Question

What's the total value today of paying $150,000 today, then receiving $18,000 per month starting next month and lasting for a total of 180 months, and also receiving $90,000 at the time 180 months from now? Use an 11% annual required rate of return. (Please show work so I can follow and understand).

Answer 1

Assuming required return is 11% compounded monthly. If 11% is compounded annually then substitute 10.4815% (=((1+11%)^(1/12)-1)*12)in place of 11%

The stream can be borken down into three streams
First stream: 150000 today
Present value=150000

Second stream: 18000 per month for 180 months
Present value=Present value of annuity=18000/(11%/12)*(1-1/(1+11%/12)^180)=1583674.8677

Third stream: 90000 at time 180
Present value=Present value of future lumpsum=Future Value/(1+r)^n=90000/(1+11%/12)^180=17414.9019

Total value=150000+1583674.8677+17414.9019=1751089.7696