Question

Your best friend won the Washington State Lottery and has been promised by the state annual payments of $300,000 forever, starting two months from today. Currently, the risk-free rate of interest is 0.7%/year, the market rate on Washington State Bond’s is 1.8%/year, and the expected return of the stock market is 7%/year. Provide an equation, including all of the inputs, to calculate the present value of the expected future cash payments. Explain how you determined the appropriate discount rate.

Answer 1

As the Lottery is sponsored by the Washington state , the appropriate discount rate to be use would be the market rate of Washington state bond's . This is because these bonds also capture the risk premium of state bonds in addition to risk free rate. As these bonds provide the expected return on debt obligation, this is the most appropriate discount rate as lottery payable is like a debt obligation that needs to be honored.

Perpetual cash flows, CF = $ 300,000

Discount rate , r = 1.8% pa

Present Value of the expected future cash payments = CF/r = 300,000/ 1.8% = $ 16,666,666.67 =$ 16.67 Mn