As discussed in the chapter, abnormal earnings (AE) are
AEt = Actual earningst - Required or “normal” earningst
which may be expressed as
AEt = NOPATt - (r × BVt-1)
where NOPAT is the firm’s net operating profit after taxes, r is the cost of equity capital, and BVt-1 is the book value of equity at time t - 1.

Required:
Solve the following problems:
1. If NOPAT is $5,000, r = 15%, and BVt-1 is $50,000, what is AE?
2. If NOPAT is $25,000, r = 18%, and BVt-1 is $125,000, what is AE?
3. Assume the firm in requirement 2 can increase NOPAT to $30,000 by instituting some cost-cutting measures. What is the new AE?
4. Assume the firm in requirement 2 can divest $25,000 of unproductive capital with NOPAT falling by only $2,000. What is the new AE?
5. Assume the firm in requirement 2 can add a new division at a cost of $40,000, which will increase NOPAT by $7,600 per year. Would adding the new division increase AE?
6. Assume the firm in requirement 1 can add a new division at a cost of $25,000, which will increase NOPAT by $3,500 per year. Would adding the new division increase AE?