Question

Mike is trying to value the Tools Limited. To easily see how a change in one or more of his assumptions affects the estimated value of the stock, he is using a spreadsheet model. The model has projections for the next four years based on the follow¬ing assumptions.

• Sales will be $300 million in Year 1.
• Sales will grow at 15 percent in Years 2 and 3 and 10 percent in Year 4.
• Operating profits (EBIT) will be 17 percent of sales in each year.
• Interest expense will be $10 million per year.
• Income tax rate is 30 percent.
• Earnings retention ratio would stay at 0.60.
• The per-share dividend growth rate will be constant from Year 4 forward, and this final growth rate will be 200 basis points less than the growth rate from Year 3 to Year 4.

The company has 10 million shares outstanding. Trey has estimated the required return on Resources’ stock to be 13 percent.

A. Estimate the value of the stock at the end of Year 4 based on the above assumptions.

B. Estimate the current value of the stock using the above assumptions.

C. Mike is wondering how a change in the projected sales growth rate would affect the estimated value. Estimate the current value of the stock if the sales growth rate in Year 3 is 10 percent instead of 15 percent.

Answer 1

By the given information in the question following spread sheet is prepared:

( $ in millions )

Payout means dividend distribution. Total outstanding Shares is 10 million. So per share dividend is Payout or dividend / Shares Outstanding

Year	1	2	3	4
Dividend	$11.48 million	$13.62 million	$16.09 million	$17.97 million
Shares O/S	10 million	10 million	10 million	10 million
Per Share Dividend = Dividend / Shares O/s	D1 = 1.148	D2 = 1.362	D3 = 1.609	D4​​​​​​​ = 1.797

Per share dividend growth rate will be constant from year 4 forward, and this final growth rate will be 200 basis points less than the growth rate from year 3 to year 4.

Dividend growth Rate year 3 to year 4 =  

=

=

= 11.68%

If 1 Basis point = 0.01%

then, 200 basis points = 2%

Hence, growth rate year 4 forward = Dividend growth Rate year 3 to year 4 - 2%

= 11.68 - 2

= 9.68%

A ) Value of Stock at end of year 4

Once growth rate become constant we can apply perpetuity formula. After 4th year perpetuity value from 9.68% groth rate

P₄ = Price per share at the end of year 4

D₄ = Dividend in year 4

g = growth rate year 4 ownwards

K_e = required return

  

  

  = $59.36

Value of Stock = Price per Share * Number of Shares

= $59.36 * 10 million

= $593.6 million

B )

Current price of share = Present Value of all dividends + Present value of perpetuity or price of share at end of year 4

Year	Dividend	PVIF @ 13%	Present Value = Dividend * PVIF
1	1.148	0.8850	1.016
2	1.362	0.7831	1.067
3	1.609	0.6931	1.115
4	1.797	0.6133	1.102
4	59.36	0.6133	36.405
			40.705

PVIF = 1/(1+r)ⁿ or from PVIF tables

Current price per share = $40.705 or $40.71

Current Value of Stock = Price per Share * Number of Shares

= $40.71 * 10 million

= $407.1 million

C ) Again solve from 10% sales growth in year 3

( $ in millions )

Payout means dividend distribution. Total outstanding Shares is 10 million. So per share dividend is Payout or dividend / Shares Outstanding

Year	1	2	3	4
Dividend	$11.48 million	$13.62 million	$15.26 million	$17.07 million
Shares O/S	10 million	10 million	10 million	10 million
Per Share Dividend = Dividend / Shares O/s	D1 = 1.148	D2​​​​​​​ = 1.362	D3 = 1.526	D4​​​​​​​ = 1.707

Per share dividend growth rate will be constant from year 4 forward, and this final growth rate will be 200 basis points less than the growth rate from year 3 to year 4.

Dividend growth Rate year 3 to year 4 =  

=

=

= 11.86%

If 1 Basis point = 0.01%

then, 200 basis points = 2%

Hence, growth rate year 4 forward = Dividend growth Rate year 3 to year 4 - 2%

= 11.86 - 2

= 9.86%

Once growth rate become constant we can apply perpetuity formula. After 4th year perpetuity value from 9.68% groth rate

P₄ = Price per share at the end of year 4

D₄ = Dividend in year 4

g = growth rate year 4 ownwards

K_e = required return

  

  

  = $59.72

Current price of share = Present Value of all dividends + Present value of perpetuity or price of share at end of year 4

Year	Dividend	PVIF @ 13%	Present Value = Dividend * PVIF
1	1.148	0.8850	1.016
2	1.362	0.7831	1.067
3	1.526	0.6931	1.058
4	1.707	0.6133	1.047
4	59.72	0.6133	36.626
			40.814

PVIF = 1/(1+r)ⁿ or from PVIF tables

Current price per share = $40.814 or $40.81

Current Value of Stock = Price per Share * Number of Shares

= $40.81 * 10 million

= $408.1 million

Change in the projected sales growth rate would affect the estimated value. If the sales growth rate in Year 3 is 10 percent instead of 15 percent. The Current Value of Stock is increased.