Questions for Investment Planning, CFP

Following questions have been suggested by one of the reader. Hence I don’t own any of the question.

1. Mr. A is of 35 yrs with spouse and a kid of an age 5 yrs. His strategic asset allocation is 50:35:15 in equity, debt and liquid. He is able to invest rs 1.5lakh pa immediately to work various life goal. At age 40 the allocation would change to 40:50:10 in equity, debt and liquid asset with annual investment going up to 2.5 lakh for 5 more years. At age 45, for next 10 year he adapts the conservative wealth protection allocation 25:70:5 in eq, debt & liquid asset with 3 lakh pa investments. The per annum return expected in this stage are; from equity : 12%.11% & 10%, from debt : 9%,8% & 7%, from liquid asset : 6,5%,5.5% & 4.5%.What amount could he accumulate by his age 55 years?
a. 113.9 lakhs
b. 97.21 lakhs
c. 66.65 lakhs
d. 117.91 lakhs

SOLUTION:

	150000		FV	FV	FV
E	75000	12	$533,639.18	$899,213.05	$2,332,327.07
D	52500	9	$342,475.06	$503,208.23	$989,886.75
L	22500	6.5	$136,433.87	$178,313.61	$276,915.59
					$3,599,129.41
	250000		FV	FV
E	100000	11	$691,285.96	$1,793,017.74
D	125000	8	$791,991.13	$1,557,966.43
L	25000	5.5	$147,201.28	$228,599.08
				$3,579,583.24
	300000		FV
E	75000	10	$1,314,837.53
D	210000	7	$3,104,555.86
L	15000	4.5	$192,617.68
			$4,612,011.07	$11,790,723.72

2. Your client wants to buy a house in 3 years in an area where the current price are 60 lakhs appreciating at 8% pa. He can afford loan up to Rs 40 lakh. He has an FD of Rs 8 lakh which are maturing shortly. You find that reinvesting in FD would not fetch good return. You advice to shift the entire FD maturity to long run debt scheme, expected to return 12% pa for next 2 years. He can additionally invest rs 30000 pm for the goal which you advice to invest in equity which you expect to return 15% pa in the next 2 years. You shift the debt & equity accumulation to liquid fund returning 5% pa in the third year while additionally investing in that fund. You estimate achievement of own fund for house to be?
a. The difference between own fund required and available may swell over 16 lakh
b. Shortfall of 12.58 lakh in own fund after 3 yrs
c. Achieve the goal with surplus of 3 lakh
d. Shortfall of 6 lakh

SOLUTION: Solve this question using monthly nominal rate to get the exact answer.

CV	6000000	FD	800000	EQ	$844,063.05
3 Y VALUE	7558272	FV	1003520
LOAN	4000000			TOTAL	$1,847,583.05
DP REQUIRED	3558272
INVESTMENT VALUE WITH ADDITIONAL INVESTMENT	$23,10,475
SHORT	$12.48 L

3. Mr. A has gross annual salary of 9 lakh of which he saves 30% which include statutory EPF deduction, PPF and monthly systematic investment in long term MF scheme. Another 30% goes toward servicing of household & car loan & taxes. His financial planner advice him to accumulate 6 months household expense in liquid fund. HE change job and expect immediate rise of 20% in his gross income .You estimate that other heads would not change materially except his household expense which would rise by 5% due child education. How many months will it take to accumulate liquid reserve?
a. 25 months
b. 11 months
c. 14 months
d. 13 months

SOLUTION:

900000	INCOME	1080000
270000	EPF	270000
270000	LOAN	270000
360000	HOUSEHOLD	378000
	SAVINGS	162000
REQUIREMENT	189000
SAVINGS PA	162000
MONTHS	=189000/162000=1.16667*12 = 14

4. An individual start investing immediately for 10 year annually Rs 80000 in the ratio 70:30 in equity and debt products. He expects the return from equity and debt to be 12.5% pa & 9.5% pa. during this period. To protect the wealth he rebalance the portfolio in 40:60 of equity and debt after 10 yrs and invest in same ratio annually rs 1.5 lakh for next 10 years. The return expected from equity and debt in this period subsides to 10.5% pa and 7.5% pa respectively. What could be his total investment at the end of the entire tenure of his investment?
a. 60.38 lakh
b. 60.31 lakh
c. 70.42 lakh
d. 61.58 lakh

5. A bond with par value of rs 1000 and coupon rate of 11% (payable semi-annually, next coupon due immediately) and maturing after 5 years is available at Rs.942.50 in the market. If the coupon received can be reinvested till maturity at average rate of 8.5% pa. What could be realized rate of return from such investment if the bond is held till maturity?
a. 13.33%
b. 13.15%
c. 13.90%
d. 13.60%

SOLUTION:

	C	FV AT NOM RATE OF 8.5%
1	55	82.6984719
2	55	79.39332767
3	55	76.22027752
4	55	73.17404214
5	55	70.24955324
6	55	67.44194507
7	55	64.74654634
8	55	62.15887248
9	55	59.67461813
10	55	57.28965
11	55	55
		748.0473045
		1000
	TOTAL	1748.047304
	RY	13.150%

PV = 942.5, FV = 1178.04, N = 5, I/Y =?

