Question

Path to the Mountain Inc. just announced earnings per share of $6 for the current quarter (which ended today). Path to the Mountain has just paid out 20% of these earnings as a dividend and reinvested the rest in new projects earning a return of 38% per year. Path to the Mountain will continue to pay quarterly dividends under these policies and investment returns until two years from today. Two years from today and thereafter forever, the return on Path to the Mountain’s new projects will fall to 3% per year and Path to the Mountain will begin paying out 75% of its earnings as a dividend. Set up the calculations needed to determine the price per share of Path to the Mountain stock if Path to the Mountain’s equity cost of capital equals 9.5% per year and the firm pays dividends quarterly.

Answer 1

1) we will aprroach the problem by finding out NPV of outflows and inflows and then will ad both of thse to get the NPV of net earnings made by the company per share and that will be our price per share.

therefore let's start with NPV of outflows:

NPV=6*0.2/(1+.095/12)^3+1.2/((1+0.095/12)^6.+.......+1.2/(1+.095/12)^24+0.75*6/(1+.095/12)^27+......infinity.

NPV=8.64(of 8 quarters)+ sum of infinite GP(a/1-r) wher(a=1+.095/12)^27,r=1/(1+.095)^3

NPV=8.64+52.92

NPV=$61.56 per share(outflow)

Now calculating totla inflow from reinvestments of earnings.

Now the first 8 quarters will have inflows starting from quarter 4 for investments done in quarter 1 till quarter 12th for investment done untile 8 as per initial policy and thereafter invetments done in quarter 9 to quarter 48(assuming that reinvestments will only be done if the returns are greted than cost of equity.)

NPV=inflows from quarter 4 to 12(6.624(6*.80*(1.38)

After quarter 8 the investments policy changes and new inflows =

13-16 2.025

17-20 1.98

21-24 1.935

24-28 1.89

29-32 1.845

33-36 1,80

37-40 1.755

41-44 1.71

45-48 1.665

NPV of ablove all =$83.199

Therfore net present value of earnings per share=$83.199-$61.56

Price per share=$21.639