Question

Problem #1: Time Value of Money Compute the unknowns for each of the following independent questions. (1) How much does Ned Winslow have to contribute to his investment account at the end of each year in order to accumulate $95,400 by the end of year 7? Ned points annual contribution (2 points) target balance $95,400 interest rate 6.8% # years 7 (2) Alfred Hitchcock has $11,540 in his savings account today. He needs $14,270 six years from now. What interest rate does the bank need to pay to make this points annual interest rate (2 points) target balance $14,270 current balance $11,540 # years 6 (3) An engineer at the XYZ Company has identified a piece of equipment that will generate after tax labor savings of $644,500 at the end of each year for five points max purchase price (2 points) amoint of annuity $644,500

Answer 1

i P year A is P= annual contribution at the end of each number of periods - 4 yeats periodic interest fate 6.87 = 0.068 FV of 7-year annuity = Target balance Pf + . مملكة $ Ev of annuity 95.,400 P P f(1.068) .= 1 0-068 95,400 P x 8.6013 P = 95.400 8.6013 $ 11,091-34 2x 6 years Az target balances $ 14,220 P = Current balance = & the 540 number of periods is intesest rate (io decimal) A- Pfiti)? 16,270 = 4540 [lti] منو 6 14,220 Il.540 نهلا to is (lo (14,270 lli540 3-6024°||

34 ie گل.۵ By P P = amount of annuity discount sale no. of years Pu of 6 year annuity Pu of annuity $ 644,500 11:54 6 maximum purchase price of equipment Pf (1+i) +" . i litinº 664.500 f(!$15.30 - 0:115 (11115) 646,500 X 4019029 $ 2,687,954.50 47 no. of years i = discount date = Ho5% = 0,115 4 PW of 4. year annuity purchase price purchase price = $1,250, 500 p = annual labor savings PV of annuity - PfCl+) - 1 . i 1,250,soo (1.115) -1 اردلاكلاء 1,250,500 P X 3.069614 P = 1,250,500 3:069614 $ 407, 380.24

(5) Soitial Jovestment $ 3.000 Net Cash flow per period = $1,100 Payback period - Initial Investment Net Cash flow per period 3000 1100 = | 2- 43 years PV of Cash Inflows 1) PU of s- year annuity 1,100 x PVAF (184,5) [ (1:1899 0-18 (1.18 جاجورا X S tileo X 3.12717 $ 3,439.89 Initial Cash outflow NPV = PU of Cash Inflows 3,439.89 3.000 $ 439.89

S) ( I contd.) IRR = re / AtIRR - - PU of Cash Inflows discounted @ IRR Initial Cash Outflow . 1,1000_x_PvAE [ 01/2, 5) 3,000 २ PUAEL22/-75) 3000 1100 21223 At है : २० > PUAF(20415 ) २.११06 At r %3D 25, - Py [25/-,5) = २.6893 20 ज 25 २.9906 2-7223 2.6893 २० - ४ 25-२० 2.4906 - 2-7273 २. 6893 - २.११06 %3D २०-४ 5 -_0,8739 20- - 4.3694 : %3D २०+ ५.१०१५ [ २५.36१५/- IRR = २५ : 31