Question

I have a number of questions for a finance assignment that is meant as a review for our final. However my final is being written earlier than the rest of the class so the answers aren't up yet. I was hoping someone could answer two or three of the questions so that I can check my answers and ensure they are correct. Most have to do with time value of $, dividend growth models, and cash flows.

1) Genetics Inc. plans to retain all earnings for 30 years. In yr 31, the firm will pay a $9 dividend. From then on the dividend will increase at 6%. Given a required return of 12% what should the current price be?

2) Bobby wishes to save for retirement. He will deposit a fixed amnt for 180months at 15% compounded monthly. one year after his final deposit, he will begin withdrawing $75,000 anually. His fund will continue to earn 15% monthly. How much should his monthly deposits be?

3) What is the discounted payback period of the following project if the required return is 12%? Yr 0 -$150 Yr 1 $45 Yr 2 $50 Yr 3 $40 Yr 4 $ 50 Yr 5 $20

Answer 1

These look a bit more complicated than the routine "finance" question usually seen here.
1. As I see it you want the present value of
$9 30 years from now , $9(1.06) 31 years from now, $9(1.06)^2 32 years from now, as a perpetuity, all brought back at 12%

I see:
PV = 9(1.12)^-31 + 9(1.06)(1.12)^-32 + 9(1.06)^2(1.12)^-33 + ...

This is an infinite geometric series
where a = 9(1.12)^-31 =
and r = (1.06)(1.12)^-1

S∞ = a/1-r) = 5.0067

Check for "reasonableness"
invest $5.0067 for 30 years at 12%
amount = 5.0067(1.12)^30 = 149.99 or $150

2. How long will the $75000 withdrawals continue?
Until he dies? Then it becomes a life annuity and it jumps into actuarial math, with mortality tables needed.
until the money runs out?
Then we have to convert the 15% per annum compounded monthly to an annual rate at year 15.

Let me know, I know how to do that one.

3. Don't know what "discounted payback period" is.
I am not familiar with some of the financial terminology of your country.