In: Finance
You will have to make 15 annual payments of $7.5 million each with the first payment in eight years. If you can earn 6.5% interest, how much must you deposit today to cover your obligation?
Step-1:Calculating present value of annual payments seven years from now | |||||||||||
Present value | = | Annual payments * present value of annuity of 1 | |||||||||
= | $ 7.50 | * | 9.402669 | ||||||||
= | $ 70.52 | million | |||||||||
Working: | |||||||||||
Present value of annuity of 1 | = | (1-(1+i)^-n)/i | Where, | ||||||||
= | (1-(1+0.065)^-15)/0.065 | i | 6.50% | ||||||||
= | 9.402669 | n | 15 | ||||||||
Step-2:Calculation of present value of amount now | |||||||||||
Present value | = | Present value calculated above 7 years from now*Present value of 1 | |||||||||
= | $ 70.52 | * | (1.065^-7) | ||||||||
= | $ 70.52 | * | 0.643506 | ||||||||
= | $ 45.38 | million | |||||||||
Thus, | |||||||||||
Amount to be deposited today | $ 45.38 | million | |||||||||