ANNUITY: ALL THE CASH ARE EQUAL + TIME GAP BETWEEN CASH ARE EQUAL. PRESENT VALUE OF ANNUITY = ANNUITY X PVAF (R%, N) DEFFERED ANNUITY: AN ANNUITY (EQUAL CASH & EQUAL GAP) BEGINS LATE BY M PERIOD BUT CONTINUES THEREAFTER FOR N PERIOD. PRESENT VALUE OF DEFERRED ANNUITY = ANNUITY X PVAF (R%, N) (1+R %) M NOW CONSIDER THE FUSION OF BOTH: AN ANNUITY STARTED FROM 1 ST YEAR TO 6 TH YEAR CALLED ANNUITY a, THEREAFTER THE AMOUNT OF ANNUITY CHANGES CALLED ANNUITY b FOR NEXT 2 YEARS. PRESENT VALUE OF ANNUITY a + PRESENT VALUE OF DEFERRED ANNUITY b = ANNUITY a X PVAF (R%, 6) + ANNUITY b X PVAF (R%, 2) (1+R %) 6 OR PRESENT VALUE OF ANNUITY a + PRESENT VALUE OF DEFERRED ANNUITY b = ANNUITY a X PVAF (R%, 6) + ANNUITY b X [PVF @ R% OF 7 TH YEAR + PVF @ R% OF 8 TH YEAR] TAX BENEFIT: WHERE LEASE RENT IS PAYABLE MONTHLY WHICH ALSO CHANGES ON A YEARLY BASIS. NO PVAF SHALL BE USED IN SUCH CASE. WE NEED TO MAKE A TABLE AS UNDER: YEAR MONTHLY LR ANNUALISED LR TAX BENEFIT NET CASH 1 3000 3000X12XAF 3000X12X TAX RATE 2 2800 2800X12XAF 2800X12X TAX RATE 3 2500 2500X12XAF 2500X12X TAX RATE 4 2300 2300X12XAF 2300X12X TAX RATE 5 2100 2100X12XAF 2100X12X TAX RATE NPV = Σ(NCFi X PVCi) SOMETIMES AS PER THE TERMS OF THE AGREEMENT; AFTER LEASE PERIOD (SAY 5 YEARS) ASSETS SHALL BE GIVEN TO THE LESSEE AGAINST INITIAL DEPOSIT MADE BY THE LESSEE AT THE BEGINNING (IT IS A INTIAL CASH OUT). IN SUCH CASE DEPRECIATION & TAX BENEFIT ON DEPRECIATION SHALL BE AVAILABLE TO THE LESSE AS FOLLOWS PVF YEAR LEASE RENT TAX BENEFIT ON PVF DEPRECIATION 1-5 XX -- XX 6 *INITIAL DEPOSIT X RATE OF DEP. X TAX RATE XX
7 (1-D) X 1 ST TB ON DEP XX 8 (1-D) X 2 ND TB ON DEP *AT THE TIME OF PAYING INITIAL DEPOSIT, LEASE S.D. A/C SHALL BE DEBITED WHILE CASH A/C SHALL BE CREDITED. AT THE END OF TENUE OF LEASE I.E. 5 TH YEAR FIXED ASSETS A/C SHALL BE DEBITED WHILE LEASE S.D. A/C SHALL BE CREDITED. THEREFORE DEPRECIATION SHALL BE ALLOWED FROM THE 6 TH YEAR AND LEASE RENT SHALL NOT BE PAID FROM 6 TH YEAR. XX INTERNAL RATE OF RETURN METHOD EXAMPLE: INITIAL INVESTMENT Rs. 1.00 LAKH, LIFE OF PROJECT 5 YEARS, ANNUAL CASH Rs. 26,000/-, COST OF CATITAL 8% P.A. CALCULATE NET PRESENT VALUE. NPV = 26000 X PVAF (8%, 5) = 26000 X 3.9927 LESS Rs. 1.00 LAKH = Rs. 3,810/-. QUESTION ARISE WHAT IS THE MEANING OF Rs. 3,810/-. IT MEANS IN THIS PROJECT WE SHALL RECOVER INITIAL INVESTMENT Rs. 1.00 LAKH + RETURN ON INVESTMENT @ 8% + EXTRA PROFIT WHICH HAVE THE PRESENT VALUE OF Rs. 3,810/-. EVEN IF NPV IS ZERO (INSTEAD OF Rs. 3,810/-) WE COULD RECOVER THE PRINCIPAL AMOUNT + RETURN ON INVESTMENT @ 8% AND THE PROPOSAL IS ACCEPTABLE. NOW, Rs. 3,810/- SHOULD ALSO BE EXPRESSED IN % FOR BETTER UNDERSTANDING RATHER THAN 8% + Rs. 