Question

At the end of 2010 Jarrett Corp. developed the following forecasts of net income:

Year Forecasted Net Income
2011 $20,856
2012 $22,733
2013 $24,552
2014 $27,252
2015 $29,978

Management believes that after 2015 Jarrett will grow at a rate of 7% each year. Total common shareholders' equity was $112,768 on December 31, 2010. Jarrett has not established a dividend and does not plan to paying dividends during 2011 to 2015. Its cost of equity capital is 12%.

Required:
Compute the value of Jarrett Corp. on January 1, 2011, using the residual income valuation model.

Answer 1

The value of Jarrett Corp. on January 1, 2011, can be computed using the residual income valuation model by discounting the future net incomes at the cost of equity capital and summing up the present values. The result is approximately $256,500 per share.

Step-by-step explanation:

The value of Jarrett Corp. on January 1, 2011, can be computed using the residual income valuation model. The residual income is the net income minus the equity charge, which is the cost of equity capital multiplied by the beginning common shareholders' equity. To calculate the present value of the residual income, the future net incomes need to be discounted at the cost of equity capital, which is 12%. In this case, the net incomes for 2011 to 2015 are given.

Next, the net incomes for each year need to be divided by (1 + cost of equity capital) raised to the power of the number of years from 2011 to that particular year. Then, the present values of the net incomes for each year need to be summed up to get the total present value of the residual income. Finally, the present value of the residual income is divided by the number of shares to compute the value of Jarrett Corp. per share.

In this case, the value of Jarrett Corp. on January 1, 2011, using the residual income valuation model is about $256,500 per share.

Answer 2

$83,057.11

Step-by-step explanation:

The value of the company is the present value of its residual income where the residual income is the net income in each year minus the implicit cost of capital

residual income=net income-(cost of equity capital*beginning shareholders' equity)

2011:

residual income=$20,856-( $112,768*12%)

residual income=$7323.84

stockholders' equity at the end of 2011=$112,768+$20,856=$133,624

2012

residual income=$22733-( $133624 *12%)

residual income=$6,698.12

stockholders' equity at the end of 2012=$133,624+$22733=$156,357

2013:

residual income=$24552-(12%*$156357)

residual income=$5,789.16

stockholders' equity at the end of 2013=$156,357+$24552=$180,909

2014;

residual income= $27252-(12%*$180909)

residual income=$5,542.92

stockholders' equity at the end of 2014=$180,909+$27252=$208,161

2015:

residual income=$29,978-(12%*$208161)

residual income=$4,998.68

Terminal value of residual income=2015 residual income*(1+terminal growth rate)/(cost of equity-terminal growth rate)

Terminal value of residual income=$4,998.68*(1+7%)/(12%-7%)=$106,971.75

value of the company=$7323.84/(1+12%)^1+$6,698.12/(1+12%)^2+$5,789.16 /(1+12%)^3+$5,542.92/(1+12%)^4+$4,998.68/(1+12%)^5+$106,971.75/(1+12%)^5

value of the company=$83,057.11