Hire Purchase

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 = 36+35+34…….1

366 * 4199840 = 2308020 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 credit 800 * 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