Solutions - Arka Roy 1) A) ELSS scheme Equity Growth scheme 1-Apr-06-3000 1-May-06-3000 1-Jun-06-3000 1-Jul-06-3000 1-Jul-06-7000 1-Aug-06-3000 1-Aug-06-7000 1-Sep-06-3000 1-Sep-06-7000 1-Oct-06-3000 1-Oct-06-7000 1-Nov-06-3000 1-Nov-06-7000 1-Dec-06-3000 1-Dec-06-7000 1-Jan-07 522 1-Jan-07 197 1-Feb-07-3000 1-Feb-07-7000 1-Mar-07-3000 1-Mar-07-7000 1-Apr-07-3000 1-Apr-07-7000 1-May-07-3000 1-May-07-7000 1-Jun-07-3000 1-Jun-07-7000 1-Jul-07-3000 1-Jul-07-7000 1-Aug-07-3000 1-Aug-07-7000 1-Sep-07-3000 1-Sep-07-7000 1-Oct-07-3000 1-Oct-07-7000 1-Nov-07-3000 1-Nov-07-7000 1-Dec-07-3000 1-Dec-07-7000 1-Jan-08 12278 1-Jan-08 95654 1-Feb-08-3000 1-Feb-08-7000 1-Mar-08-3000 1-Mar-08-7000 1-Apr-08-3000 1-Apr-08-7000 1-May-08-3000 1-May-08-7000 1-Jun-08-3000 1-Jun-08-7000 1-Jul-08-3000 1-Jul-08-7000 1-Aug-08-3000 1-Aug-08-7000 1-Sep-08-3000 1-Sep-08-7000 1-Oct-08-3000 1-Oct-08-7000 1-Nov-08-3000 1-Nov-08-7000 1-Dec-08-3000 1-Dec-08-7000 1-Jan-09 95140 1-Jan-09 107670 xirr 11.9% 4.7% FPSB India/Public 1
2) A) Deposit Interest Deposit 1-Apr-06 5000 33.33 5000*0.08/12 1-May-06 5000 66.67 10000*0.08/12 1-Jun-06 5000 100 15000*0.08/12 1-Jul-06 5000 133.33 20000*0.08/12 1-Aug-06 5000 166.67 25000*0.08/12 1-Sep-06 5000 200 30000*0.08/12 1-Oct-06 5000 233.33 35000*0.08/12 1-Nov-06 5000 266.67 40000*0.08/12 1-Dec-06 5000 300 45000*0.08/12 1-Jan-07 5000 333.33 50000*0.08/12 1-Feb-07 5000 366.67 55000*0.08/12 1-Mar-07 5000 400 60000*0.08/12 2600.00 62600.00 Balance on 1st April 2007 This activity of fresh contribution with residual interest will continue for 15 years until matutity of the Account on 1st April, 2022. For balance in each PPF A/c as on 1st April 2009 Alternatively, nper 2 1st April 2008 130208 62600*1.08+62600 rate 0.08 1st April 2009 203225 130208*1.08+62600 pmt 62600.00 1st April 2010 282083 mode 0 1st April 2011 367249 pv 62600 1st April 2012 459229 1st April 2009 203,225 1st April 2013 558567 1st April 2014 665853 For balance in each PPF A/c as on 31st March 2022 1st April 2015 781721 nper 15 1st April 2016 906859 rate 0.08 1st April 2017 1042008 pmt 62600 1st April 2018 1187968 mode 0 1st April 2019 1345606 pv 62600 1st April 2020 1515854 1st April 2022 1,898,300 2nd April 2021 1699722 3rd April 2022 1898300 1699722*1.08+62600 3) A) Arka Current annual gross salary 2520000 210000*12 Post-tax salary 2066400 2520000*0.82 Salary to be replaced 1239840 2066400*0.6 Rate of growth of salary 0.05 p.a. FPSB India/Public 2
Rate of discounting 0.07 p.a. Net rate of discounting 0.019048 p.a. (1+0.07)/(1+0.05)-1 Term 20 years Present Value of replaceable post-tax salary 20460728 PV(0.019048,20,-1239840,0,0) Gap in life insurance 15460728 20460728-5000000 Shamli Current annual gross salary 720000 60000*12 Post-tax salary 648000 720000*0.9 Salary to be replaced 388800 648000*0.6 Rate of growth of salary 0.05 Rate of discounting 0.07 Net rate of discounting 0.019048 (1+0.07)/(1+0.05)-1 Term 20 Present Value of replaceable post-tax salary 6416256 PV(0.019048,20,-388800,0,0) Gap in life insurance 4416256 6416256-2000000 4) A) 30-Apr-06-200000 31-May-07-240000 31-Dec-07-50000 30-Apr-08-280000 27-Feb-09 850000 0.0607323 Return per annum effective This can be calculated by using XIRR function of Excel 0.0049254 Return per month effective (1+0.0607323)^(1/12)-1 Value of investment on 30th April 2009 858394 850000*(1+0.0049254)^2 Induction expenses of Rs. 6,50,000 withdrawn from scheme Remaining value of investment on 30th April 2009 208394 858394-650000 Value of investment on 31st May 2009 209420 208394*(1+0.0049254) We require present value of three series of payments a) 12 monthly payments of Rs. 20,000 each at effective monthly rate of liquid scheme FPSB India/Public 3