3,810/-. WE SHOULD DISCOUNT THE CASH WITH A RATE AT WHICH NPV IS EQUAL TO ZERO, BECAUSE WE WANT Rs. 3,810/- ALSO IN %. THEREFORE, APPLYING TRIAL & ERROR, DISCOUNTING WITH 8% WE GET NPV OF Rs. 3,810/- & DISCOUNTING WITH 10% WE GET NPV Rs. 1,440/-. APPLYING INTERPOLATION WE GET 9.44% UNLESS WE KNOW BOTH IN & OUT WE CAN T CALCULATE IRR. SO IN BOTH LEASE & LOAN OPTION WE CAN T CALCULATE IRR BECAUSE THERE ARE NO INS UNDER LEASE & LOAN OPTION. THEREFORE WE COMPARE BOTH WITH A THIRD OPTION WHICH IS BUY OPTION. IN BUY OPTION THERE WILL BE OUT ON PURCHASE OF ASSETS & IN OF TAX BENEFIT ON DEPRECIATION. HENCE WE SHALL COMPARE LEASE Vs BUY OPTION & LOAN Vs BUY OPTION. OPTION-1 : LEASE Vs. BUY OPTION (WITHOUT LOAN) LEASE Vs. BUY OPTION MEANS LEASE LESS BUY COMPARISON OF LEASE OPTION & LOAN OPTION CASH LEASE OPTION BUY OPTION INITIAL CASH --- OUT OF COST OF ASSETS ANNUAL CASH 1. LEASE RENT 2. T.B. ON LEASE RENT TAX BENEFIT ON DEPRECIATION TERMINAL CASH --- SALVAGE VALUE ± TAX EFFECT ANNUAL CASH YEAR LEASE OPTION (A) BUY OPTION (B) NET C (A-B) BY T& E & INTER. FIND A RATE AT WHICH NPV IS ZERO.
0 (RELEVANT FOR BUY OPTION) 1 -LEASE RENT AFTER --- -COST OF ASSETS TAX 2 -LEASE RENT AFTER TAX 3 -LEASE RENT AFTER TAX (USE OF OWN FUNDS) + T.B. ON DEPRECIATION + T.B. ON DEPRECIATION + T.B. ON DEPRECIATION 3 --- + SALVAGE VALUE ± TAX EFFECT +VE -VE -VE -VE -VE NPV SHOULD BE ZERO NOW FOCUS ON COLUMN C ABOVE, LET US ASSUME THAT WE HAVE TAKEN A LOAN EQUAL TO COST OF ASSETS (AS SHOWN BY + VE SIGN) WHICH IS REPAID IN 3 INSTALEMENTS (AS SHOWN BY VE SIGN). BY TRAIL & ERROR & INTERPOLATION, WE FIND A RATE AT WHICH NPV SHOULD BE EQUAL TO ZERO AND THIS RATE IS THE COST OF BORROWING. BUT HERE THIS RATE IS THE COST OF LEASE OPTION. IRR OF LOAN Vs. BUY OPTION IS ALWAYS EQUAL TO Kd. BECAUSE UNDER OPTION-1 (LEASE Vs. BUY) & UNDER OPTION-2 (LOAN Vs. BUY) BUY OPTION IS COMMON, THEREFORE COST OF LEASE SHALL BE COMPARED WITH AFTER TAX COST OF BORROWING. IF COST OF LEASE RENT > Kd LOAN IS BETTER IF COST OF LEASE RENT < Kd LEASE IS BETTER. JUST CALCULATE THE NET PRESENT VALUE OF LEASE OPTION SEPARATELY & NET PRESENT VALUE OF BUY OPTION SEPARATELY IF PV OF OUT UNDER LEASE OPTION IS HIGHER, SELECT BUY OPTION. IF PV OF OUT UNDER BUY OPTION IS HIGHER SELECT LEASE OPTION. OPTION-2: LOAN Vs BUY OPTION (WITH LOAN) BOWER-HERRINGER-WILLIAMSON (BHW) METHOD UNDER NPV METHOD, WE USED TO DISCOUNT ALL THE CASH UNDER LEASE OTPION & LOAN OPTION WITH A SINGLE DISCOUNTING RATE TO CALCULATE NET PRESENT VALUE OF EACH OPTION. THE ENTIRE CASH S ARE CLASSIFIED AS CASH UNDER LEASE OPTION & CASH UNDER LOAN OPTION. UNDER BHW METHOD ALSO, NET PRESENT VALUE SHALL BE CALCULATED BY DISCOUNTING THE CASH S. THE ONLY DIFFERENCE IS UNDER BHW METHOD ALL THE CASH S SHALL BE CLASSIFIED UNDER TWO HEADS (1) FINANCING CASH (2) OPERATING CASH AND THE DISCOUNTING RATE SHALL BE DIFFERENT BECAUSE IT IS INCORRECT TO DISCOUNT ALL THE CASH S WITH A SINGLE RATE. HIGHER THE RISK INVOLVED IN CASH S, HIGHER SHOUBLE BE THE DISCOUNTING RATE. CASH MEANING DISCOUNTING
