Question 1.

(a) Calculate the NPV of a project with the following cash flows CF0 = $1,500, CF1 = $1,500, and CF2 = $1,125 using the discount rate of 0%. How would your answer change if the discount rate is 50%? 100% ?

(b) What is the IRR of this project? Is the IRR unique? (hint: unique means that there exists only one positive rate of return such that the NPV equals zero)

Question 2.

A bank offers you a $2M loan with an IRR of 7% (i.e. the bank makes a return of 7% on the loan; note that 7% is not the rate of interest payments). The bank requires you to repay the loan in 7 equal annual installments, starting next year.

(a) What is the annual payment on the loan that the bank charges?

(b) What is the NPV of the loan to you if your opportunity cost of capital is 12%?

Question 3.

Suppose you are a financial manager and you have the following investment opportunities:

Project Initial Investment/Cost (in $1,000) NPV (in $1,000)

1 400 100

2 100 -20

3 200 300

4 150 150

5 250 100

Which of the following projects should you pursue if you have only $700,000 allocated for capital expenditures? How much does the budget limit cost the company in terms of forgone NPV? The opportunity cost of capital for each project is 12%.

Question 4. Consider a project with the following cash flows: C0 = $250, C1 = $300, and C2 = $70.

1. Compute the IRR(s) for this project. (Hint: use the formula for IRR in the lecture notes and multiply everything by (1 + IRR)^2. This gives you a quadratic equation. Now use the quadratic formula to solve this equation for IRR. Ignore the negative solution for IRR.)
2. Would you accept this project if the opportunity cost of capital is 30%? 50%?
3. Would your decision change if you use the NPV rule?