233635 PV(0.0049254,12,-20000,0,1) b) 12 monthly payments of Rs. 22,000 each at effective monthly rate of liquid scheme discounted by one year to 31st May 2009 242284 PV(0.0049254,12,-22000,0,1)/(1+0.0607323) b) 12 monthly payments of Rs. 24,200 each at effective monthly rate of liquid scheme discounted by two years to 31st May 2009 251253 PV(0.0049254,12,-24200,0,1)/(1+0.0607323)^2 Total funds required for the 3-year period beginning 31st May 2009 727172 251253+242284+233635 Additional funds required to be invested on 31st May, 2009 517752 727172-209420 5) A) Principal o/s Interest Princ comp. Principal outstanding 203827 Month 0 tenure 72 months 202005 Month 1 2378 1822 rate 0.011666667 p.m. 200162 Month 2 2357 1843 pmt 4200 p.m. 198297 Month 3 2335 1865 pv 203827 196410 Month 4 2313 1887 194,502 Month 5 2291 1909 192,571 Month 6 2269 1931 190,618 Month 7 2247 1953 188,642 Month 8 2224 1976 186,642 Month 9 2201 1999 184,620 Month 10 2177 2023 182,574 Month 11 2154 2046 180,504 Month 12 2130 2070 178,410 Month 13 2106 2094 176,291 Month 14 2081 2119 174,148 Month 15 2057 2143 171,980 Month 16 2032 2168 169,786 Month 17 2006 2194 167,567 Month 18 1981 2219 165,322 Month 19 1955 2245 163,051 Month 20 1929 2271 160,753 Month 21 1902 2298 158,428 Month 22 1875 2325 156,077 Month 23 1848 2352 153,697 Month 24 1821 2379 151,291 Month 25 1793 2407 FPSB India/Public 4
148,856 Month 26 1765 2435 146,392 Month 27 1737 2463 143,900 Month 28 1708 2492 141,379 Month 29 1679 2521 138,828 Month 30 1649 2551 136,248 Month 31 1620 2580 133,638 Month 32 1590 2610 130,997 Month 33 1559 2641 128,325 Month 34 1528 2672 125,622 Month 35 1497 2703 122,888 Month 36 1466 2734 120,122 Month 37 1434 2766 117,323 Month 38 1401 2799 114,492 Month 39 1369 2831 111,627 Month 40 1336 2864 108,730 Month 41 1302 2898 105,798 Month 42 1269 2931 102,833 Month 43 1234 2966 99,832 Month 44 1200 3000 96,797 Month 45 1165 3035 93,726 Month 46 1129 3071 90,620 Month 47 1093 3107 87,477 Month 48 1057 3143 84,298 Month 49 1021 3179 81,081 Month 50 983 3217 77,827 Month 51 946 3254 74,535 Month 52 908 3292 71,205 Month 53 870 3330 67,835 Month 54 831 3369 64,427 Month 55 791 3409 60,978 Month 56 752 3448 57,490 Month 57 711 3489 53,960 Month 58 671 3529 50,390 Month 59 630 3570 46,778 Month 60 588 3612 Total 94951 157049 252000 The sale proceeds would be lower by Rs. 6778 than the principal outstanding 46778-40000 FPSB India/Public 5
6) A) pv 5400000 Princ. o/s Month Interest Princ comp. rate 0.008125 5400000 0 nper 216 5390749 1 43875 9251 521402 pmt 53126 5381423 2 43800 9326 371402 150000 PMT(0.008125,216,-5400000,0,0) 5372021 3 43724 9402 0.71 29% 5362543 4 43648 9478 150000/521402 5352987 5 43571 9555 5343354 6 43493 9633 5333643 7 43415 9711 5323853 8 43336 9790 5313983 9 43256 9870 5304033 10 43176 9950 5294003 11 43095 10031 5283890 12 43014 10112 521402 116110 7) A) India range 1200000 1500000 Payoli 15 years Abroad range 2500000 3000000 Shantanu 10 years Funds required for Shantanu Beginning