What is the value of an investment that pays $30,000 every other year forever, if the first payment occurs one year from today and the discount rate is 13 percent compounded daily? What is the value today if the first payment occurs four years from today? Assume 365 days in a year.
Answers
Answer:
While it might seem like calculating something that goes forever would mean a long series of calculations, in fact there's a very simple formula: C / i, where C is the cash payment and i is the interest rate. But there are a few wrinkles in your problem we need to handle.
Since the payment is made every other year, you need to determine a two-year interest rate. Since the compounding is daily, the formula is (1 + (i / 365)) ^ (365 * 2) - 1 (i is the interest rate); that's (1 + .13 / 365) ^ 730 - 1 = .29687, or 29.687%. Thus, the present value of the infinite annuity is 6700 / .29687 = 22,568.82.
However, this is the formula annuity in arrears (i.e., first payment is at the end of the compounding period). To get the value when the first payment is made immediately, add the first payment: 22,568.82 + 6700 = 29,268.82.
Not done yet, though; that's the value four years from now. We now need to PV that amount years at 13% compounded daily: 29,268.82 / (1 + .13 / 365) ^ (365 * 4) = 17,402.54. (Alternatively, you could have calculated from the annuity in arrears, then pulling that two years forward: 22,568.82 / (1 + .13 / 365) ^ (365 * 2) = 17,402.54.)