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Homework answers / question archive / 1) Pensions Meg's pension plan is an annuity with a guaranteed return of 4% per year (compounded quarterly)
1) Pensions Meg's pension plan is an annuity with a guaranteed return of 4% per year (compounded quarterly). She would like to retire with a pension of $10,000 per quarter for 5 years. If she works 21 years before retiring, how much money must she and her employer deposit each quarter? (Round your answer to the nearest cent.)
2) New York Times Co. (NYT) recently earned a profit of $1.71 per share and has a P/E ratio of 19.45. The dividend has been growing at a points 6.25 percent rate over the past six years. If this growth rate continues, what would be the stock price in six years if the P/E ratio remained unchanged? What would the price be if the P/E ratio increased to 22 in six years? (Round your answers to 2 decimal places.)
1) We can calculate the present value by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Present value
Rate = 4%/4 = 1% (quarterly)
Nper = 5*4 = 20 periods (quarterly)
Pmt = $10,000
FV = $0
Substituting the values in formula:
= -pv(1%,20,10000,0)
= $180,455.53
We can calculate the quarterly deposit by using the following formula in excel:-
=pmt(rate,nper,pv,-fv)
Here,
Pmt = Quarterly deposit
Rate = 4%/4 = 1% (quarterly)
Nper = 21*4 = 84 periods (quarterly)
PV = $0
FV = $180,455.53
Substituting the values in formula:
= pmt(1%,84,0,-180455.53)
= $1,380.98 Or $1,381
2) Computation of the stock price in six years (P6):-
Current stock price (P0) = (P/E ratio) * Earnings (E0)
= 19.45 * $1.71
= $33.26
EPS after 6 years (E6) = E0*(1+growth rate)^n
= $1.71 * (1+6.25%)^6
= $1.71 * 1.4387
= $2.46
P6 = (P/E ratio) * E6
= 19.45 * $2.46
= $47.85
Computation of the stock price in six years (P6) with new P/E:-
P6 = (P/E ratio) * E6
= 22 * $2.46
= $54.12
