Finance Numericals

Lump Sum Cash Flow:  It is a single cash flow on which interest earn for fixed period. Multiple Cash Flows:  It is a fixed or uneven series of cash flows for fixed period. Formulas for Lump Sum and Multiple Cash Flows: Variables Formula PV FV/ (1+r)  n FV PV (1+r)  n N In(FV / PV)/In (1+r) R (FV /PV)  1/n -1 Where, FV =Future Value PV =Present Value N = Number of periods R = rate of interest Example 1:  Mr. Sharma deposit Rs.20000 for 12 years @7% compounded quarterly into saving a/c. Find out the future value of investment? FV = PV (1+r)  n = 20000 (1+0.0175)  48 =  45991.97 Example 2:  If someone wants to have Rs.10, 00,000 after his retirement then how much amount he would have to invest now @8% per annum compounded annually for 20 years? PV = FV / (1+r)  n = 10, 00,000 / (1+0.08)  20 = 10, 00,000 / 4.66095714 = 214548.20 Example 3:  Nikhil borrow Rs.500, 000 @

Perpetuity:   It is a fixed series of payments received in infinite periods. Example: Console bond has no maturity period and it pays fixed coupon. Growing Perpetuity:  It is a fixed series of payments receives at a constant growth rate for infinite periods.                              Deferred Perpetuity: It is fixed series of cash flows received at a future date.                                  Perpetuity Vs Annuity: In perpetuity payment received for infinite period and in annuity payment received for fixed period.The formula to calculate perpetuity and annuity is also different, in annuity the formula is  C[1-(1/(1+r) n /r) and the formula for perpetuity is C/r. Formula: Simple  perpetuity Growing   Perpetuity Deferred  Perpetuity Deferred Growing  Perpetuity PV C 1 /r C 1 /r-g PV p /(1+r) t PV GP /(1+r) t Where, C 1 = Initial cash flow R= rate per period G= growth rate

Growing Annuity :  It is a fixed series of cash flow for fixed time, where initial cash flow is growing at a constant rate. Deferred Annuity:   It is a fixed series of payments which is received in some future date. For example in retirement plan amount invested into annuity a/c and after completion of fixed period, payments are received by plan holder. Formulas: Growing Annuity Deferred Annuity Present Value (PV 0 ) P/r-g[1-(1+g)  n / (1+r)  n ] PV GA /(1+r)  t Future Value P[(1+r)  n -(1+g)  n /r-g] FV  GA *(1+r)  t Present Value (PV AD ) P/r-g[1-(1+g)  n / (1+r)  n ] (1+r) PV  G AD  /(1+r)  t Future Value  (FV  AD ) P[(1+r)  n -(1+g)  n /r-g](1+r) FV  G AD  *(1+r)  t Where, P = cash flows R = rate per period G = growth rate N= time period T= deferred time period PV G AD = Present Value of Growing Annuity Due PV GA = Present Value of Growing Annuity FV