OPERATING CASH FINANCING CASH WHICH ARISE DUE TO INCOME TAX WHICH ARE NOT OPERATING CASH S. [IF INCOME TAX IS NOT APPLICABLE (IF GIVEN-IGNORE TAX), ALL THE CASH S ARE FINANCIAL CASH S.] COST OF CAPITAL RATE OF INTEREST FINANCING ASPECT: DISCOUNTED AT RATE OF INTEREST WE CONSIDERED INITIAL CASH, ANNUAL CASH & TERMINAL CASH OF LEASE & LOAN OPTION AT THE SAME TIME. (AS SHOWN IN TABLE BELOW) TYPE OF CASH INITIAL CASH ANNUAL CASH ANNUAL CASH TERMINAL CASH NATURE OF CASH BELONGS TO ± IF WE HAVE SELECTED LOAN OPTION -- -- -- -- PRESENT VALUE OF E.M.I. (COST OF ASSETS) = E.MI. X PVAF (R%, N) PRESENT VALUE OF LEASE RENT PRESENT VALUE OF SALVAGE VALUE LOAN +VE THERE WOULD BE OUT OF EMI EACH YEAR. NON HAPPENING OF OUT IS EQUAL TO IN. LEASE -VE N.A. LOAN -VE THERE WOULD BE IN OF SALVAGE VALUE. NON HAPPENING OF IN IS EQUAL TO OUT. AFTER DISCOUNTING @ RATE OF INTEREST (BORROWING RATE) WE SHALL GET THE 1. NET FINANCING ADVANTAGE OR 2. NET FINANCING DISADVANTAGE. OPERATING ASPECT: DISCOUNTED AT COST OF CAPITAL WE CONSIDERED INITIAL CASH, ANNUAL CASH & TERMINAL CASH OF LEASE & LOAN OPTION AT THE SAME TIME. (AS SHOWN IN TABLE BELOW) TYPE OF CASH INITIAL CASH ANNUAL CASH ANNUAL CASH NATURE OF CASH PRESENT VALUE OF TAX BENEFIT ON LEASE RENT PRESENT VALUE OF TAX BENEFIT ON INTEREST BELONGS TO ± IF WE HAVE SELECTED LOAN OPTION -- -- -- -- LEASE +VE N.A. LOAN -VE THERE WOULD BE TAX BENEFIT ON INTEREST. NO TAX BENEFIT IS
ANNUAL CASH TERMINAL CASH EQUAL TO OUT. PRESENT VALUE OF TAX LOAN -VE THERE WOULD BE TAX BENEFIT BENEFIT ON ON DEPRECIATION. NO TAX DEPRECIATION BENEFIT IS EQUAL TO OUT. -- -- -- -- AFTER DISCOUNTING @ COST OF CAPITAL, WE SHALL GET THE 1. NET OPERATING ADVANTAGE OR 2. NET OPERATING DISADVANTAGE. FINANCING ADVANTAGE IF PRESENT VALUE OF LEASE RENT IS LESSER THAN ( PRESENT VALUE OF E.M.I. LESS SALVAGE VALUE) FINANCING DISADVANTAGE IF PRESENT VALUE OF LEASE RENT IS HIGHER THAN ( PRESENT VALUE OF E.M.I. LESS SALVAGE VALUE) OPERATING ADVANTAGE (IF T.B. OF LEASE OPTION IS HIGHER THAN T.B. OF LOAN OPTION) OPERATING DISADVANTAGE (IF T.B. OF LEASE OPTION IS LESSER THAN T.B. OF LOAN OPTION) NPV SHALL BE +VE NPV SHALL BE VE NPV SHALL BE +VE NPV SHALL BE -VE LEASE OPTION IS BETTER LOAN OPTION IS BETTER KEEPING IN VIEW THE TAXATION, LEASE OPTION IS BETTER. KEEPING IN VIEW THE TAXATION, LOAN OPTION IS BETTER. WE CAN SAY - LEASE IS BETTER IF THERE ARE FINANCING ADVANTAGE - LOAN IS BETTER IF THERE ARE FINANCING DISADVANTAGE - LEASE IS BETTER IF THERE ARE OPERATING ADVANTAGE - LOAN IS BETTER IF THERE ARE OPERATING DISADVANTAGE FINALLY - LEASE IS BETTER ON ADVANTAGE - LOAN IS BETTER ON DISADVANTAGE --------------------------------------------------------------------------------------------------------------------- FROM LESSOR S POINT OF VIEW
IT IS AN INVESTMENT PROPOSAL (BASED ON CAPITAL BUDGETING TECHNIQUES). LESSOR SHOULD COLLECT SUCH LEASE RENT SO THAT HE CAN GET BACK THE AMOUNT OF INVESTMENT MADE BY HIM + RETURN ON INVESTMENT. FOLLOWING ARE THE VARIOUS CASH S FOR THE LESSOR, WHICH SHALL BE DISCOUNTED @ DESIRED RATE OF RETURN. 1. INITIAL CASH : a. OUT OF COST OF ASSETS 2. ANNUAL CASH : a. IN OF LEASE RENT b. OUT OF INCOME TAX ON LEASE RENT c. IN OF TAX BENEFIT ON DEPRECIATION. 3. TERMINAL CASH : a. IN OF SALVAGE VALUE b. IN OF T.B. ON CAPITAL LOSS OR OUT OF TAX LOSS ON CAPITAL GAIN. 1. IF NPV IS +VE: ACCEPT (BUY THE EQUIPMENT & GIVE IT ON LEASE) 2. IF NPV IS VE: REJECT 3. IF NPV IS ZERO: ACCEPT BECAUSE THE AMOUNT INVESTED SHALL BE RECOVERED FULLY TOGETHER WITH DESIRED RATE OF RETURN. BREAK EVEN LEASE RENT IS THE AMOUNT OF MINIMUM LEASE RENT WHICH A LESSOR SHOULD CHARGE FROM THE LESSEE TO RECOVER THE AMOUNT OF INVESTMENT TOGETHER WITH DESIRED RATE OF RETURN. HERE SET NPV EQUAL TO ZERO. CALCULATION OF BREAK-EVEN LEASE RENT: S.NO. PARTICULARS PARTICULARS 1 -COST OF ASSETS -COST OF ASSETS 2 + LEASE RENT X PVAF (R%, N) ARREARS 3 -T.L. ON LR X PVAF (R%, N) ARREARS OR ADVANCE 4 +T.B.ON DEP. X PVAF (R%, N) DEP. UNDER SLM METHOD 5 + S.V. X PVF (R%, Nth) + T.B. ON C.L. X PVF (R%, Nth) WHERE S.V. > W.D.V. SHORT- CUTW.D.V FORMULA AS FOLLOWS + LEASE RENT X PVADF (R%,N ) ADVANCE -T.L. ON LR X PVAF (R%, N) ARREARS OR ADVANCE PV OF TB ON DEPRECIATION UNDER W.D.V. METHOD FORMULA AS FOLLOWS + S.V. X PVF (R%, Nth) -T.L. ON C.G. X PVF (R%, Nth) TAX LOSS WHERE S.V. < W.D.V. SHORTCUTW.D.V FORMULA AS FOLLOWS
THERE ARE TWO METHOD OF CALCULATING PRESENT VALUE OF TAX BENEFIT ON DEPRECIATION UNDER W.D.V. METHOD. 1. TABLE METHOD 2. FORMULA METHOD (AVOID IN EXAM) TABLE METHOD YEAR DEPRECIATION TAX BENEFIT (A) 1 2 3 PVF @ R% (B) PRESENT VALUE (AXB) PV = Σ (TBi X PVi) FORMULA METHOD SUM OF PV OF TB ON DEP. UNDER W.D. V = COST OF ASSETS X [1-{(1-D)/ (1+R)} N ] DXT/ (R+D) D = DEPRECIATION RATE, R = RATE OF DISCOUNTING, N = YEARS, T = TAX RATE CALCI: 1-D/1+R = X = N-1 TIMES 1 R +D X D X T X COST OF ASSETS = SUM OF PV OF TB ON DEP. UNDER W.D. V SHORT-CUT METHOD FOR CALCULATING W.D.V. = W.D.V. = COST OF ASSETS X (1-D) N THIS FORMULA IS DERIVED FROM FV = PV X (1 + R) N WHERE FV > PV. BUT