1) Your parents have an investment portfolio of $400,000, and they wish to take
ID: 2627980 • Letter: 1
Question
1) Your parents have an investment portfolio of $400,000, and they wish to take out cash flows of $50,000 per
year as an ordinary annuity. How long will their portfolio last if the portfolio is invested at an annual rate of
4.90%? Use a calculator to determine your answer.
2) Johnson Construction Inc. has issued 20-year $1,000 face value, 17% annual coupon bonds, with a yield to
maturity of 11%. The current price of the bond is ________.
3) Suppose you invest $1,000 today, compounded quarterly, with the annual interest rate of 5.50%. What is
your investment worth in one year?
4) Your firm intends to finance the purchase of a new construction crane. The cost is $1,500,000. What is the
size of the annual ordinary annuity payment if the loan is amortized over a six-year period at a rate of 8.50%?
5) The next dividend (Div1) is $1.80, the growth rate (g) is 9%, and the required rate of return (r) is 12%.
What is the stock price, according to the constant growth dividend model?
6) You want to invest in a stock that pays $5.00 annual cash dividends for the next four years. At the end of
the six years, you will sell the stock for $20.00. If you want to earn 12% on this investment, what is a fair price
for this stock if you buy it today?
7) Johnson has an annuity due that pays $600 per year for 15 years. What is the present value of the cash flows
if they are discounted at an annual rate of 9.50%?
Explanation / Answer
1)
Let period be n
Present value of all cash flows= $400,000
$400,000 = 50000*(1-1/1.049^n)/4.9%
N= 10.40 years
their portfolio last for 10.40 years
2)
current price of the bond = 17%*1000*(1-1/1.11^20)/11% + 1000/1.11^20=$1477.80
3)
investment worth in one year = 1000*(1+5.5%/4)^4=$1056.14
4)
1500000 = annual payment*(1-1/1.085^6)/8.5%
Annual payment =$329,410.63
5)
stock price = 1.8/(12%-9%)= $60.00
6)
fair price for this stock = 5/1.12 + 5/1.12^2 + 5/1.12^3 + 5/1.12^4 +20/1.12^6= $25.32
7)
present value of the cash flows = 600 + 600*(1-1/1.095^14)/9.5%= $5,143.11
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