Motor Homes Inc. (MHI) is presently in a stage of abnormally high growth because of a surge in the demand for motor homes. The company expects earnings and dividends to grow at a rate of 20% for the next 4 years, after which time there will be no growth (g=0) in earnings and dividends. The company's last dividend was $1.50. MHI's bets is 1.6, the return on the market is currently 12.75%, and the risk-free rate is 4%. What should be the current common stock price?

When I am working this problem, I continue to get required rate of return < growth rate causing a negative market price.
Required rate of return= Risk-free rate + Market risk premium (required rate of return- risk-free rate) * beta
r= 4+(12.75-4)1.6= 18%
Price= dividend (1+ growth rate) / (required rate of return- growth rate)
Po= 1.50(1+.20)/(.18-.20)=1.8/-.020=-90.00

Any help would be appreciated. Thank you.

The 'constant-growth' pricing formula you're using can only model a situation where the growth is expected to be constant, as in continuing indefinitely (hence the name).

Your calculation of MHI's discount rate is correct. The most quick way to price MHI's stock is

1) present-value the next 4 years' dividends separately, remembering that each one is 120% of the previous.

2) Since MHI's growth flatlines after 4 years, the dividends for year 5 and beyond are just the same as year 4's dividend. Price that dividend stream as a perpetuity, giving you the PV at the end of year 4, then discount that single amount back 4 years to arrive at today's value.

3) Add the results of (1) and (2), and you can call it a day.

I believe I understand what you are saying. When taking your advice this is what I have come up with.
d1= 1.50(1.20)=1.80---->1.80/1.20=1.50
d2= 1.80(1.20)=2.16----> 2.16/(1.20)^2=1.50
d3=2.16(1.20)=2.59
d4= 2.59
P3= 2.59/.18=14.389+ d3= 16.979 ----> 16.979/(1.20)^3=9.826

1.50+1.50+9.826=$12.826~$=$12.83= Po

Is that what you were suggesting?

You'll be on the right track with a couple of tweaks...

First, you need to shift your timing a bit. The company's last dividend was a buck-fifty, and for pricing the stock today the only relevant dividends are the sequence beginning one year from now.

Next, remember that you've determined that the appropriate risk-adjusted discount rate for this outfit is 18% (you're trying to use the growth rate). Thus, the pricing computation plays out like...

\frac{1.8}{1.18}\ +\ \frac{2.16}{1.18^2}\ +\ \frac{2.59}{1.18^3}\ +\ \frac{3.11}{1.18^4}\ +\ \frac{3.11\div0.18}{1.18^4}

Give that one a spin.

I think I may have it now. (Thanks.) This is what I came up with.
1.525+1.551+1.578+1.604+8.913~ $15.17= Po

Now you nailed it.

Awesome! Thank you so very much for your help with this problem. I am so appreciative (once again!)