Business finance FINS1613 Tutorial Week 02 Financial Mathematics II BDHFMF: Chapter 4

You have just received a windfall from an investment you made in a friend’s business. She will be paying you $24,857 at the end of this year, $49,714 at the end of the following year, and $74,571 at the end of the year after that (three years from today). The interest rate is 8.7% per year. Q. What is the PRESENT value of the windfall? A. $24,857 $49,714 $74,571 For anyone wondering... Google says that a “windfall” is “a large amount of money that is won or received unexpectedly.” PV  CF1 t=0  CF2 t=1 t=2 t=3  CF3 In general, if you’re investing in a friend’s business, any money you 0 1  r1 1  r2 1  r3 manage to get back could probably be considered a “windfall”....  $24,857  1  0.087 1  $49,714  1  0.087 2  $74,571  1  0.087 3  $22,867.53  $42,074.56  $58,060.58  $123,002.66 A. If we invest $123,002.66 in an account earning 8.7% p.a. at t=0: STARTING TIME STARTING BALANCE 8.7% INTEREST ON STARTING BALANCE INVESTMENT PAYOUTS ENDING BALANCE t  0 t  1 t  2 t  3 $123,002.66 $108,846.90 $68,602.58 $0.00 $10,701.23 $9,469.68 $5,968.42 $24,857.00 $108,846.90 $49,714.00 $68,602.58 $74,571.00 $0.00 That is to say… $123,002.66 is the exact amount that we would have to invest today in an account that could earn 8.7% p.a. such that we would be able to withdraw the three cash flows from the original problem ($24,857 at t=1, $49,714 at t=2, and $74,571 at t=3) and be left with an exact account balance of $0.00 at t=3. So why would you pay anything OTHER than $123,002.66 today for an investment offering those three future cash flows if the appropriate interest rate was 8.7%?! You wouldn’t!