Question

Problem 1. Net Present Value. ​You are a gym manager. Based on your estimates, the gym will generate the profits of $330 in a year, $270 in two years, and $190 in three years. The interest rate is 8%.

a) Calculate the Present Value of the stream of profits.

PV =

b) You are considering adding a swimming pool. What is the maximum amount you would be willing to pay for it if it will increase the profits by 30% in the first year, and by 20% in both the second and the third year?

Maximum amount =

c) A stock pays a random perpetual dividend at the end of each year. The dividend is either $60 or $120 with equal probabilities. Find the value of the stock if the interest rate is 5 percent.

Value =

Answer 1

a)

PV of a future cash flow =FV/(1+r)^n

PV of a series of future cash flows is equal to PV of each cash flow. So,

PV of profit streams=330/(1+8%)^1+270/(1+8%)^2+190/(1+8%)^3=$687.87

b)

Additional profit at the end of year 1=330*30%=$99

Additional profit at the end of year 2=270*20%=$54

Additional profit at the end of year 3=190*20%=$38

Maximum Cost=PV of additional profit streams

=99/(1+8%)^1+54/(1+8%)^2+38/(1+8%)^3=$168.13

c)

Expected dividend per year=D=0.5*60+0.5*120=$90

Discount rate=r=5%

Value of stock=D/r=90/5%=$1800