Question

Pacific Health care stock is currently Dec.31,2017 selling for $8 per share, current dividend is 0.480 per share paid Dec. 31, 2017, and beta coefficient is 1.2. The yield on long term treasury bond is 5.0% and that a market return of 11% is expected . Most analysis forecast that pacific will grow 10% per year for the next five years and 4% per year thereafter. Based on these forecast the the following table was created for the forecast dividends per share.

Historical Forecast

2012 0.215 2018 0.528

2013 0.324 2019 0.581

2014 0.353 2020 0.639

2015 0.362 2021 0.703

2016 0.391 2022 0.773

2017 0.480 2023 0.804

2024 0.836

a. What is the estimated value of Pacific Healthcare stock on December 31, 2017?

b. Is the stock underpriced or overpriced?

c. If investors estimate that Pacific Healthcare will grow about 10 percent per year for the next five years (2018-2022), what constant growth rate (2023+) are they using to actually price the stock? (Hint: What constant growth rate (2023+) produces an actual December 31, 2017, stock price of $8?) 2. What is the estimated value on December 31, 2018, 2019, 2020, 2021, and 2022, assuming that the stock is in equilibrium?

I need to know how to solve for these questions not just the answer please.

Answer 1

Before we get into this question, we need to understand two concepts:

1. Price of a stock at any time is sum of the present value of all the future dividends it will pay
2. Horizon value of the dividend at the end of time period, t = D_t+1 / (K_e - g_T) '

where

D_t+1 is the expected dividend in the year t + 1,

K_e = Cost of equity = required return by the shareholders

g_T = terminal growth rate

Let's now look at the question.

Part (a)

The dividend here is displaying a two stage growth.

• In the first stage the growth rate is g₁ = 10%
• In the second stage, the growth rate is terminal growth rate, g_T = 4%

Cost of equity as per CAPM, K_e = Risk free rate + Beta x (Expected Market return - Risk free rate)

Risk free rate = yield on long term treasury bond = 5.0%

Beta = 1.2

Expected market return = 11%

Cost of equity as per CAPM, K_e = 5% + 1.2 x (11% - 5%) = 12.2%

Hence, Price of the stock, P

$=\frac{D_{2018}}{1 +K _{e} }+\frac{D_{2019}}{(1 +K _{e})^{2}}+\frac{D_{2020}}{(1 +K _{e})^{3}}+\frac{D_{2021}}{(1 +K _{e})^{4}}+\frac{D_{2022}}{(1 +K _{e})^{5}} + \frac{D_{HV,2022}}{(1 +K _{e})^{5}}$

Where D₂₀₁₈ = Forecast dividend for year 2018...and so on and

D_{HV, 2022} = Horizon value of the dividend at the end of year 2022

$=\frac{D_{2023}}{K _{e}-g_{T} }$

= 0.804 / (12.2% - 4%) = 9.80

Hence, Price, P

$=\frac{0.528}{1 +0.122 }+\frac{0.581}{(1 +0.122)^{2}}+\frac{0.639}{(1 +0.122)^{3}}+\frac{0.703}{(1 +0.122)^{4}}+\frac{0.773}{(1 +0.122)^{5}} + \frac{9.80}{(1 +0.122)^{5}}$

= $ 7.78 / share

Part(b)

Current trading price of the stock = $ 8 / share

Since current trading price = $ 8 is more the the intrinsic value of the share = $ 7.78, the share is overpriced.

Part (c)

Let's assume the terminal growth rate assumed by the market is g_T.

As price of the stock today is present value of all its future dividends, the following equation must be satisfied:

Price of the stock, P

$=\frac{D_{2018}}{1 +K _{e} }+\frac{D_{2019}}{(1 +K _{e})^{2}}+\frac{D_{2020}}{(1 +K _{e})^{3}}+\frac{D_{2021}}{(1 +K _{e})^{4}}+\frac{D_{2022}}{(1 +K _{e})^{5}} + \frac{D_{HV,2022}}{(1 +K _{e})^{5}}$

Hence,

$8 =\frac{0.528}{1 +0.122 }+\frac{0.581}{(1 +0.122)^{2}}+\frac{0.639}{(1 +0.122)^{3}}+\frac{0.703}{(1 +0.122)^{4}}+\frac{0.773}{(1 +0.122)^{5}} + \frac{D_{HV, 2022}}{(1 +0.122)^{5}}$

Hence,

$8 =2.262825589 + \frac{D_{HV, 2022}}{(1 +0.122)^{5}}$

Hence, D_{HV, 2022} = Horizon value of the dividend at the end of year 2022 = (8 - 2.262825589) x 1.122⁵ =  10.201460

We know that

$D_{HV, 2022}=\frac{D_{2023}}{K _{e}-g_{T} }$

D₂₀₂₃ = D₂₀₂₂ x (1 + g_T) = 0.773 x (1 + g_T)

Hence,  10.201460 = 0.773 x (1 + g_T) / (12.2% - g_T)

Hence, g_T = (10.201460 x 12.2% - 0.773) / (0.773 + 10.201460) = 4.30%

So, the investors / market is assuming the forever growth rate of 4.30% in the dividends in 2023+

Sub part (2)

Assuming that the stock is in equilibrium,

P₂₀₁₈ = Estimated value of share on December 31, 2018 i.e. one year ahead from now = Current share price x (1 + Required rate of return, K_e) = 8 x (1 + 12.2%) = $ 8.976 / share

Similarly, estimated value of share on December 31, 2019 = P₂₀₁₈ x (1 + K_e) = 8.976 x 1.122 = $ 10.071

Similarly, estimated value of share on December 31, 2020 = P₂₀₁₉ x (1 + K_e) = 10.071 x 1.122 = $ 11.30

Similarly, estimated value of share on December 31, 2021 = P₂₀₂₀ x (1 + K_e) = 11.30 x 1.122 = $ 12.68

Similarly, estimated value of share on December 31, 2022 = P₂₀₂₁ x (1 + K_e) = 12.68 x 1.122 = $ 14.23