT 60% - 80%.

EXAMPLE OF ANNUITY CALCUATIONS

GIVEN : Investment in a plant is to total $12,500,000.

WANTED : Determine which funding option is best for the facility.

BASIS : The funding will be based on a 30% equity position. The available funding combinations (Term, Interest Rate, Loan Cost) are:Case 1: 10 Years, 6.75%, 1.25%:Case 2: 15 Years, 6.95%, 1.375%Case 3: 20 Years, 7.15%, 1.5%Case 4: 25 Years, 7.5%, 1.75%.

SOLUTION : Equity 0.3 Debt 1 Equity Debt 0.70InvestmentTot 12500000 PInv Debt InvestmentTotPInv 8750000.00Calculate the loan principal and the payment for each case:

ANNUITY EXAMPLE

For Case 1: n 10 i 0.0675 Pts 0.0125

PactPInv

1 Pts( ) Pact 8860759.49

R1 Pacti 1 i( )

n

1 i( )n

1 R1 1247033.30

For Case 2: n 15 i 0.0695 Pts 0.01375

PactPInv

1 Pts( ) Pact 8871989.86

R2 Pacti 1 i( )

n

1 i( )n

1 R2 971022.77

ANNUITY EXAMPLE

R4 798950.00R4 Pacti 1 i( )

n

1 i( )n

1

Pact 8905852.42PactPInv

1 Pts( )

Pts 0.0175i 0.075n 25For Case 4:

R3 848316.57R3 Pacti 1 i( )

n

1 i( )n

1

Pact 8883248.73PactPInv

1 Pts( )

Pts 0.015i 0.0715n 20For Case 3:

RESULTS OF EXAMPLE

THE RANGE OF VALUES FOR THE REGULAR PAYMENTS IS $798,950 TO $1,247,033 PER YEAR

THE LOWEST PAYMENT VALUES OCCUR WHEN THE NOTE IS PAID OVER THE LONGEST PERIOD OF TIME

THIS IS ALSO ASSOCIATED WITH THE HIGHEST INTEREST RATE

RESULTS OF EXAMPLE

THE RANGE OF THE PRESENT WORTH VALUES IS FROM $8,860,759 TO $8,905,852

THE LOWEST PRESENT WORTH OCCURS WHEN THE LOAN COSTS (POINTS) ARE MINIMIZED

THIS IS ALSO ASSOCIATED WITH THE LOWEST INTEREST RATE AND SHORTEST TERM

SO THE BEST OPTION IS THE ONE THAT HAS THE LOWEST PRESENT WORTH VALUE

PRESENT WORTH ANALYSIS

PRESENT WORTH VALUE THIS IS NET PRESENT WORTH OF ALL THE

PAYMENTS THAT WILL BE MADE TO COMPLETE THIS LOAN

THIS METHOD PROVIDES AN OBJECTIVE BASIS OF COMPARISON EVEN THOUGH THE TERMS, INTEREST RATES AND LOAD COSTS ALL VARY.

THIS IS ONE VARIATION OF THE DISCOUNTED CASH FLOW RATE OF RETURN (DCRR)

FORMAL DCRR

SEE PAGE 328 FOR REFERENCE FORMAL VERSION OF CALCULATES THE

DCRR INTEREST RATE THAT WOULD YIELD A NET PRESENT WORTH OF $0 FOR A PROJECT OVER A SPECIFIED LIFETIME

SOMETIMES CALLED INTERNAL RATE OF RETURN, INTEREST RATE OF RETURN, INVESTOR’S RATE OF RETURN

INVESTMENT PERIOD (DCRR)

FOR THIS CALCULATION, AN INVESTMENT IS MADE IN A FACILITY OVER A SPECIFIED CONSTRUCTION TIME PERIOD

THESE VALUES START AT YEAR ZERO THEY ARE EXPRESSED IN CURRENT

(CONSTANT VALUE) DOLLARS FOR EACH YEAR

THEY ARE CONSIDERED NEGATIVE VALUES BECAUSE THEY ARE EXPENDITURES

PROFIT PERIOD (DCRR)

