Question

Adam wants to prepare in order to enter retirement in 30 years. He expects that he will be in retirement for 25 years and he wants to have a monthly income of $2,500 in order to support his lifestyle. At the end of that period he wants to have $20,000 left to take care of end of life expenses. a) How much will he need to have at the time of retirement to accomplish these goals if he car earn 3 % annually on these funds? b) He currently has 25,000 in a savings account that earns 4 % annually and is compoundin monthly. If he does not touch that money till retirement, how much would be in his savirn account at that time? c) How much would he need to invest monthly on an annuity that is earning 8% annually in om to meet his retirement goals, assuming that he puts no starting money in the annuity? (20 a) PV PMT 2500 i = n ころ0

Answer 1

answer a) After retirement required fund ,

Monthly Payment (PMT)= 2500

Time = 25 years

Number of payment (nper) = 25*12= 300 months

Payment at end (FV)= 20,000

Return (r) = 3% annual = 3/12=0.25%(monthly)

retirement required fund = PV(0.25%,300,-2500,-20000) = $ 536,647.31

Answer b)Value of saving account at the retirement age ,

Return (r) = 4% annual = 4/12=0.333%(monthly)

Present value(PV) =$ 25,000

Time (nper)= 30 year = 30*12 = 360

Future value = FV(0.333%,360,0,-25000) = $ 82,738.43.

Answer c) so , addition fund required for retirement = $ 536,647.31- $ 82,738.43= 453,908.88

Monthly investment

Rate (r) = 8% annual = 8/12= 0.666%(monthly)

Future value= $453,908.88

Number of payment (Nper) = 30*12=360

PMT= PMT(0.667%,360,0,-453908.88) = $ 304.32.

Section B

Answer 1) The concept is two stage dividend discount model ,

$V=\sum_{i=1}^{5}\frac{D_i}{(1+r)^i}+\frac{D_5(1+g)}{(r-g)*(1+r)^5}$

Year	0	1	2	3	4	5
D	2	2.2	2.398	2.58984	2.74523	2.882492
growth		10%	9%	8%	6%	5%
Discounted Dividend		1.929825	1.845183133	1.748068	1.625397	1.497076
r	14%
1st stage value	8.645549

2nd stage = 1.497076*(1+0.04) / (0.14-0.04)*(1+0.14)^5 = 8.086357

Value of stock =8.645549+8.086357= 16.73191 = $16.74