of 11th year 1233537 (250000/3)*(1.04)^10 Beginning of 12th year 1282878 (250000/3)*(1.04)^11 Beginning of 13th year 1334194 (250000/3)*(1.04)^12 PV of funds in the beginning of 11th year at 9.5% pa discount rate 3517847 1233537+(1282878/1.095)+(1334194/1.095^2) Funds required for Payoli Beginning of 16th year 1586085 (1500000/3)*(1.08)^15 Beginning of 17th year 1712971 (1500000/3)*(1.08)^16 Beginning of 18th year 1850009 (1500000/3)*(1.08)^17 PV of funds in the beginning of 11th year at 9.5% pa discount rate 2981358 (1586085/1.095^5)+(1712971/1.095^6)+(1850009/1.095^7) Total PV of funds required in the beginning of 11th year 6499206 2981358+3517847 This corpus is to be accumulated over 10 years (120 months) by way of monthly contributions FPSB India/Public 6
in a balanced fund investment vehicle yielding 9.5% pa effective p a effective = 0.007592 pm effective (1.095)^(1/12)-1 pmt = 33126 PMT(0.007592,120,0,-6499206,1) 8) A) Current monthly expenses 70,000 Expenses inflation adjusted after 20 yrs 185731 70000*(1.05)^20 Reduced expenses post-retirement 120725 March, 2029 185731*0.65 Pension fund rate of investment = Inflation rate post-retirement = Post-retirement period for annuity = 0.075 per annum effective = 0.006045 per month effective (1+0.075)^(1/12)-1 0.05 pa = 0.004074 per month effective (1+0.05)^(1/12)-1 240 months PV of annuity at the time of retirement 23133590 March, 2029 120725*(1+0.006045)*(((1+0.006045)^(240))-((1+0.004074)^(240)))/((0.006045-0.004074)*(1+0.006045)^(240)) This is to be done in such a way that first 5 years are invested @ 10% pa, next 10 years @ 8.5% pa and last 5 years @ 7% pa while increasing investment amount by 50% of the previous amount at every stage Let the monthly investment in the initial 5 years be Rs. 100 First 5 years Rate p.a. 0.10 Rate p.m. 0.00797 (1+0.1)^(1/12)-1 FV after 5 years 7717 FV(0.00797,60,-100,0,1) Next 10 years (The per month contribution increases by 50% of Rs. 100, i.e. Rs. 150) This FV = 7717 after 5 years is the PV for contributions of Rs. 150 accumulated in a fund yielding 8.5% pa Next 10 years Rate p.a. 0.085 Rate p.m. 0.00682 (1+0.085)^(1/12)-1 FV after 15 years 45366 FV(0.00682,120,-150,-7717,1) Last 5 years (The per month contribution increases by 50% of Rs. 150, i.e. Rs. 225) This FV = 45,366 after 15 years is the PV for contributions of Rs. 225 accumulated in a fund yielding 7% pa FPSB India/Public 7
Last 5 years Rate per ann 0.070 Rate per mon 0.00565 (1+0.07)^(1/12)-1 FV after 20 years 79737 FV(0.00565,60,-225,-45366,1) This FV should equate with the desired corpus to be amassed i.e. Rs. 23,133,590 Using Unitary method, the monthly contribution comes to 29012 23133590/79737*100 9) A) Current wedding cost of both the children 3000000 1500000*2 Saving on account of joint wedding function 2250000 3000000*0.75 Wedding cost (inflated) after 20 years 5969920 2250000*(1.05)^20 Option 1 Invest quarterly Rs 24,100 in a Growth Equity MF scheme for 15 years and allow it to grow in next 5 years Per annum yield 0.11 Per quarter yield 0.026433 (1+0.11)^(1/4)-1 15 years has 60 such quarters Value of corpus after 15 years 3541724 FV(E307,60,-24100,0,1) This is allowed to grow at 11% for the next 5 years Value after 20 years 5968011 3541724*(1.11)^5 Option 2 Start PPF A/c. in both children's name and invest Rs. 35,000 cumulatively per quarter for 