Problem
Set # 1
(due
2/10,
4 p.m.)
1. Yuppie Yates intends to retire 30 years from now. He plans to save equal amounts each year for the next 30 years to provide for his retirement needs. When he retires, he will spend the first 3 years sailing around the world. His expenses during this period will be $120,000 per year. He will then buy a house for $200,000 (at the end of the third year), and settle down to a normal life, with expenses of $65,000 per year. If he earns 6% per year on his savings, how much must he save each year to finance his retirement dreams? (Assume savings occur at the end of each year, and expenses are paid at the beginning of each year.)
(15 points)
2. An investment company offers the following savings plan: you invest $500 at the end of each year for 12 years. In return, you and your descendants receive $500 a year forever, starting at the end of the 11th year. What rate of return is this savings plan offering?
(15 points)
3. Diabolitech
Inc. allows you to choose your own interest rate on a loan you plan to
take from them. The choices are:
a) 6.16% per year compounded annually
b) 6.08% per year compounded every 6 months
c) 6.02% per year compounded quarterly
e) 6.01 % per year compounded monthly
d) 6% per year compounded every 5 days
f) 5.99% per year compounded daily (assume 365 days)
Which rate should you accept?
(10 points)
4.
An ordinary annuity pays $4000 at the end of each year for 4 years.
What is the present value of the annuity, if the interest rate is 5% per
year
compounded monthly?
(10 points)
5. The EAR with semi-annual compounding is 9.25%. If the same stated rate were compounded quarterly, what would the EAR be?
(5 points)
6 a) An investment will generate
cashflows for five years, starting at time 1.
The first cashflow is expected to be $12,000 per year .
Future cashflows will grow at the expected inflation rate of 2%.
What are the real cashflows from the investment?
b) A project requires investment
of $20,000 today. The future real
cashflows are as follows:
Time 1
Time 2
Time
3
5,000
10,000
15,000
The expected inflation rate is 2.5% per year, the nominal discount rate is 7.5%. What is the NPV of the project when you discount real cashflows at the real discount rate? What is the NPV when you discount nominal cashflows at the nominal discount rate?
(15 points)
a) If their required return is 10%, what is the growth rate in dividends?
b) If the payout ratio is 40%, what is their ROE?
(10 points)
8. The Better Mousetrap
Corporation is expected to pay the following dividends starting at time 2: $3, $4
and $5. After that, dividends are
expected to grow at 7% forever.
a) What is the price of BMC’s stock today, if the stock’s required
return is 11%?
b) What is their expected stock price one year from now?
(15 points)
(REMEMBER TO FOLLOW THE RULES FOR ROUNDING FROM THE SYLLABUS)