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# 2. Suppose you will receive \$1,000 in 4 years. If your opportunity cost is 6% annually,...

2. Suppose you will receive \$1,000 in 4 years. If your opportunity cost is 6% annually, what is the present value of this amount if interest is compounded every six months? (8 points) What is the effective annual rate? (8 points) 3. Suppose you have deposited \$10,000 in your high-yield saving account today. The savings account pays an annual interest rate of 4%, compounded semi-annually. Two years from today you will withdraw R dollars. You will continue to make additional withdraws of R dollars every 6 months, until you have a zero balance after your last withdrawal 5 years from now. Find R. (10 points) 4. Zero coupon bond ZCB has a maturity value of \$1,000 and will mature in 5 years from today. If the current market price of ZCB is \$716.85, what is the market required annual rate of return? (10 points) 5. Company Y just made a dividend payment of \$0.50 per share. Investors expect the dividend to grow by 10% per year in the first two years and then by 2% per year starting in the third year. What's the maximum price investors are willing to pay for Company Y's stocks if they require an annual return rate of 12%? (15 points) 2 6. Company XYZ is considering issuing 10-year corporate bonds. The face value is \$1,000 and coupon rate is 5.5% paid semi-annually. If investors’ required return on similar corporate bonds is 8%, how many does XYZ need to issue in order to raise \$2,000,000 (assuming no fees or any issuing costs). (10 points) 7. Robbie plans to retire in 20 years and has just established a personal retirement account where the annual return rate is 6%. If at the end of every month in the coming 20 years, Robbie will deposit \$500 in the retirement account, what’s the monthly amount (at the end of each month) he can withdraw from this retirement account in the 10 years after retirement (Robbie will have a zero balance after the last withdrawal)? (10 points) 8. You want to have \$2 million in real dollars in an account when you retire in 35 years. The nominal return on your investment is 8% and the annual inflation rate will be 2% (HINT: do not use the approximation when finding the real interest rate). What real amount must you deposit each year to achieve your goal? (10 points)

Solution:

2.a)Computation of Present value

Present Value=Future Value/(1+r/m)^m*t

Where,

r=yearly interest rate(i.e 6% or 0.06 in given case)

m=no. of compounding period per year(i.e 2 in given case)

t=No. of years(i.e 4 in given case)

Present Value=\$1000/[(1+0.06/2)^2*4]

=\$1000/1.2667701

=\$789.41

Thus Present value of \$1000 is \$789.41

b)Calculation of effective annual rate

Effective annual rate=[1+(r/m)^m]-1

=[1+(0.06/2)^2]-1

=1.0609-1

=0.0609 or 6.09%

Thus effective annual rate is 6.09%

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