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Calculating abnormal earnings and analyzing investment options

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Abnormal earnings are: AEt= Actual earning t-Required or "normal" earnings t
Which may be expressed as Aet= NOPAT t- (r x BVt-1)

Where NOPAT is the firm's net operating profit after taxes, r is the cost of equity capital and BV 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 that the firm in requirement 2 can increase NOPAT to $30,000 by instituting some cost cutting measures. What is the new AE?
4. Assume that the firm in requirement 2 can divest $25,000 of unproductive capital, which NOPAT falling by only $2,000. What is the new AE?
5. Assume that 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 that 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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Abnormal earnings (AE) are: AEt= Actual earning t-Required earnings t
Which may be expressed as AEt= NOPAT t- (r x BVt-1)

Where NOPAT is the firm's net operating profit after taxes, r is the cost of equity capital and BV t-1 is the book value of equity at t-1.

Appearing next is the NOPAT, BVt-1 and cost of equity capital of two firms.

Company A 2001 2002 2003 2004 2005
NOPAT $66,920 $79,632 $83,314 $89,920 $92,690
BVt-1 $478,000 $504,000 $541,000 $562,000 $598,000
Cost of equity capital 0.152 0.167 0.159 0.172 0.166

Company B 2001 2002 2003 2004 2005
NOPAT $192,940 $176,341 $227,700 $198,900 $282,964
BVt-1 $877,000 $943,000 $989,999 $1,020,000 $1,199,000
Cost of equity capital 0.188 0.179 0.183 0.175 0.186

Required:

1. Calculate each firm's AE each year from 2001 to 2005.
2. Which firm was a better investment for its shareholders over the 2001-2005 period? Why?

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The price equation for a firm with positive growth opportunities is
P0 = x0 + NPVGO
R

Where P0 is the current stock price, X0 is current reported earnings per share, r is the cost of equity capital, and NPVGO is the net present value of future growth opportunities. The recent values of P0, X0, and r for several companies are:

P0 X0 R
Dell Computer $26.74 $0.82 0.138
eBay 67.82 0.82 0.198
Form Motor 9.30 0.99 0.114
Home Depot 24.02 1.55 0.121
Wal-Mart 50.51 1.83 0.090

Required:

1. Why does eBay have a higher cost of equity capital ( r ) than does Wal-Mart?
2. Compute NPVGO for each company.
3. Why is the NPVGO of eBay larger than that for Home Depot?
4. Why does Ford Motor and Wal-Mart have such different NPVGO amounts?

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