Question

1.
A)You own a share in Red Hat. Every period it has a 15 percent chance of going bankrupt. The interest rate is 0. If it survives to the end of the first period, it will pay $2 in dividends, $3 in dividends at the end of the second period, $3 in dividends at the end of the third period, and $4 in dividends at the end of the fourth period. It will pay no dividends after the end of the fourth period What is its efficient market price at the beginning of the first period?

B) Hula Hoops has an eight percent chance of going bankrupt each period. In period seven it will pay $30, if it survives. The interest rate is 0. Prior to that point, and afterwards, it will pay nothing. What is the efficient market price for Hula Hoops at the beginning of period 1?

Answer 1

A)

The efficient market price at the beginning of the first period is the present values of the dividends for the future periods

Now the dividends shall be paid only if the Red har does not go into bankruptcy

Probability of survival = 85% = p

Now Probability of bankruptcy = 15% = 1 - p

Dividen in period 1 = D1 = 2

Dividen in period 2 = D2 = 3

Dividen in period 3 =D3 = 3

Dividen in period 4 =D4 =4

As the interst rate is 0 hence the present value will be the dividend amount itself as

Presnt value of dividend = Dividend / ( 1 + interest rate) ^n where n is the no of years

= Dividend / ( 1 + 0 ) ^n = Dividend amount

Efficient market price = D1 * P + D2 * p^2 +D3 * p^3 + D4 * p ^4

= 2 * 0.85 + 3 * 0.85^2 + 3 * 0.85 ^3 + 4 * 0.85^4

= 1.70 + 2.17 + 1.84 + 2.09

= $7.80

(ii)

The efficient market price at the beginning of the first period is the present values of the dividends for the future periods.

Hula hoops pays dividend only in year 7 and no dividends before or after that

Dividend amount will be expected dividend = Probability of survival ^ n * Dividend

Now Probability of bankruptcy = 8%

Probability of survival = 1 - 8% = 92%

Price shall be present value of expected dividend. As the interest rate is 0 hence the presnt value shall be tyhe expected dividend itself as explained earlier

Price of the hula hoop share = Probability of survival ^ no of years of survival * Dividend

= 0.92 ^7 * 30

= 0.5578 * 30

= $16.73