Question

you are evaluating a stock for purchase. you estimate that the firm will pay the following dividends in the coming years:

Year 1: $2

Year 2: $2.50

Year 3: $3

After the third year, the dividend is expected to grow at a long-term rate of 8%. Your required rate of return is 10%.

A. What is the intrinsic value of this stock?

B. If you purchase the stock at $120 and your estimates (of future dividends and prices) are correct, what is the EXPECTED RATE OF RETURN on your investment?

**PLEASE SHOW ALL WORK

Answer 1

(a)-Intrinsic value of this stock

Step-1, Dividend for the next 3 years

Dividend in Year 1 (D1) = $2.00 per share

Dividend in Year 2 (D2) = $2.50 per share

Dividend in Year 3 (D3) = $3.00 per share

Step-2, The Price of the stock in year 3 (P3)

Dividend Growth Rate after 3 years (g) = 8.00% per year

Required Rate of Return (Ke) = 10%

Therefore, the Share Price in year 3 (P3) = D3(1 + g) / (Ke – g)

= $3.00(1 + 0.08) / (0.10 – 0.08)

= $3.24 / 0.02

= $162.00 per share

Step-3, Intrinsic value of this stock

As per Dividend Discount Model, the Intrinsic value of this stock is the Present Value of the future dividend payments and the present value the share price in year 3

Year	Cash flow ($)	Present Value factor at 10%	Present Value of cash flows ($)
1	2.00	0.90909	1.82
2	2.50	0.82645	2.07
3	3.00	0.75131	2.25
3
TOTAL			127.85

“Therefore, the Intrinsic value of this stock will be $127.85”

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.

(b)-Expected Rate of Return on the Investment

Expected Rate of Return on the Investment = [(Intrinsic value – Purchase Price) / Purchase Price] x 100

= [($127.85 - $120.00) / $120.00] x 100

= [$7.85 / $120.00] x 100

= 6.54%