calculating average repayment maturity for ibrd...

Calculating Average Repayment Maturity for IBRD Loans

Concepts and Examples

May 2011

Contact: [email protected]

Calculating Average Repayment Maturity

Definition: Weighted average period of time between the expected loan approval date and scheduled principal repayments – the weighted average time it takes to repay the full loan amount.

Average repayment maturity considers both repayment dates and amounts to provide a better estimation of how quickly a loan is being repaid.

ARM is calculated as the average of the number of years until each principal repayment amount is due, weighted by the principal repayment amounts:

Sum of Weighted RepaymentsSum of Total Repayments

Commitment-Linked Loans

ARM

Example A: Level Principal Repayment $140 mn, 3-year grace period, 10-year final maturity

PeriodYears Principal Repayments Weighted Repayments

(a) (b) c = (a*b)

Gra

ce P

erio

d

0 - -0.5 - -1 - -

1.5 - -2 - -

2.5 - -3 - -

Rep

aym

ent

Peri

od

3.5 10.00 35.00 4 10.00 40.00

4.5 10.00 45.00 5 10.00 50.00

5.5 10.00 55.00 6 10.00 60.00

6.5 10.00 65.00 7 10.00 70.00

7.5 10.00 75.00 8 10.00 80.00

8.5 10.00 85.00 9 10.00 90.00

9.5 10.00 95.00 10 10.00 100.00

SUM 140.00 945.00

Sum of Weighted Repayments

Sum of Total Repayments

945

1406.75 years

Example B: Bullet Principal Repayment$140 million, 5-year final maturity

PeriodYears Principal Repayments Weighted Repayments

(a) (b) c = (a*b) G

race

Per

iod

0 - -0.5 - -1 - -

1.5 - -2 - -

2.5 - -3 - -

3.5 - -4 - -

4.5 - -Repayment Period 5 140.00 700.00

SUM 140.00 700.00



700

1405.00 years

A bullet loan has the same ARM and final maturity.

Example C: Custom Principal Repayment$140 mn, 3-year grace period, 10-year final maturity



1,197

140

8.55 years

Higher Payments towards the End Higher Payments at the Beginning

PeriodYears Principal Repayments Weighted Repayments Principal Repayments Weighted Repayments

(a) (b1) c = (a*b1) (b2) c = (a*b2)

Gra

ce P

erio

d

0 - - - -0.5 - - - -1 - - - -

1.5 - - - -2 - - - -

2.5 - - - -3 - - - -

Rep

aym

ent

Peri

od

3.5 2.00 7.00 24.40 85.40 4 2.00 8.00 24.40 97.60

4.5 2.00 9.00 24.40 109.80 5 2.00 10.00 24.40 122.00

5.5 2.00 11.00 24.40 134.20 6 2.00 12.00 2.00 12.00

6.5 2.00 13.00 2.00 13.00 7 2.00 14.00 2.00 14.00

7.5 2.00 15.00 2.00 15.00 8 24.40 195.20 2.00 16.00

8.5 24.40 207.40 2.00 17.00 9 24.40 219.60 2.00 18.00

9.5 24.40 231.80 2.00 19.00 10 24.40 244.00 2.00 20.00

SUM 140.00 1,197.00 140.00 693.00



693

140

4.95 years

Notice that the ARM is shorter

when more of the loan is repaid

earlier in the life of the loan.

Disbursement-Linked Loans

ARM

Calculating Average Repayment Maturity for Disbursement-Linked Loans

Average Disbursement Period (ADP) is taken into account for calculation = average of the number of years until each disbursement is due, weighted by disbursement amounts.

When ADP and ARM are summed, the result must be less than 18 years.

Only necessary to calculate the ARM for one tranche: Grace period and amortization schedule are the same for each disbursement. ARM is equal for each tranche because years until each principal repayment is counted starting at the corresponding disbursement.