6. An investor purchased 5000 units of an equity oriented MF scheme under dividend reinvestment scheme on 1st June 2012 at NAV of rs 18.46 along with systematic investment plan of rs 5000, each for 6 months. The SIP dates are 1st of every month beginning 1st July 2012. The NAV at which additional unit were bought through SIP were rs 19.06, rs 18.51, rs 17.23, rs 18.97, rs 16.75 and rs 17.95 on 15 October 2012. The scheme declared a dividend of 25% on face value of rs 10 per unit which record date being 21st October 2012. The NAV on 22nd October 2012 was rs 16.50. The investor redeemed all units on 28 January 2013 at a price of rs 19.10 . What holding period return was obtained by investor?
a. 27.83%
b. 23.58%
c. 15.89%
d. 18.46%

Solution:

DATE	AMT	NAV	UNITS
1-Jun-12	92300	18.46	5000
1-Jul-12	5000	19.06	262.3294858
1-Aug-12	5000	18.51	270.1242572
1-Sep-12	5000	17.23	290.1915264
1-Oct-12	5000	18.97	263.5740643
22-Oct-12	15215.55	16.5	922.1544445
1-Nov-12	5000	16.75	298.5074627
1-Dec-12	5000	17.95	278.551532
28-Jan-13	-144882	19.1	7585.432773
	122300	Total investment
	18.46%

Final step: (144882-122300)/122300 = 18.46%

7. Mr. B bought the house by availing a housing loan of rs 25 lakh for 15 yrs at a variable rate of interest. The initial rate was 8.5% & the fixed EMI was in May 2008. The finance company raise the rate to 9.25% pa effective from EMI due on April 2009. The finance company retain the same EMI but increased the outstanding tenure. Mr. B received a bonus of rs 2.5 lakh from her employer in May 2010. What amount she should prepare to invest to bring back tenure to original contract period with effect from June 2010?
a. 75,814
b. 111,215
c. 78,681
d. 109,543

SOLUTION:PV=2500000N=180

I/Y = 8.5/12

PMT = 24618

P1=1, P2=11

BAL = 2421238

PMT = 24618

I/Y = 9.25/12

N = ? 184.8

P1=1, P2=14

BAL = 2333570

PMT = 24618

N = 180-25 = 155

I/Y = 9.25/12

PV = 2222303

HENCE PREPAYMENT REQUIRED   = 2333570-2222303 = 111267 APPROX

8. You purchase 500 shares of a company at rs 205 per share on 1st July 2011. The dividend of rs 1100 and rs 1300 were received respectively in August 2011 and September 2012. On 1st January 2013 the share were sold for rs 1.15 lakh. Your holding period return comes to?

9. An investor allocated equal amount of rs 2 lakh each to bond, stock and gold ETF three years ago. His investment in bond has yielded coupon of rs 7500 every six months & is presently redeemable at rs 2.13 lakh. The stock portfolio is valued at rs 2.79 lakh. He has also received rs 2725 as dividend from stock in year one, rs 3125 in year two and rs 2965 lately. The gold ETF unit have a market value of rs 2.58 lakh. The coupon and dividend received remain in the bank saving account yielding an annual interest of 4.5%. If the inflation remained at 10.5%, 9.6% and 8.5% in those three year. What real rate of return he stands to generate on liquidation of entire portfolio?
a. 1.02% pa
b. 0.77% pa
c. 0.88% pa
d. 0.71% pa

10. A invested 1o lakh in beginning of year in equity, corporate bond, government sec and alternate investment in proportion 35:35:20:10. A year after making investment it generated  return which were 14%,10%,6%,16% respectively. If investor followed constant mix policy his plan of action would be?
a. Keep the portfolio under changed
b. Buy equity of rs 9800 and alternate investment of rs 4800 and sell corporate bond of rs 4200 and government sec of rs 10,400.
c. Increase the exposure of alternate investment and equity
d. Sell equity of rs 9800 and alternate investment of rs 4800 and buy corporate bond of rs 4200 and government sec of rs 10,400.

11. XYZ company paid dividend 2, recently of common stock; dividend expected to grow by 20% for next 3 years, after which expect to stabilize at 10% growth. If required rate of return is 15%. How much maximum price would you pay today to buy stock?
a. 82.5
b. 43.5
c. 52
d. 50