Present Value of a Series of Cash Flows - An Example Quick Check . We could solve the problem like this . . . You go Into the car dealership and want to buy a PVa = A/r - A/r x (1/((1+r)")) Honda Accord. They give you two alternative = 60/0.12 x (1 - 1/1.125) a PAY CASH: Cash price is $24,020 FINANCE CAR: Credit terms: $611 per month for 48 months = 500 x (1 - 1/1.762) = 500 x (1 - 0.567) You can borrow from your bank at 6% interest (0.5% per month). = 500 x 0.433 Use the annuity formula to figure which is the better deal. What do you think happened? (Hint: extended = $216,287.57 warranty is $2000 and undercar sealant is $700) a. Better to pay cash by $2700 (present value) . Note: don't forget to retain the precision in the b. Better to pay cash by $2000 calculator! C . Better to finance by $2000 d. Better to finance by $2700 25 26 Supercool shortcut!! Calculation . Have you ever wondered how to present value an infinite series of payments of $P . PVa = Air - A/r x (1/((1+r)*)) where per year? OA = 611 $ per month - This is called a perpetuity Or = 0.005 (0.5% per month) Valuation formula is PVp = P/r Ot = 48 months . Perpetuity example - British consols pay $2.50 per year and prevailing interest rates are 4% for perpetuities, what is the price of the consols? Solution : Price = PV of perpetuity = $2.50/0.04 = $62.50 28 27