HERE W.D.V. < COST OF ASSETS MEANS FV < PV THEREFORE (1-D) USED IN PLACE OF (1+R). DESIRED RATE OF RETURN BY THE LESSOR IS PRE-TAX OR POST TAX? NO CAPITAL GAIN OR CAPITAL LOSS: IF SLM METHOD IS FOLLOWED & THERE IS NO SALVAGE VALUE. BETTER SAY IF SLM METHOD IS FOLLOWED THERE WILL BE CAPITAL GAIN ONLY (IN CASE THERE ARE SOME SALVAGE VALUE) IN NO CASE THERE WILL CAPITAL LOSS UNLESS SALVAGE VALUE IS IN NEGATIVE TERMS (EXAMPLE COST OF DISMANTLING THE PLANT AFTER ITS USEFUL LIFE). DIFFERENCE BETWEEN USEFUL LIFE & ECONOMIC LIFE? WHERE ANY EXPENSES CHARGED BY THE LESSOR FOR MEETING OVERHEAD COST FOR EXAMPLE LEASE MANAGEMENT FEE CHARGED DURING THE INITIATION OF AGREEMENT TO COVER INITIAL EXPENSES. THERE WILL BE IN & OUT AT THE SAME TIME. HENCE IT SHALL BE IGNORED. LEVERAGED LEASE IF A LESSOR BORROWS MONEY FOR FINANCING THE ASSETS TO BE GIVEN ON LEASE, IT IS CALLED LEVERAGED LEASE. (FOR EG. WHERE THE COST OF ASSETS IS VERY HIGH & LESSOR DOES NOT HAVE
OWN FUND TO FINANCE SUCH INVESTMENT ON THE OTHER HAND HE HAS AN OPPORTUNITY TO GIVE THE ASSETS ON LEASE AT A LUCRATIVE LEASE RENT, HE MAY BORROW MONEY, BUY THE ASSETS & GIVE IT ON A LEASE) FOLLOWING ARE THE VARIOUS CASH S FOR THE LESSOR, WHICH SHALL BE DISCOUNTED @ DESIRED RATE OF RETURN. 1. INITIAL CASH : a. IN OF LOAN AMOUNT (ADDITIONAL CASH ) b. OUT OF COST OF ASSETS 2. ANNUAL CASH : a. IN OF LEASE RENT b. OUT OF INCOME TAX ON LEASE RENT c. IN OF TAX BENEFIT ON DEPRECIATION. d. OUT OF INSTALEMNT (ADDITIONAL CASH ) e. IN OF TB ON INTEREST (ADDITIONAL CASH ) 3. TERMINAL CASH : a. IN OF SALVAGE VALUE b. IN OF T.B. ON CAPITAL LOSS OR OUT OF TAX LOSS ON CAPITAL GAIN. EXAMPLE: COST OF ASSETS 100 LAKH, SOURCE 60 LAKH FROM LOAN, 40 LAKH FROM EQUITY, LIFE 3 YRS, INCOME TAX RATE 30%, RATE OF INTEREST ON LOAN 15%, DESIRED RATE OF RETURN 20%, DEPRECIATION S.O.Y.D. METHOD. BOOK VALUE OF ASSETS AT THE END OF 3 RD YEAR 34 LAKH, SALVAGE VALUE 20 LAKH. PRINCIPAL AMOUNT OF LOAN IS REPAYABLE IN EQUAL INSTALMENT, LEASE RENT PAYABLE AT THE END. STEPS 1 COST OF ASSETS -100 LAKH 2 IN OF LOAN +60 LAKH 3 LEASE RENT =LR +0.70LR X PVAF (20%,3) +1.4745LR 4 PV OF TB ON DEP. COST-S.V. = DEP +14.74 LAKH 5 PV OF TB ON INTEREST & PV OF PRINCIPAL 66X3/6X30%XPVFi(20%,1 ST ) 66X2/6X30%XPVFi (20%,2 ND ) 66X1/6X30%XPVFi (20%, 3 RD ) PRIN INTT. TB NET PV -20-9 +2.7 - - -51.51 LAKH
