Question

The company paid a dividend of $1.12 per share quarterly, totalling to $4.48 for the most recent full year, on its common stock. Based on a study of the risk of owning this stock, analysts at Schaumburg Investment Management Funds have determined that the required annual rate of return should be ke or r = 7.8%. Finally Analyst #4, Mr. Trenton, considers the strength of Naperville’s product lines in growing international markets. He has adopted the expectation that earnings and dividends will grow by 23% in year 1, by 17% in year 2, and by 12% in year 3, before leveling off to a fairly steady pattern that he can sensibly model as 2.6% constant annual growth in year 4 and all following years. Under this set of assumptions, what is the highest price analyst Trenton thinks the Schaumburg funds should be willing to pay for a share of Naperville Nurseries, Inc.’s common stock? (Try not to do rounding in intermediate steps; work with enough decimal places to assure accuracy.)

• A. $128.06
• B. $158.90
• C. $121.92
• D. $130.15
• E. $84.19

Answer 1

Option D is correct

g1 = growth rate = 23%

g2 = growth rate = 17%

g3 = growth rate = 12%

g = growth rate = 2.6%

r = required return = 7.8%

Current Dividend = D0 = $4.48

Dividend in Year 1= D1 = D0*(1+g1) = $4.48 *(1+23%) = $5.5104

Dividend in Year 2 = D2 = D1*(1+g2) = $5.5104 *(1+17%) = $6.447168

Dividend in Year 3 = D3 = D2*(1+g3) = $6.447168 *(1+12%) = $7.220828

Dividend in Year 4 = D4 = D3*(1+g) = $7.220828 *(1+2.6%) = $7.408570

Horizon Value = D4 / (r-g)

= $7.408570 / (7.8%-2.6%)

= $142.4725

Current Price of stock = [D1/(1+r)^1] + [D2/(1+r)^2] + [D3/(1+r)^3] + {Horizon Value / (1+r)^3]

= [$5.5104 / (1+7.8%)^1] + [$6.447168 / (1+7.8%)^2] + [$7.220828 / (1+7.8%)^3] + [$142.4725 / (1+7.8%)^3]

= [$5.5104 / 1.078] + [$6.447168 / 1.162084] + [$7.220828 / 1.252727] + [$142.4725 / 1.252727]

= $5.111688 + $5.547936 + $5.764087 + $113.729887

= $130.153598

Therefore, highest price can pay for stock is $130.15