# Question: As discussed in the chapter abnormal earnings AE are AEt

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?

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