15 years, extend maturity for the balance term without further contribution Deposit Apr-09 35000 233.33 35000*0.08/12 May-09 233.33 35000*0.08/12 Jun-09 233.33 35000*0.08/12 Jul-09 35000 466.67 (35000+35000)*0.08/12 Aug-09 466.67 (35000+35000)*0.08/12 Sep-09 466.67 (35000+35000)*0.08/12 Oct-09 35000 700.00 (35000+35000+35000)*0.08/12 Nov-09 700.00 (35000+35000+35000)*0.08/12 Dec-09 700.00 (35000+35000+35000)*0.08/12 Jan-10 35000 933.33 (35000+35000+35000+35000)*0.08/12 Feb-10 933.33 (35000+35000+35000+35000)*0.08/12 Mar-10 933.33 (35000+35000+35000+35000)*0.08/12 7000.00 FPSB India/Public 8
147000 Balance in March 2010 This activity of fresh contribution with residual interest will continue for 14 more years until March 2024 The maturity proceeds will be available on March 31st, 2025 provided a minimum of Rs. 500 for the final year is contributed in each account. For balance in both PPF A/c as on 31st March 2024 nper 14 rate 0.08 pmt 147000 mode 0 pv 147000 March 31st 2024 3991361 FV(0.08,14,-147000,-147000,0) Maturity proceeds March 31st 2025 4310750 (3991361*1.08)+1000*0.08 This account is extended for a term of five years without contributions but the whole money is withdrawn at the end of 4 more years, i.e. on March 31st, 2029 5864727 4310750*(1.08)^4 Option 3 Invest Rs. 30,000 quarterly in an equity-oriented balanced fund yielding 9% p.a. for 15 years and allow the accumulated sum to grow in the same fund for 5 more years Per annum yield 0.09 Per quarter yield 0.021778 (1+0.09)^(1/4)-1 Accumulated sum after 15 years Amount after 20 years 3719362 FV(0.021778,60,-30000,0,1) 5722699 3719362*1.09^5 Option 4 Start PPF A/c. in both children's name and invest Rs. 15,000 in each account per quarter for 15 years, this amount is invested in Equity Growth scheme of a mutual fund yielding 11% p.a. Apr-09 15000 100.00 May-09 100.00 Jun-09 100.00 Jul-09 15000 200.00 Aug-09 200.00 Sep-09 200.00 Oct-09 15000 300.00 Nov-09 300.00 Dec-09 300.00 Jan-10 15000 400.00 FPSB India/Public 9
Feb-10 400.00 Mar-10 400.00 3000.00 63000 Balance in March 2010 This activity of fresh contribution with residual interest will continue for 14 more years until March 2024 The maturity proceeds will be available on March 31st, 2025 provided a minimum of Rs. 500 for the final year is contributed in each account. For balance in both PPF A/c as on 31st March 2024 nper 14 rate 0.08 pmt 63000 mode 0 pv 63000 March 31st 2024 1,710,583 Maturity proceeds March 31st 2025 1847470 10) D) Maturity proceeds in both accounts 3694940 Amount to be received after 4 years, i.e. on March 31st 2029 after investing both PPF A/c maturity proceeds in Equit Growth scheme yielding 11% pa of a mutual fund 5609179 11) A) 12) D) 13) A) 14) D) FPSB India/Public 10
Solutions - Anil Bhai 15) C) Net Profit as per projection= 3890000 Salary paid to working partners: (10000*12)*7= 840000 (@10000 per month to all 7 working partners) Book Profit 4730000 840000+3890000 Maximum Remunration Allowed to working partners= On first 75000@90%= 67500 75000*0.9 Next 75000@60%= 45000 75000*0.6 on balance @40%= 1832000 (4730000-150000)*0.4 Total 1944500 Max allowable remunration divided equally in all working partners= 1944500/7= 277786 annually 1944500/7 23149 monthly 277786/12 So approximate new salary of Anil (& all pertners) should be Rs. 23,000 per month 16) A) Amount CII Original