Question

Slowtrac, Inc. will be initiating a dividend for the first time, and will be paying it tomorrow. It is expected that the dividend cash flow will be $1.25/share. Over the next 2 years, the consensus is that Slowtrac will increase the dividend by 5% per year. Following the two year growth, the dividend is then expected to grow at 2% per year in perpetuity.Additional information on Slowtrac and the financial markets: Beta of Slowtrac is 0.75 Expected market risk premium is 6% per year Risk-Free rate is 2% per year

a)   Value a share of Slowtrac.

b) If the risk-free interest rate increases to 3% per year, and assuming everything else (and specifically Slowtrac’s expected cash flows, Slowtrac’s beta and the market risk premium) are unchanged, calculate what you think a share of Slowtrac would be.

Consider another firm, Ziptrac, trading in the same market as Slowtrac. Ziptrac has an expected dividend one year from now of $4.00 per share. This dividend is expected to grow at 3% per year in perpetuity. Ziptrac’s beta is also 0.75

c)    Value a share of Ziptrac if the riskless interest rate is 2% per year; and also value it after the riskless interest rate increases to 3% per year.

d) Which company, if any, has a value that is more sensitive to a change in the riskless interest rate? Why do you think this is so?

Answer 1

a) Slowtrac 's cost of equity = Risk free rate + beta * risk premium

= 2% +6% *0.75 = 6.5%

using dividend discount model

C0 = 1.25

C1=1.25*1.05

C2 = 1.25* 1.05²

C3 = 1.25* 1.05² * 1.02

After the 2nd year, the dividends follow constant growth forever and hence the Terminal value at end of 2nd year

T₂ = C3/ (r-g) where r is the cost of equity and g is the constant growth rate

T₂ = 1.25* 1.05² * 1.02 / (0.065-0.02) = 31.2375

So, the Price = 1.25+ 1.25*1.05/1.065 + 1.25*1.05²/ 1.065² + T₂ / 1.065²

= $ 31.24 per share

b) If Risk free rate changes to 3 %

Slowtrac 's cost of equity = Risk free rate + beta * risk premium

= 3% +6% *0.75 = 7.5%

C0 = 1.25

C1=1.25*1.05

C2 = 1.25* 1.05²

C3 = 1.25* 1.05² * 1.02

After the 2nd year, the dividends follow constant growth forever and hence the Terminal value at end of 2nd year

T₂ = C3/ (r-g) where r is the cost of equity and g is the constant growth rate

T₂ = 1.25* 1.05² * 1.02 / (0.075-0.02) = 25.55795

So, the Price = 1.25+ 1.25*1.05/1.075 + 1.25*1.05²/ 1.075² + T₂ / 1.075²

= $ 25.78 per share

c) Since Ziptrac's beta is the same as Slowtrac's, its cost of equity will also be 6.5% and 7.5% in case risk free rate is 2% and 3% respectively

C1=4 and expected to grow at 3% per year forever

So, from the Constant Growth model

Price = C1/ (r-g) = 4/ (0.065-0.03) =$ 114.29 per share

In case Risk free rate is 3%

Price = C1/ (r-g) = 4/ (0.075-0.03) =88.89 per share

d) Ziptrac's share price is more sensitive to change in Risk free rate as it has higher perpetual growth rate of dividends as compared to Slowtrac