Question

6. You won the big prize in the California lottery and you have to choose one of the following two payment plans:

Payment Plan 1: If you choose this payment plan, you will receive semiannual payments for a fixed period of time. The first payment of Rs. 150,000 will be paid on January 01, 2007 and it will grow by 2% every six months. You will receive the last payment on January 01, 2016

Payment Plan 2: If you choose this payment plan, you will receive yearly payments for 10 years. You will receive your first payment on January 01, 2007 and your last payment on January 01, 2016. However the payment amount in odd years is Rs. 200,000 whereas the payment amount in even years is Rs. 500,000.

Assuming the interest 8% compounded semiannually. If your decision is solely based on the present value of cash flows streams corresponding to the payment plans, which payment plan would you choose

Answer 1

Payment Plan -1

We need to find the present value as sum of $ 150000 PLUS PV of growing annuity

using the formula,

PV of the pmts.= 150000+(Pmt./(r-g))*(1-((1+g)/(1+r))^n)*(1+r)

where, PV of the pmts. ----- is the answer needed

Pmt.=the first pmt.= 150000*1.02

r= the semi-annual interest rate, ie. 8%/2= 4% or 0.04 per s/a period

g= growth rate per s/a period= 2%   or 0.02

n= no.of payment periods= leaving out the 1st one-- 19-1=18

so, plugging in the values, in the formula,

PV of the given pmts.=150000+((150000*1.02)/(0.04-0.02))*(1-((1+0.02)/(1+0.04))^18)=

2406577.79

PV as at Jan.1,2007

Payment Plan -2

AS the pmt. Amt. differs , for different years, we find the PV in a columnar calculation as follows:

Plan-2
No.of pmts.	Month	Year	Pmts.	PV F at 8%	PV at 8%
0	1-Jan	2007	200000	1	200000
1	1-Jan	2008	500000	0.92593	462962.963
2	1-Jan	2009	200000	0.85734	171467.7641
3	1-Jan	2010	500000	0.79383	396916.1205
4	1-Jan	2011	200000	0.73503	147005.9706
5	1-Jan	2012	500000	0.68058	340291.5985
6	1-Jan	2013	200000	0.63017	126033.9254
7	1-Jan	2014	500000	0.58349	291745.1976
8	1-Jan	2015	200000	0.54027	108053.7769
9	1-Jan	2016	500000	0.50025	250124.4836
				Total	2494601.80

Total PV for Plan -2 as at Jan 1,2007= $ 2494601.80

As the decision is solely based on the present value of cash flows streams corresponding to the payment plans,

PLAN-2 will be selected as the PV of its cash flows are more than that for Plan-1

Verification for

Plan-1
No.of pmts.	Month	Year	Growing amt.(2%)	PV F at 4%	PV at 4%
0	1-Jan	2007	150000	1	150000
1	jul1 1	2007	153000	0.96154	147115.38
2	1-Jan	2008	156060	0.92456	144286.24
3	jul1 1	2008	159181.2	0.88900	141511.51
4	1-Jan	2009	162364.8	0.85480	138790.13
5	jul1 1	2009	165612.1	0.82193	136121.09
6	1-Jan	2010	168924.4	0.79031	133503.38
7	jul1 1	2010	172302.9	0.75992	130936.01
8	1-Jan	2011	175748.9	0.73069	128418
9	jul1 1	2011	179263.9	0.70259	125948.43
10	1-Jan	2012	182849.2	0.67556	123526.34
11	jul1 1	2012	186506.1	0.64958	121150.84
12	1-Jan	2013	190236.3	0.62460	118821.01
13	jul1 1	2013	194041	0.60057	116535.99
14	1-Jan	2014	197921.8	0.57748	114294.92
15	jul1 1	2014	201880.3	0.55526	112096.94
16	1-Jan	2015	205917.9	0.53391	109941.23
17	jul1 1	2015	210036.2	0.51337	107826.97
18	1-Jan	2016	214236.9	0.49363	105753.38
				Total	2406577.79