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.

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