Sum of Weighted Disbursements

Sum of Total Disbursements

Example D: $140 million loan, 3-year grace period, 8-year final maturity for each tranche

PeriodYears Disbursements Weighted Disbursements

(a) (b) c = (a*b)

Gra

ce P

erio

d

0 - -0.5 20.00 10.00 1 50.00 50.00

1.5 40.00 60.00 2 30.00 60.00

2.5 - -3 - -

Rep

aym

ent

Peri

od

3.5 - -4 - -

4.5 - -5 - -

5.5 - -6 - -

6.5 - -7 - -

7.5 - -8 - -

SUM 140.00 180.00

Sum of Weighted Disbursements

Sum of Total Disbursements

180

140

1.29 years

Step 1. Calculate the Average Disbursement Period

4 tranches

Example D: Step 2Calculate the ARM for the tranches

Period Years DisbursementsPrincipal Repayments Principal Repayments Principal Repayments Principal Repayments

Tranche 1 Tranche 2 Tranche 3 Tranche 4

Gra

ce P

erio

d

0 -0.5 20.00 1 50.00

1.5 40.00 02 30.00 0.5

2.5 - 13 - 1.5

Rep

aym

ent

Peri

od

3.5 - 24 - 2.00 2.5

4.5 - 2.00 5.00 35 - 2.00 5.00 4.00 3.5

5.5 - 2.00 5.00 4.00 3.00 6 - 2.00 5.00 4.00 3.00

6.5 - 2.00 5.00 4.00 3.00 7 - 2.00 5.00 4.00 3.00

7.5 - 2.00 5.00 4.00 3.00 8 - 2.00 5.00 4.00 3.00

8.5 - 2.00 5.00 4.00 3.00 9 - - 5.00 4.00 3.00

9.5 - - - 4.00 3.00 10 - - - - 3.00

SUM 140.00 20.00 50.00 40.00 30.00

Notice that even when it might seem that the first principal repayment for tranche 3 is made in year 5, it was actually made in year 3.5, counting from the corresponding disbursement. Each tranche has its own grace period starting at disbursement of the tranche.

Example D: Calculate the ARM for Tranche 1

PeriodYearsLoan

Years Tranche 1

DisbursementTranche 1

Principal RepaymentsTranche 1

Weighted RepaymentsTranche 1

a b c = (a*b)

Gra

ce P

erio

d

0 -0.5 0 20.00 1 0.5 -

1.5 1 -2 1.5 -

2.5 2 -3 2.5 -

Rep

aym

ent

Peri

od

3.5 3 - - -4 3.5 - 2.00 7.00

4.5 4 - 2.00 8.00 5 4.5 - 2.00 9.00

5.5 5 - 2.00 10.00 6 5.5 - 2.00 11.00

6.5 6 - 2.00 12.00 7 6.5 - 2.00 13.00

7.5 7 - 2.00 14.00 8 7.5 - 2.00 15.00

8.5 8 - 2.00 16.00 SUM 20.00 20.00 115.00


115

205.75 years

$140 million loan, 3-year grace period, 8-year final maturity for each tranche

Example D: Calculate the ARM for Tranche 4


172.5

305.75 years

PeriodYearsLoan

Years Tranche 4

DisbursementTranche 4

Principal RepaymentsTranche 4

Weighted RepaymentsTranche 4

a b c = (a*b)

Gra

ce P

erio

d

0 -

0.5 -

1 -

1.5 -

2 0 30.00

2.5 0.5 -

3 1 -

Rep

aym

ent

Peri

od

3.5 1.5 - - -

4 2 - - -

4.5 2.5 - - -

5 3 - - -

5.5 3.5 - 3.00 10.50

6 4 - 3.00 12.00

6.5 4.5 - 3.00 13.50

7 5 - 3.00 15.00

7.5 5.5 - 3.00 16.50

8 6 - 3.00 18.00

8.5 6.5 - 3.00 19.50

9 7 - 3.00 21.00

9.5 7.5 - 3.00 22.50

10 8 - 3.00 24.00

SUM 30.00 30.00 172.50

$140 million loan, 3-year grace period, 8-year final maturity for each tranche

Example D: Step 3Add the ADP to the ARM


Sum of Weighted DisbursementsSum of Total Disbursements

ADP = ARM =

1.29 years 5.75 years

7.04 years

calculating average repayment maturity for ibrd...

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