Question

Don Draper has signed a contract that will pay him $55,000 at the beginning of each year for the next 9 years, plus an additional $150,000 at the end of year 9. If 8 percent is the appropriate discount​ rate, what is the present value of this​ contract?

The present value of the contract is $_______?

Answer 1

PV of Annuity Due:
Annuity due is series of cash flows that are deposited at regular intervals for specific period of time at the begginig of the period.

PV of Annuity Due = Cash Flow + [ Cash Flow * [ 1 - [(1+r)^-(n-1)]] /r ]
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$          55,000.00
Int Rate	8.000%
Periods	9

PV of Annuity Due = [ Cash Flow + Cash Flow * [ 1 - [(1+r)^-(n-1)]] / r ]
= [ $ 55000 + $ 55000 * [ 1 - [(1+0.08)^-8] ] / 0.08 ]
= [ $ 55000 + $ 55000 * [ 1 - [(1.08)^-8] ] / 0.08 ]
= [ $ 55000 + $ 55000 * [ 1 - [0.5403] ] / 0.08 ]
= [ $ 55000 + $ 55000 * [0.4597] ] / 0.08 ]
= [ $ 55000 + $ 316065.14 ]
= $ 371065.14

The present value of the contract = Present value of Annual cash flows for 9 years + present value of addtional payment at the end of 9^th year

PV of contract = $ 371065.14 + $ 150000 * 1/(1+0.08)^9

= $ 371065.14 + $ 150000 * 1/(1.08)^9

= $ 371065.14 + $ 150000 * 1/2

= $ 371065.14 + $ 150000 * 0.5

= $ 371065.14 + $ 75000

= $ 446065.14

Please comment if any further assistance is required