HIRE PURCHASE

PRACTICAL PROBLEM • Tri star chemicals has acquired an equipment of Rs.100 lacs

under hire purchase scheme from Synergy finance & has accepted installment of Rs 3, 94,440 per month for 36 months

• Calculate flat rate of interest charged by Synergy Finance

• Calculate effective rate of interest p.a. implicit in the scheme assuming installments are paid at the end of every month

• Tri star follows SOYD for allocating interest charged over three year period. Calculate the interest allocated each year

SOLUTION

• Cash price 100 lacs

• Monthly installment 394440

• Total Hire price(36 months) 141,99,840

• Flat rate = 14199840 – 10000000

= 4199840/10000000

= 42 %

= 14 % P.A

Or 4199840/3=1399946.667

1399946.667/10000000*100=13.99 or 14%

SOLUTION• Rate of interest implicit in scheme is that rate which would

equate the PV of rental to cash price

• 394440 * 12* PVIFA p( i , 3) = 10000000

• PVIFA p( i , 3) = 10000000 / 4733280 = 2.1127

• i / i 12 * PVIFA (i,3) = 2.1127

• For i = 0.26 LHS of equation is 2.14

• For i = 0.28 LHS of equation is 2.09

• Interpolating in the range 26 & 28 %

• i = 27.42%

• If installment are paid in advance , use i /d12 instead i /i12

SOLUTION

• An alternative method to trial & approach method is approximation method

• i = n .2F

n + 1

• i = 36/37 * 2 * 14

• i = 27.24%

• For advance EMI

• i = n .2F

n – 1

SOLUTION• Year 1• 36+35+34…..25 = 366 * 4199840 = 2308020

36+35+34…….1 666

• n ( n + 1 ) n ( n + 1 ) - n ( n + 1)

2 2 2• 36*37/2 = 666 36*37/2 - 24*25/2 = 366• Year 2• 24+23+22…..13 = 222* 4199840 = 1399947

36+35+34…….1 666• 24*25/2 – 12*13/2 = 222• Year 3• 12+11+10…..1 = 78 * 4199840 = 491873

36+35+34…….1 666

PRACTICAL PROBLEM

• Narmada finance offers a Hire purchase plan for corporate borrowers

• Rate of interest 13 % flat

• Repayment 3 years monthly in arrear

• Down payment 20 %

• Calculate APR (annual percentage rate) by trial error & approximation approach

• What would be the answer if payment is in advance

SOLUTION

• Amount of loan 800

• Total charge for credit800 * 0.13 * 3 = 312

• Monthly installment (800 + 312) / 36 = 30.89

• (30.89 * 12 ) * PVIFA p (i,3) = 800

• i / i 12 * PVIFA (i,3) = 2.158

• For i= 24 LHS = 2.191

• For i= 26 LHS = 2.143

• i= 25.38

• Approximate formula

• 36/37 * 2 * 13 = 25.3%

SOLUTION contd.

• (30.89 * 12 ) * PVIFA p (i,3) = 800

• i / d 12 * PVIFA (i,3) = 2.158

• For i= 26 LHS = 2.185

• For i= 28 LHS = 2.141

• i= 27.23%

• Approximate formula

• 36/35 * 2 * 13 = 26.74%

CALCULATION OF INTEREST REBATE

• Effective rate of interest method

• Considering previous illustration if borrower wishes to pay the outstanding loan after paying 24th installment , what would be the interest rebate

• Total amount of outstanding installments – discounted value of outstanding installments as on date of payment

• 30.89 * 12 = 370.68 (A)

• 30.89 * 12 * PVIFA p (25.38,1) (B)

• = 328.68

• A – B = 370.68 – 328.68

• = 42

CALCULATION OF INTEREST REBATE

• Rule 78 method (prescribed by Hire Purchase Act 1972 (amended)

• Considering previous illustration if borrower wishes to pay the outstanding loan after paying 24th installment , what would be the interest rebate

• R = t ( t + 1) * D

n ( n + 1 )

• 12 * 13 * 312

36 * 37

• = 36.54

• Interest rebate under rule 78 is beneficial for lender

PRACTICAL PROBLEM

• Considering previous illustration if borrower wishes to pay the outstanding loan after paying 24th installment , calculate effective rate of interest implied in complete transaction in both methods

• Under Effective rate of interest method

• 30.89 * 12 * PVIFA p (i,2) + (370.68 – 42 ) * PVIF (i,2) = 800

• = 25.38

• Under Rule 78 method (prescribed by Hire Purchase Act 1972 (amended)

• 30.89 * 12 * PVIFA p (i,2) + (370.68 – 36.54 ) * PVIF (i,2) = 800

• = 26

• Effective rate in complete transaction is higher & lender gets benefit if he applies Rule 78

COST OF HIRE PURCHASE FOR HIREE Vs COST OF LEASE FOR LESSEE

• Down payment

• + PV of Hire payments

• + Service fees

• - PV of tax shield on charge on credit of HP

• - PV of tax shield on Service Fees

• - PV of tax shield on Depreciation

• - PV of salvage

• PV OF Lease payments

• + Lease management fees

• - PV of tax shield on Lease payments

• - PV of tax shield on Lease management Fees

COST OF LEASE FOR LESSEE