26.3 21.92-20 -6 +1.8-24.2-20 -3 +0.9-22.1-16.81-12.79-51.51 6 PV OF SALVAGE VALUE + CAP LOSS B.V. 34 S.V. 20 = LOSS 14 TAX BENEFIT 14 X 30% = 4.2 PV OF 20 + 4.2 = 24.20 X PVF (20%, 3RD) +14 LAKH LR = 42.57 LAKHS CUSTOMISATION OF LEASE RENT TYPES OF CUSTOMED LEASE RENT 1. STEPPED UP LEASE RENT 2. STEPPED DOWN LEASE RENT 3. DEFERRED LEASE RENT STEPPED UP LEASE RENT WHERE LEASE RENT IS INCREASING 10% EACH YEAR. COST OF ASSETS Rs. 1000/-, LIFE 5 YEARS. DESIRED RATE OF RETURN 24% YEAR LEASE RENT PV @ 24% 1 LR LR X 1/(1.24) 1 2 1.1 LR 1.1 LR X 1/(1.24) 2 3 1.21 LR 1.21 LR X 1/(1.24) 3 4 1.331 LR 1.331 LR X 1/(1.24) 4 5 1.4641 LR 1.4641 LR X 1/(1.24) 5 Σ = PV OF LR = 3.218LR CALCI: 1 X 1.1 X = = = FOR 1 ST YEAR TO 5 TH YEAR -COST OF ASSETS + PV OF LEASE RENT = 0 PV OF LEASE RENT = COST OF ASSETS 3.218LR = 1000, LR = 310/- PER 1000 STEPPED DOWN LEASE RENT
WHERE LEASE RENT IS DECREASING 20% EACH YEAR. COST OF ASSETS Rs. 1.00 LAKH, LIFE 4 YEARS, INCOME TAX 40%, DEPRECIATION SLM, SALVAGE VALUE NIL, DESIRED RATE OF RETURN 16% YEAR LEASE RENT AFTER PV @ 16% TAX 1 LR X.60 0.60 LR X 1/(1.16) 1 2 0.80 LR X.60 0.48 LR X 1/(1.16) 2 3 0.64 LR X.60 0.384 LR X 1/(1.16) 3 4 0.512 LR X.60 0.3072 LR X 1/(1.16) 4 Σ = PV OF LR = 1.2896 LR CALCI: 1 X.80 X = = FOR 1 ST YEAR TO 4 TH YEAR PV OF TB ON DEP 1,00,000 4 YEARS = 25000 X.40 X PVAF (16%, 4) = 25,000 X 2.7982 = 69,955/- -COST OF ASSETS + PV OF LEASE RENT (AFTER TAX) PV OF TB ON DEP = 0 PV OF LEASE RENT (AFTER TAX) PV OF TB ON DEP = COST OF ASSETS 1.2896 LR 69,955 = 1,00,000/-, LR = 23,267/- APPROX LET CHECK IT YEAR LEASE RENT LEASE RENT AFTER TAX PVF @ 16% PRESENT VALUE 1 23,267.00 13,960.20 0.8621 12,035.09 2 18,613.60 11,168.16 0.7432 8,300.18 3 14,890.88 8,934.53 0.6406 5,723.46 4 11,912.70 7,147.62 0.5523 3,947.63 30,006.36 PV OF LR = 30,006 APPROX + PV OF TB ON DEP = 69,955/- COST OF ASSETS = 1, 00,000/- DEFFERED LEASE RENT DESIRED RATE OF RETURN 12%, FIVE ANNUAL PAYMENT STARTING FROM 3 RD YEAR COST Rs. 1,000/-. MEANS NO LEASE RENT SHALL BE PAID FOR 1 ST TWO YEARS. 1 ST LEASE RENT SHALL BE PAID ON 3 RD YEAR & 5 TH LEASE RENT SHALL BE PAID ON 7 TH YEAR. PVDAF = PVAF (12%, 5) X PVF (12%, 2) = 2.874 LR 2.874 LR = 1000, LR = 348/- PER 1000 PAYABLE EACH YEAR STARTING FROM 3 RD YEAR
LET CHECK IT YEAR INSTALMENT LEASE RENT PVF @ 12% PRESENT VALUE 1 - - 0.8928-2 - - 0.7972-3 1 348.00 0.7117 247.67 SEE NOTE BELOW 4 2 348.00 0.6355 221.15 5 3 348.00 0.5674 197.46 6 4 348.00 0.5066 176.30 7 5 348.00 0.4523 157.40 999.98 IF IT HAS BEEN ASKED IN THE QUESTION TO COMPUTE LEASE RENT PAYABLE AS ON TODAY I.E. AT YEAR-0 THEN FV = PV (1+R) N 348 = PV (1.12) 3 PV = 248 --------------- BELL SHAPED LEASE RENT STANDARD NORMAL PROBABILITY DISTRIBUTION DIAGRAM EXAMPLE: LIFE IS 5 YEARS. THEN, 1 ST YEAR S & 5 TH YEAR S LEASE RENT SHALL BE SAME. 2 ND YEAR S & 4 TH YEAR S LEASE RENT SHALL BE SAME. 3 RD YEAR S LEASE RENT SHALL BE HIGHEST. DESIRED RATE OF RETURN IS 12%, FIVE ANNUAL LEASE PAYMENT WILL BE STEPPED UP BY 25% THEN BY 40% & SUBSEQUENTLY STEPPED DOWN IN REVERSE ORDER.