THE RETURN IS CALCULATED FROM THE PROFIT EARNED DURING OPERATIONS

THESE VALUES START IN THE FIRST YEAR AFTER CONSTRUCTION

THEY ARE EXPRESSED IN CURRENT DOLLARS, OVER THE LIFE OF THE FACILITY

THESE ARE CONSIDERED POSITIVE VALUES BECAUSE THEY REPRESENT NET PROFITS

DCRR CALCULATION

BOTH THE INVESTMENT AND THE PROFIT RETURN ARE DISCOUNTED BACK TO A COMMON TIME AT YEAR ZERO FOR THE OVERALL PERIOD j WHICH IS THE SUM OF THE CONSTRUCTION AND OPERATION PERIODS

FOR EACH YEAR THE CALCULATION COULD BE BASED ON THE FORMULA

)( 681 Nnn iFP

DCRR INTEREST CALCULATION

THE DCRR IS THE VALUE OF i WHEN

WHERE j IS THE LIFETIME OF THE PROJECT

Pnj 0

DCRR EXAMPLEGIVEN : Investment in a plant.

WANTED : Determine the DCRR for this project.

BASIS : The investment in the plant (in current $) will be $5,000,000 PER YEAR expended over a three year period. The plant is expected to operate for a period of 20 years and produce a profit (in current $) of $2,500,000 each year of operation

SOLUTION : The investment costs can be calculated using equation 7.24 over a three year period:

nc 3 Rc 5000000 NPWInv Rc1 i( )

nc1

i 1 i( )nc

The return can be calculated using equation 7.24 for the 20 year period from year 4 to year 24 using 7.24:

no 20 Ro 2500000

DCRR EXAMPLE CALCULATION

The easiest way to complete this calculation is to first calculate a NPW based on then end of construction as year 0, which would actually be a future worth in year 4:

S4 Ro1 i( )

no1

i 1 i( )no

and then discount this value back to the start of construction:

NPWRetS4

1 i( )4

The DCRR occurs for i when: NPWInv NPWRet 0

This is a trial and error solution. Assume : i 0.1

DCRR TRIAL & ERROR

NPWInv Rc1 i( )

nc1

i 1 i( )nc

NPWInv 12434260

S4 Ro1 i( )

no1

i 1 i( )no

S4 21283909

NPWRetS4

1 i( )4

NPWRet 14537196

NPWProj NPWInv NPWRet NPWProj 2102936

DCRR EXAMPLE RESULTS

Completing the Trial and Error Calculation:

f i( ) Rc1 i( )

nc1

i 1 i( )nc

Ro1 i( )

no1

i 1 i( )no

1 i( )4

For an initial guess: i 0.15

root f i( ) i( ) 0.1185 DCRR root f i( ) i( ) DCRR 11.85 %

ANALYSIS OF DCRR RESULTS

THE RESULTS INDICATE A DCRR OF 11.85%

IN THEORY, IF THE PLANT WERE 100% FINANCED, A LOAN AT A RATE OF 11.85% COULD BE PAID BACK OVER THE LIFE OF THE PROJECT

DCRR APPLICATION

THE EXAMPLE CAN BE USED TO DEMONSTRATE THE ADVANTAGES OF DEBT FINANCING

THE CALCULATION CAN BE REPEATED WITH AN ASSUMPTION OF 25% EQUITY FINANCING AND REDUCING THE PROFIT EACH YEAR TO ACCOUNT FOR INTEREST PAYMENTS

THE RESULT SHOWS THE DCRR INCREASES TO 30% FOR THE DEBT FUNDING APPROACH

COMPARISON OF ALTERNATES

THE RESULTS OF THE REVISED DCRR CALCULATION SHOW THAT A PROJECT THAT HAS 100% FUNDING MIGHT HAVE A RELATIVELY SMALL DIFFERENCE ABOVE CURRENT INTEREST RATES AND NOT BE ATTRACTIVE

THE SAME PROJECT WITH DEBT FUNDING MAY HAVE A RETURN COMFORTABLY ABOVE THE CURRENT INTEREST RATES

OTHER COMPARISONS

THE SIGNIFICANT VALUE TO THIS TYPE OF CALCULATION IS BASED ON OBJECTIVE COMPARISON OF VARIOUS TYPES OF PROJECTS AND/OR VARIOUS CONFIGURATIONS OF ONE PROJECT

INDEPENDENT OF PROJECT LIFE INDEPENDENT OF CURRENT

INTEREST RATES