Question

Question 1: An annuity pays $100 at the end of each period for 10 periods. Set up the CFs in an Excel spreadsheet as follows: 0 1 100 2 100 3 100 4. 100 5 100 6 100 7 100 8 100 9 100 10 100 For these cash flows the appropriate discount rate is 6%. What is the PV of this series of cash ws? Solve the problem using the following approaches: a. Estimate the PV as the sum of the PVs of each of the CFs. b. Use the annuity formula. c. Use the excel built-in function PV.

Answer 1

Solution r=Rate of Interest=6% n=No of period A=Annul inflow=$100 Part a) Statement showing computation of the present value of the cash flows as the sum of the PV's Present value factor @6% Present value amount (B) (AXB) 0.94340 $ 94 1 2 0.8900 $ 89 3 0.8396 $ 84 4 0.7921 $ 79 5 0.7473 $ 75 Period Cash inflow Present value factor @6% (n) (A) (B) $ 100 = 1/(1+r)^n "=1/(1+6%)^1 S 100 = 1/(1+r)^n l'=1/(1+6%)^2 S 100 =1/(1+r)^n = 1/(1+6%)^3 S 100 = 1/(1+r)^n l'=1/(1+696)*4 5 S 100 = 1/(1+r)^n = 1/(1+6%)^5 S 100 = 1/(1+r)^n = 1/(1+6%)^6 S 100 = 1/(1+r)^n '=1/(1+6%)*7 S 100 = 1/(1+r)^n '=1/(1+6%)*8 S 100 = 1/(1+r)^n '=1/(1+6%)*9 S 100 = 1/(1+r)^n l'=1/(1+696) 10 Total Present value of cash inflows 0.7050 $ 70 7 0.6651 $ 67 col 0.62741 $ 63 9 0.5919 $ 59 10 0.5584 $ 56 S 736

Part B) Computation of Pv using Annuity formula = A x [1-1/(1+r)^n]/r =$100 x [1-1/(1+6%)*10]/6% = $100 X 7-3600 =$736 Hence the Pv of the annuity is $736

Part C) PV using Excel formula = PV(6%,10,-100,0,0) $ 736 Hence the PV using Excel built-in formula is $736