Question

Martin Office Supplies paid a $3 dividend last year. The dividend is expected to grow at a constant rate of 5 percent over the next four years. The required rate of return is 14 percent (this will also serve as the discount rate in this problem). Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods. a. Compute the anticipated value of the dividends for the next four years. b. Calculate the present value of each of the anticipated dividends at a discount rate of 14 percent. c. Compute the price of the stock at the end of the fourth year (P4). d. Calculate the present value of the year 4 stock price at a discount rate of 14 percent. e. Compute the current value of the stock. f. Use the formula given below to show that it will provide approximately the same answer as part e. g. If current EPS were equal to $4.20 and the P/E ratio is 6% higher than the industry average of 8, what would the stock price be? h. By what dollar amount is the stock price in part g different from the stock price in part f? i. With regard to the stock price in part f, indicate which direction it would move if: (1) D1 increases (2) K_e increases (3) g

**I only need the answers for D-I

Answer 1

a.

Given,

Current year dividend (D₀) = $3

Growth rate (g) = 5% or 0.05

Required rate of return (K_{e )} = 14%

D₁ = D₀ *(1 +g)

    = $3 *(1 + 0.05)

    = $3.15

D₂ = D₁ * (1 + g)

    = $3.15 * (1 + 0.05)

    = $3.3075 or $3.30

D₃ = D₂ * (1 +g)

    = $ 3.3075 * 1.05

    = $3.472875 or $ 3.47

D₄ = D₃ * (1+ g)

    = $ 3.472875 * 1.05

    = $3.646518 or $3.64

b.

Computation of Present Value is as:

PV of D₁ = D₁ / (1 + discount rate)

               = $3.15 / [(1 + 0.14) ^ 1]

               = $3.15 / 1.14

               = $2.76

PV of D₂ = D₂ / (1 + discount rate)

               = $3.30/ [(1 + 0.14) ^ 2]

               = $3.30 / 1.14 ^ 2

               = $3.30 / 1.2996

               = $2.540

PV of D₃ = D₃ / (1 + discount rate)

               = $3.47/ [(1 + 0.14) ^ 3]

               = $3.47 / 1.14 ^ 3

               = $3.47 / 1.4815

               = $2.34

PV of D₄ = D₄ / (1 + discount rate)

               = $3.64/ [(1 + 0.14) ^ 4]

               = $3.64 / 1.14 ^ 4

               = $3.64 / 1.6890

               = $2.15

Total = $2.76 + $2.540 + $2.34 + $2.15

        = $9.79

c.

The stock price for Year 4 is as:

Year 4 = D₅ / (K_e - g)

            

Where D₅ = D₄ * (1.14)

               = $3.64 * 1.14

               = $4.15

So,

Year 4 = $4.15 / (0.14 - 0.05)

           = $4.15 / 0.09

           = $46.11

d.

Computation of PV of year 4 at discount rate of 14%

PV of Year 4 stock price = Stock price / [(1 + Discount rate) ^ 4]

                                        = $46.11 / [(1 + 0.14) ^4]

                                        = $46.11 / 1.680

                                        = $27.45

e.

Computation of current value of the stock is as:

Present Value of Stock = PV of dividends of first four years + PV of Year 4 stock price

                                     = $9.79 + $27.45

                                     = $37.24

f.

Present Value = D₁ / (K_e - g)

                      = $3.15 / (0.14 - 0.05)

                      = $3.15 / 0.09

                      = $35

g.

Stock Price = P/ E ratio * EPS

                  = (6% + 8) * $4.20

                  = 8.06 * $4.20

                  = $32.40

h.

Difference = $35 - $32.40

                 = $2.6

By $2.6 amount is the stock price is different.

i.

1. D₁ increases then the stock price increases.

2. K_e increases then the stock price decreases.

3. g increases then the stock price increases.

EXTRA EXPLANATION-

Dividend paid=3

Growth=5%

Dividend at 1st year(D1)=3*1.05=3.15

PRICE AT ZERO YEAR = D1/Ke-G

=3.15/0.14-0.05

= 3.15/0.09

=35

Now the question is what will happen to stock price if D1 increases?

Its oblivious if the numerator will increase in the formula the answer(which is stock price) will increase

Still lets take an illustration explaining how Stock price will increase in D1 increases.

Suppose, other things remaining constant, D1 increases to 4(instead of 3.15)

PRICE AT ZERO YEAR = D1/Ke-G

=4/0.14-0.05

= 4/0.09

=44.44

Thus, D₁ increases, stock price increases.