Question

You just received notification that you have won the 1.25 million first prize in the centennial lottery. However, the prize will be awarded on your 100th birthday, 79 years from now. The appropriate discount rate is 6.4 percent. What is the present value of your winnings

Answer 1

Solution :

The present value of a cash inflow at period 'n' is calculated using the following formula:

PV = C_n / (1 + r )ⁿ

PV = Present Value   ; C_n : Cash Inflow at period n ;

r = discount rate ; n = Number of periods or years

As per the information given in the question we have

r = 6.40 % = 0.064 ; n = 79 year

C₇₉ = $ 1,250,000

Applying the above values in the formula we have

PV = $ 1,250,000 / ( 1 + 0.064 ) ⁷⁹

= $ 1,250,000 / ( 1.064 ) ⁷⁹

= $ 1,250,000 / 134.396701

= $ 9,300.8235

= $ 9,300.82 ( when rounded off to two decimals )

Thus, the Present value of a $ 1,250,000 payment in 79 years when the discount rate is 6.4 percent is

= $ 9,300.82       

The present value of winnings = $ 9,300.82

Note : The value of ( 1.064 ) ⁷⁹   has been calculated using the excel function =POWER(Number,Power).

Thus =POWER(1.064,79) = 134.396701