Gift on 13-04-1981 200000 100 1164000 Gift on 13-04-1994 100000 259 224710 Gift on 13-04-1995 100000 281 207117 Gift on 13-04-1996 100000 305 190820 Gift on 13-04-1997 100000 331 175831 Gift on 13-04-1998 100000 351 165812 Gift on 13-04-1999 100000 389 149614 Gift on 13-04-2000 100000 406 143350 Gift on 13-04-2001 100000 426 136620 Gift on 13-04-2002 100000 447 130201 Gift on 13-04-2003 100000 463 125702 Gift on 13-04-2004 100000 480 121250 Gift on 13-04-2005 100000 497 117103 3052130 Indexed Cost= 3052130 Sale Price= 4850000 LTCG= 1797870 4850000-3052130 Invested in new residential house= 2350000 LTCG Exempted= 871133 1797870*2350000/4850000 Taxable LTCG= 926737 1797870-871133 Tax on LTCG= 185347 926737*0.2 Or 185350 FPSB India/Public 11
17) A) Interest from firm 157590 Income from UK 320000 exempt (Exempt being received in UK and Naveen is non resident STCG (u/s 111A) 96414 Taxable @15% in FY 2008-09) 80C Invt 60000 Normal Income= (157590-60000) 97590 157590-60000 Tax payable on normal income Nil STCG @15% 14462 96414*0.15 E Cess 434 14462*0.03 Total 14896 434+14462 Or 14900 18) A) Rs. 5 lakh shall be added to Apoorva s income for FY 2008-09 and further the interest paid by partnership firm to her loan shall be her individual income of all respective years because as of date of gift this amount to Apoorva by Anil, she was not a relative of Anil. 19) A) Purchase Price on 30/09/2006= 6215600/1000= 6215.6 per bond As of date of purchase time till maturity= 6.5 years So YTM at the time of purchase= PV= 6215.6 N= 6.5 FV= 10000 R= 7.59% RATE(6.5,0,-6215.6,10000,1) Current Yield= (7.59%-.80%)= 6.79% 7.59%-0.8% Time Till Maturity Bal= 4.00 years Current Selling Price=10000/1.0679^4= 7689.14 10000/1.0679^4 Buying Price= 6215.60 per bond Selling Price= 7689.14 per bond Holding Period= 2.5 years CAGR= 8.88% p.a. RATE(2.5,0,-6215.6,7689.14,1) 20) B) Today is: 31-Mar-2009 Inflation= 0.06 pa 0.004867551 pm (1+0.06)^(1/12)-1 Return from balanced fund = 0.075 pa 0.006044919 pm effective ((1+0.075)^(1/12))-1 FPSB India/Public 12
Outflows Required: 1-Jul-2009 2500000 2536684.615 2491232 1-Jan-2012 2500000 2934479.893 2405237 1-Jan-2015 2500000 3495012.505 2305951 Total PV required= 7202420 Funds Available: PV on 01-04-2009 @0.075 pa 1/4/2009 2500000 2500000 1/4/2011 1200000 1038399 1200000/(1+0.075)^2 1/4/2014 1500000 1044838 1500000/(1+0.075)^5 Total PV available= 4583237 PV= 2619183 R= 0.006044919 pm N= 69 months FV= 0 Mode= 1 Begin Pmt= -46,258 or 46300 pm PV of shortfall = 2619183 7202420-4583237 21) A) Firm is liable to pay gratuity to the family of the employee as in case of death or disablement no service tenure condition is there and it's also not mendatory that cause of death should be official only 22) A) 23) C) (Rule 808) 24) B) 25) B) V=D1/(K-G) G=Retention Ratio * ROE Retention Ratio= 1-Divident Payout ratio Growth Rate= (1-Divident Payout Ratio) * ROE G=(1-0.1)*0.15 ie 0.135 Value of Share= 1/(0.16-0.135) 40 FPSB India/Public 13
26) B) The portfolio weight for PQR Ltd is 300/500=60% and for STP Ltd, the weight is 200/500=40%. The expected return on the portfolio is 0.6(18%) + 0.4(12%) = 15.6%. The variance is (0.6)^2 * (0.2)^2 + (0.4)^2 * (0.15)^2 + (2(0.6) * (0.4)) * (0.6)(0.2)(0.15) = 0.02644. The Standard Deviation of Portfolio Return is 16.32% (0.02664)^(1/2) 27) B) 28) A) 29) B) FPSB India/Public 14