# "interest of delay"

Classified in Mathematics

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9.14 Nonconstant growth. Computech corporation is expanding Rapidly and currently needs to retain all of its earnings; hence, it does not Pay dividends. However, investors expect computech to begin paying dividends, Beginning with a dividend of \$0.50 coming 3 years from today. The dividend Should growth rapidly at a rate of 35% per year during years 4 and 5; but after Year 5, growth should be constant 7% per year. If the required return on computech Is 13%, what is the value of the stock today?

solution

Calculate the dividend cash flows and place them on a time Line.  Also, calculate the stock price at The end of the supernormal growth period, and include it, along with the Dividend to be paid at t = 5, as CF5.  Then, enter the cash flows as shown on the time line into the cash flow Register, enter the required rate of return as I/YR = 13, and then find the Value of the stock using the NPV calculation.  Be sure to enter CF0 = 0, or else your answer will be incorrect.

D0 = 0; D1 = 0; D2 = 0; D3 = 0.50; D4 = 0.50(1.35) = 0.675; D5 = 0.50(1.35)2 = 0.91125; D6 = 0.50(1.35)2(1.07) = \$0.9750375.    = ?

0 WACC=11%        1        2              3              4              5              6

|                                |            |           |                 |             |              |

0.50       0.675     0.91125                 0.9750375

0.34653                                                                                 +16.25063 =

0.41399

9.31478                                                                             17.16188

\$10.0753  \$10.08 =  p0

Ps = D6/(rs – g) = \$0.9750375/(0.13 – 0.07) = \$16.25063.  This is the stock price at the end of Year 5.

CF0 = 0; CF1-2 = 0; CF3 = 0.5; CF4 = 0.675; CF5 = 17.16188; I/YR = 13.  With these cash flows in the CFLO register, press NPV to calculate the value of the stock today:  NPV = \$10.08.

Notas

We can use in D5 = 0.675 x 1.35 = 0.91125

D6 = 0.91125 x 1.07 = 0.9750375

Para la operacion De la table se puede hacer por ejemplo 0.50 / (1.13) a la 3 = 0.34653

0.675 / (1.13) a La 4 = 0.41399

9.16 Nonconstant growth. Carnes cosmetics Co’s stock price Is \$30, and it recently paid a \$1.00 dividend. This dividend is expected to Grow by 30% for the next 3 years, then grow forever at a constant rate g, and Rs = 9%. At what constant rate is the stock expected to grow after year 3?

Solution

The value of any asset is the present value of all future Cash flows expected to be generated from the asset.  Hence, if we can find the present value of The dividends during the period preceding long-run constant growth and subtract That total from the current stock price, the remaining value would be the Present value of the cash flows to be received during the period of long-run Constant growth.

D1 = \$1.00 x (1.30)a la 1 = \$1.30                         PV(D1) = \$1.30/(1.09)a La 1                = \$1.1927

D2 = \$1.00 x(1.30)a La 2 = \$1.69                          PV(D2) = \$1.69/(1.09)a La 2                = \$1.4224

D3 = \$1.00 X(1.30)a la 3 = \$2.1970                       PV(D3) = \$2.1970/(1.09)a la 3          = \$1.6965

PV(D1 to D3)      = \$4.3116

Therefore, the PV of the remaining dividends is:  \$30.00 – \$4.3116 = \$25.6884.  Compounding this value forward to Year 3, we Find that the value of all dividends received during constant growth is \$33.27.  [\$25.6884(1.09)3 =   \$33.2672 \$33.27.]  Applying the Constant growth formula, we can solve for the constant growth rate:

P= D3(1 + g)/(rs – g)

\$33.27   = \$2.1970(1 + g)/(0.09 – g)

\$2.9943 – \$33.27g= \$2.1970 + \$2.1970g

\$0.7973= \$35.4670g

g= 2.25%.

10.12 WACC. Empire electric company uses only debt and Common equity. It can borrow unlimited amounts at an interest rate of Rd =9% as Long as it finances at its target capital structure, which calls for 35% debt And 65% common equity. Its last dividend (D0) was \$2.20, its expected constant Growth rate is 6%, and its common stock sells for \$26. EEC’s tax rate is 40%. Two projects are available: Project A has a rate of return of 12%, and project B return is 11%. These two projects are equally risky and about as risky as the Firm existing assets.

What is its cost of common equity?

What is the WACC?

Which projects should empire accept?

Solution

a.Rd = 9%, rd(1 – T) = 9%(0.6) = 5.4%.

wd = 35%; D0 = \$2.20; g = 6%; P0 = \$26; T = 40%.

Project A:  Rate of Return = 12%.

Project B:  Rate of Return = 11%.

rs = \$2.20(1.06)/\$26 + 6% = 14.97%.

b.            WACC = 0.35(5.4%) + 0.65(14.97%) = 11.62%.

c.             The Firm’s WACC is 11.62% and each of the projects is equally risky and as risky as The firm’s other assets, so EEC should accept Project A because A’s rate of Return is greater than the firm’s WACC. Project B should not be accepted, Because B’s rate of return is less than EEC’s WACC.