I need to know how this problem is solved: I have the answer, but I must show my
ID: 2668441 • Letter: I
Question
I need to know how this problem is solved: I have the answer, but I must show my work and I am missing something. I need a step by step answer showing work, if you know an Excel trick that will work too:A company currently pays a dividend of $2 per share (Do=$2). It is estimated that the companies dividend will grow at 20% per year for the next 2 years, then at a constant rate of 7%, thereafter. The company's stock has a beta of 1.2, the risk free rate of 7.5%, and a market risk premium is 4%. What is your estimate of the stock's current price?
Explanation / Answer
According to CAPM, Expected Rate of return Ks = Krf + (Km-Krf)*Beta Ks = Krf + Beta*Mkt prem = 7.5%+1.2*4% = 12.3% So expected return for Stock is Ks=12.3% For the price of stock, we have the following three steps: 1. Find the PV of the dividends during the period of (Y1 & y2) nonconstant growth(gn). 2. Find the price of the stock at the end of the nonconstant growth period (P2), at which point it has become a constant growth (g) stock, and discount this price back to the present. 3. Add these two components to find the intrinsic value of the stock, P0. STep 1. Ks=12.3%, Gn = 20%, g = 7% D0 = 2 D1=D0*(1+Gn) = 2*(1+20%) = 2.40, D2 = D1*(1+Gn) = 2.40*(1+20%) = 2.88, D3= D2*(1+g) = 2.88*(1+7%) = 3.08 So PV of Div for 2 yrs = D0 + D1/(1+Ks)^1 + D2/(1+Ks)^2 = 2 + 2.40/(1+12.3%)^1 + 2.88/(1+12.3%)^2 = 2 + 2.14 + 2.28 = 6.42....................(1) Step2 : After 2 yrs, the stock becomes a constant growth stock with g =7%, its price at end of Year 2 is given by P2 = D3/(Ks-g) ie P2 = D2(1+g)/(Ks-g) = 2.88*(1+7%)/(12.30%-7%) = 58.14 PV of P2 = 58.14/(1+12.3%)^2 = 46.10....................(2) Step 3: So value of Stock P0 = PV of Dividend of 2 yrs + PV of Stock price at end of Year 2 = 6.42+46.10 = 52.52 Sp P0 = $ 52.52..................................Ans Note : When we do rounding off, some rounding error do creep in.