'Probability' Exercises
1. In a race in which you are going to take part there is a prize of 1,000 euros for the winner. 500 euros for the runner-up and 300 euros for the person in third place. There is no prize for the rest. You believe that you will win the race with probability 0.1. come second with probability 0.2. and come third also with probability 0.2. (Implicitly you are assuming you will not win any prize with probability 0.5).
a) Plot the probability function of the prize you will get.
b) Plot the associated cumulative probability.
c) What is the average gain you expect to make by participating in the race?
2. The number of new cars registered in Spain next year is believed to follow a uniform distribution with a minimum of one million cars registered and a maximum of 1.3 million.
a) What is the probability that the number of cars registered in Spain next year will be greater than 1.1 million?
b) What is the probability that the number of cars registered will be between 1,050,000 and 1.150,000?
3. Assume that the monthly return of a stock listed on the Spanish Stock Exchange follows a normal distribution with mean u = 2% and standard deviation o = 1%.
a) What is the probability that for a given month the return of this stock will be between 1% and 3%?
b) What is the probability that the return will be between 0% and 4%?
c) Give a 70% and 90% confidence interval (around the mean 14 = 2%) for the monthly return of the stock.

'Net Present Value and Internal Rate of Return' Exercises
1. Consider the following two projects, whose yearly cash flows are:
A: (-200; 60; 60; 60; 60; 60)
B: (-300; 84; 84; 84; 84; 84)
Assume that your discount rate is 50/o.
a) Find the NPV of both projects at your discount rate.
b) Find the IRR of both projects.
c) If you had to choose only one project, which one would you choose?
2. A major lottery advertises that it will pay the winner 10 million euros. However, this prize is paid at a rate of 1 million euros each year (with the first payment being in one year from now) for a total of 10 payments.
a) What is the present value of this prize if the discount rate is r = 10%
b) What would the present value be if the first payment were now?

3. Consider the following two investments, A and B. whose cash flows are:
A: (-100; 40; 50; 60)
B: (-200; 0; 40; 280)
a) Calculate the NPV of both investments at discount rates of I = 15%; I = 20% and r = 25%. Plot the results in a graph with NPV on the vertical axis and IRR on the horizontal.
b) What is the internal rate of return of both investments?
c) If your discount rate is r = 15% and both investments are mutually exclusive, which one would you choose?

'Probability' Exercises 1. In a race in which you are going to tak...