Question

Which of the following option do you prefer?:

1) An ordinary annuity at a price of $150,000 today, and receive $1,000 per month for 20 years

2) 3,000 shares of a preferred stock at the price of $50 per share today, and received cash dividend of $2.5 per share every quarter

pls show formulas and steps

Answer 1

We chose the option with the highest Net present value

1-(1 + r) -" PV = PMT*

We assume interest rate = 10%

1)

NPV = -150000 + 1000*((1-(1+0.1)^(-20))/(0.1))

NPV = -$141486.43

2)

We first find the equivalent annual cash dividend

Equivalent annual cash dividend = Summation of {Dividend*Interest rate till end of year}

Equivalent annual cash dividend = 2.5*(1+0.1*3/4) + 2.5*(1+0.1*2/4) + 2.5*(1+0.1*1/4) + 2.5 = $10.375

NPV = -3000*50 + 10.375/0.1

NPV = -$149896.25

Since, the NPV in first part is higher than that in second part, the first part (ordinary annuity) option must be accepted