Question

You just got hired at an investment firm where you are performing equity research. You are told to prepare a buy recommendation for a company of your choice to be presented to the partners for evaluation. The TP GURU catches your attention as a possible buy. The company just paid an annual dividend of $3.75 per share. Your project dividend growth of 10% for the next 5 years in par with revenue growth. After that you project the company will grow at the equivalent GDP of 3% forever. The company uses a fixed required rate of return of 15%. At which stock price will you issue a buy recommendation for this company? Use a timeline. Calculate PV for the first 5 years. Calculate PV using indefinite growth rate of year 5 and beyond. Don't forget that you must discount year 5. This is a long problem that requires taking it step-by-step. Pay attention to your Dividend Growth Model.

Answer 1

Step 1:

Calculation of Present value of the first 5 years

Growth Rate = g = 10% for 5 years and 3% from so on

Required rate of return = r = 15%

Just Paid Dividend = D0 = $3.75

Dividend in year 1 = D1 = D0 * (1+g) = $3.75 * (1+10%) = $4.125

Dividend in year 2 = D2 = D1 * (1+g) = $4.125 * (1+10%) = $4.5375

Dividend in year 3 = D3 = D2 * (1+g) = $4.5375 * (1+10%) = $4.99125

Dividend in year 4 = D1 = D3 * (1+g) = $4.99125 * (1+10%) = $5.490375

Dividend in year 5 = D5 = D4 * (1+g) = $5.490375 * (1+10%) = $6.0394125

Present value for first 5 years = [D1/(1+r)^1] + [D2/(1+r)^2]+[D3/(1+r)^3] + [D4/(1+r)^4] + [D5/(1+r)^5]

= [$4.125 / (1+15%)^1] + [$4.5375 / (1+15%)^2] + [$4.99125 / (1+15%)^3] + [$5.490375 / (1+15%)^4] + [$6.0394125 / (1+15%)^5]

= [$4.125 / 1.15] + [$4.5375 / 1.3225] + [$4.99125 / 1.520875] + [$5.490375 / 1.74900625] + [$6.0394125 / 2.01135719]

= $3.58695652 + $3.43100189 + $3.2818279 + $3.13913973 + $ 3.00265539

= $16.4415814

Therefore, Present value for first 5 years = $16.44

Step 2:

Calculation of Present value using indefinite growth rate for year 5 and beyond

D5 = $6.0394125

D6 = D5 * (1+g) = $6.0394125 * (1+3%) = $6.22059488

Total Value of Dividends at year 5 for years 5 and beyond = D6 / (r-g)

= $6.22059488 / (15%-3%)

= $6.22059488 / 12%

= $51.8382907

Present value of Dividend for year 5 and beyond = $51.8382907 / (1+15%)^5

=$51.8382907 / 2.01135719

=$25.7727921

Therefore, Present value using indefinite growth rate for year 5 and beyond is $25.77

Step 3:

The stock price will issue to buy the share is sum of PV for first 5 years and PV for 5 years and Beyond

= $16.4415814 + $25.7727921

= $42.2143735

Therefore, The price at whcih will issue to buy the share is $42.21

Step 4:

a. The price at whcih will issue to buy the share is $42.21

b. Present value for first 5 years is $16.44

c. Present value using indefinite growth rate for year 5 and beyond is $25.77