LET US ASSUME THAT LEASE RENT = LR YEAR LEASE RENT PVF @ 12% PRESENT VALUE 1 1.00 0.8928 0.89 2 1.25 0.7972 1.00 3 1.75 0.7117 1.25 4 1.25 0.6355 0.79 5 1.00 0.5674 0.57 4.50 4.50 LR = 1000 LR FOR 1 ST YEAR = Rs. 222/- LET US CHECK IT YEAR LEASE RENT PVF @ 12% PRESENT VALUE 1 222.00 0.8928 198.20 2 277.50 0.7972 221.22 3 388.50 0.7117 276.50 4 277.50 0.6355 176.35 5 222.00 0.5674 125.96 998.23 IF TAXATION IS NOT APPLICABLE: THERE IS NO IMPORTANCE OF DEPRECIATION FOR THE LESSOR. EXAMPLE: COST OF ASSETS 4, 20,000/-, LEASE RENT 90,000/- PER YEAR, S.V. 50000/- SHOULD HE ACCEPT THE LEASING THE ASSETS IF COST OF CAPITAL IS 7%. HERE WE NEED TO CALCULATE THE RATE OF RETURN TO THE LESSOR (R) IF R > Ke, ACCEPT THE LEASING OPTION OTHERWISE REJECT. -4, 20,000 + 90,000 X PVAF (R%,5) + 50,000 X PVF (R%, 5 TH ) = ZERO BY USING TRIAL & ERROR METHOD: NPV @ 5% = 8830 WHILE NPV @ 6% -3519 BY INTERPOLATION: 5.72% HERE RETURN TO THE LESSOR IS LESS THAN HIS COST OF CAPITAL THEREFORE, REJECT THE PROPOSAL. HIGHER THE DISCOUNTING RATE LOWER THE NPV LOWER THE DISCOUNTING RATE HIGHER THE NPV, THEREFORE, WHERE NPV COMES VE WE SHOULD DISCOUNT WITH A LOWER RATE TO BRING THE NPV EQUAL TO ZERO. HINT TO START TRIAL & ERROR METHOD: HIRE PURCHASE FROM THE POINT OF VIEW OF HIRE PURCHASER (WHO PURCHASED THE H.P.ASSET) CASH UNDER HIRE PURCHASE OPTION
1. INITIAL CASH a. OUT OF DOWN PAYMENT 2. ANNUAL CASH a. OUT OF HIRE INSTALMENTS (PRINCIPAL + INTEREST) b. IN OF TAX BENEFIT ON HIRE CHARGES (INTEREST) c. IN OF TAX BENEFIT ON DEPRECIATION (AVAILABLE FROM 1 ST YEAR) 3. TERMINAL CASH a. IN OF SALVAGE VALUE b. TAX EFFECT ON CAPITAL GAIN/ LOSS HIRE PURCHASE Vs LOAN OPTION UNDER LOAN OPTION, LOAN AMORTISATION TABLE ARE PREPARED TO DIFFERENTIATE THE AMOUNT OF PRINCIPAL AND INTEREST INCLUDED IN THE INSTALMENT. THE AMOUNT OF INSTALEMNT IS CALCULATED BY THE FORMULA OF PRESENT VALUE OF ANNUITY (PVA) WHICH IS AS FOLLOWS: PVA = ANNUITY X PVAF (R%, N) OR PVA = ANNUITY X PVADF (R%, N) HERE ANNUITY = INSTALMENT (INCLUSIVE OF PRINCIPAL AND INTEREST). FORMULA OF PRESENT VALUE OF ANNUITY USES REDUCING RATE OF INTEREST TO CALCULATE THE ANNUITY OR SAY THE RATE OF INTEREST ARRIVED AT BY USING THIS FORMULA IS THE REDUCING RATE OF INTEREST.REDUCING RATE OF INTEREST MEANS INTEREST ON REDUCING PRINCIPAL. THE FORMULA OF PVA IS NOT APPLICABLE USING FIXED RATE TO DIFFERENTIATE THE AMOUNT OF PRINCIPAL AND INTEREST INCLUDED IN THE INSTALMENT. THEREFORE WE SHALL DETERMINE THE E.M.I. BASED ON SUCH FIXED RATE OF INTEREST AND PUT THIS E.MI. IN THE FORMULA OF PVA TO DETERMINE THE REDUCING RATE OF INTEREST. WHAT IS FLAT RATE? IF THE FLAT RATE OF INTEREST IS 10% P.A. ON PRINCIPAL OF Rs. 1,00,000/- AND LIFE IS 5 YEARS IT MEANS TOTAL 10% X 5 YEARS = 50% I.E. 50,000/- INTEREST