Question

1) IBM expects to pay a dividend of $5 next year and expects these dividends to grow at 77​% a year. The price of IBM is $85 per share. What is​ IBM's cost of equity ​capital?

2) Since your first​ birthday, your grandparents have been depositing $1,200into a savings account on every one of your birthdays. The account pays 9​%

interest annually. Immediately after your grandparents make the deposit on your 18th​ birthday, the amount of money in your savings account will be closest​ to:

A.$69,386.25

B.$59,473.93

C.$29,736.97

D.$49,561.61

Answer 1

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Q1) Correct Answer: 82.88 %

Working :

Since the dividend is expected to grow at a constant rate after 1 year, we will use the Gordon Growth model to find the required rate of return.

Gordon Growth Model is given by

P = D1 / ( R - G )

Here,

• P= Current Selling price of the stock
• D1= Dividend for the next year
• G = Constant growth rate
• R = Cost of Equity

Parameters provided in the question=

• P= $ 85
• D1= $ 5
• G = 77% or 0.77
• R = Cost of equity for IBM's Stock

Substituting the values in the formula.

85 = 5 / ( R - 0.77)

=>(R - 0.77) = 5 / 85

=> (R - 0.77) = 0.0588

=> R = 0.0588 + 0.77 = 0.8288 or 82..88 %

Therefore, Cost of Equity for IBM's stock = 82.88 %

Q 2 Future Value of savings account after 18 years = $ 49,561.61

The question belongs to Future value of an annuity

Future Value of annuity = P { [ (1+r)n -1 ] / r }

Here

• P is the periodic payment
• r is the interest rate per period
• n is the number of periods

Now substituting the values from the question

Savings Account balance after 18 years = 1200 { [ (1+0.09)18 -1 ] / 0.09 }

= 1200 [ (4.72-1) / 0.09 ]

=1200 X 41. 34

= $ 49,561.61 (Approx)