I need help on these two short question regarding NPV, PAYBACK AND IRR. Please show work. Thanks

1. You are offered $100 once every three years, forever, starting one year from today, but to receive these cash flows you must pay $500 immediately. If your annual cost of money is 10%, should you take the offer? 2. We saw in class that the IRR of a perpetuity project is exactly equal to the inverse of the payback period. I also noted that for non-perpetuity projects the relationship IRR = 1/PB is only an approximation, and that this approximation improves as the life of the project increases. To see how good the approximation is, calculate the IRR, the PB, and the inverse of the PB for the following projects, all of which have an investment of $1,000 and produce annual cash flows of $250 from t = 1 to t = n, where a) n = 5 years; b) n = 10 years; c) n = 20 years; d) n = 30 years. Put the results in a table containing the following four columns (from left to right): n, IRR, PB, and 1/PB. 1. You are offered $100 once every three years, forever, starting one year from today, but to receive these cash flows you must pay $500 immediately. If your annualcost of money is 10%, should you take the offer? Solution: Annual cost Cost for 3 years Payment to be received once every 3 years PV of this payment Immediate payment 10% 30.00% $100.00 $333.33 $500.00 Since PV of $100 (= $333.33)