SHALL BE PAID DURING THE TERM OF 5 YEARS. TOTAL PRINCIPAL + TOTAL INTEREST SHALL BE PAID EQUALLY IN 5 YEARS THEREFORE 1,50,000/- 5 = 30,000/- IS THE YEARLY INSTALMENT. HOWEVER, IT DOES NOT MEAN 20,000/- IS THE PRINCIPAL & 10,000 IS THE INTEREST. WE NEED TO CONVERT THE FLAT RATE INTO REDUCING RATE (OR SAY CONVERSION OF TOTAL INTEREST INTO YEARLY INTEREST SO THAT TAX BENEFIT THEREON CAN BE CALCULATED ACCORDINGLY, SINCE TAX BENEFIT IS AVAILABLE ON THE YEARLY INTEREST) OFCOURSE YEARLY INTEREST SHALL GO ON REDUCING YEAR BY YEAR. FORMULA FOR CALCULATING E.M.I. UNDER FLAT RATE E.M.I. = PRINCIPAL + TOTAL INTEREST NO. OF INSTALMENTS WHERE TOTAL INTEREST = PRINCIPAL X RATE X N [SIMPLE INTEREST = P X R% X T] E.M.I. = PRINCIPAL + PRINCIPAL X R% X T PRINCIPAL (1+RXT) NO. OF INSTALEMNTS NO. OF INSTALMENTS
E.MI. = PRINCIPAL (1+.RXT) WHERE R IS IN DECIMAL NO. OF INSTALMENTS NOW PUT THIS ANNUITY (E.MI.) IN FORMULA OF PVA TO DETERMINE THE REDUCING RATE OF INTEREST PVA = ANNUITY X PVAF (R%, N) 1,00,000 = 35,000 X PVAF (R%, 4) BY TRIAL & ERROR AND INTERPOLATION WE GET 15% AS REDUCING RATE WHILE FLAT RATE IS ONLY 10% [NOTE: REDUCING RATE IS PREFERRED ON THE PRINCIPAL AMOUNT.] WHAT IS THE USE OF REDUCING RATE? : TO PREPARE LOAN AMORTISATION TABLE. WHY LOAN AMORTISATION TALBE IS PREPARED? : TO DIFFERENTIATE THE AMOUNT OF PRINCIPAL AND INTEREST INCLUDED IN THE INSTALMENT. WHY WE NEED TO DIFFERENTIATE THE AMOUNT OF PRINCIPAL AND INTEREST INCLUDED IN THE INSTALMENT? TO CALCULATE THE TAX BENEFIT ON INTEREST CHARGED ON THE BASIS OF REDUCING RATE. FINALLY REDUCING RATE IS USED TO DETERMIN YEARLY INTEREST AND THE TAX BENEFIT ON SUCH YEARLY INTEREST. YEAR E.M.I. OP. PRIN. INTEREST @ 15% CLOS. PRINCIPAL 1 35,000.00 1,00,000.00 15,000.00 80,000.00 2 35,000.00 80,000.00 12,000.00 57,000.00 3 35,000.00 57,000.00 8,550.00 30,550.00 4 35,000.00 30,550.00 4,450.00 1,40,000.00 40,000.00 EXAMPLE: IF FLAT RATE IS GIVEN AND THE INSTALMENTS ARE PAYABLE MONTHLY FOR A PERIOD OF SAY 4 YEARS. FIRST WE SHALL CALCULATE THE ANNUITY (EMI) PER MONTH AS PER THE FLAT RATE BY USING THE FOLLOWING FORMULA: NOW PUT THIS E.MI. IN FORMULA OF PVA TO DETERMINE THE REDUCING RATE OF INTEREST PVA = ANNUITY PER MONTH X PVAF (R% 12, N X 12) OR PVA = ANNUITY PER MONTH X PVADF (R% 12, N X 12) AS THE CASE MAY BE [NOTE: HERE RATE ARE ADJUSTED ACCORDING TO FREQUENCY OF INSTALMENT] BY TRIAL & ERROR AND INTERPOLATION WE WILL GET THE REDUCING RATE P.A. PER MONTH (NOMINAL RATE). THEREAFTER, LOAN AMORTISATION TABLE SHALL BE PREPARED (USING THIS NOMINAL RATE P.A. PER MONTH) FOR 48 MONTHS TO DIFFERENTIATE PRINCIPAL AND INTEREST AMOUNT. THIS PROCESS SHALL BE LENGTHY IN TERMS OF TRAIL & ERROR FOR CALCULATING R%.
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