Question

Don Draper has signed a contract that will pay him $80,000 at the beginning of each year for the next ​7 years, plus an additional $120,000 at the end of year 7. If 7 percent is the appropriate discount​ rate, what is the present value of this​ contract?

What is the present value of ​$80,000 at the beginning of each year for the next 7 years if the discount rate is 7 ​percent?

Answer 1

Present value of annuity due = A + A * [ 1 - (1 / (1+r)^n-1) ] / r

where, A is the Annuity amount per period, r is the interest/discount rate per period, n is the number of periods

Present value of a single lumpsum amount = FV / (1+r)ⁿ

where, FV is the amount receivable at the end of nth period, r is the interest/discount rate per period, n is the number of periods.

Under the contract, Don Draper receives 80,000 at the beginning of each for 7 years and $120,000 at the end of Year 7. Discounting rate is 7%

There are two parts i.e

Annuity due for 7 years(as amount is received at beginning of each year) and

Lumpsum amount at the end of 7th year

Present value of the $80,000 receivable at the beginning of each year = 80,000 + [80,000 * [ 1 - (1 / (1+0.07)^7-1) ] / 0.07]

=> 80,000 + [80,000 * [ 1 - 0.666342] / 0.07]

=> 80,000 + [80,000 * 0.333658 / 0.07]

=> 80,000 + 381,323.1728

=> $461,323.1728

Present value of $120,000 receivable at the end of 7th year = 120,000 / (1+0.07)⁷

=> 120,000 / 1.605781

=> $74,729.9690

Present value of the contract = $461,323.1728 + $74,729.9690 => $536,053.1418

Present value of ​$80,000 at the beginning of each year for the next 7 years if the discount rate is 7 ​percent = $461,323.1728