Question

1. 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?

Answer 1

As per efficient market price; share price of Red Hat at the beginning of the first period will be present value of all its expected future cash flows; therefore first we have to calculate it’s all expected future cash flows (dividends) and then discount it to the present value. As we know that every period it has a 15 percent chance of going bankrupt, therefore

Expected dividend for period 1, D1 = expected dividend for period 1 * (1 – bankruptcy rate)

= $2 * (1-15%) = $1.70

As the interest rate is 0; therefore present value of D1 will be equal to D1 which is $1.70

Expected dividend for period 2, D2 = expected dividend for period 2 * (1 – bankruptcy rate)

= $3 * (1-15%) = $2.55

As the interest rate is 0; therefore present value of D2 will be equal to D2 which is $2.55

Expected dividend for period 3, D3 = expected dividend for period 3 * (1 – bankruptcy rate)

= $3 * (1-15%) = $2.55

As the interest rate is 0; therefore present value of D3 will be equal to D3 which is $2.55

Expected dividend for period 4, D4 = expected dividend for period 4 * (1 – bankruptcy rate)

= $4 * (1-15%) = $3.40

As the interest rate is 0; therefore present value of D4 will be equal to D4 which is $3.40

As per efficient market price; share price of Red Hat at the beginning of the first period

= PV of D1 + PV of D2 + PV of D3 + PV of D4

= $1.70 + $2.55 + $2.55 + $3.40 = $10.20

As per efficient market price; share price of Red Hat at the beginning of the first period is $10.20