Answer the following questions assuming the interest rate is 8 percent.

Time Value of Money Problems

a. What is the present value of $1,000 to be received in four years?

b. What is the present value of $1,000 in eight years? Why does the present value fall as the number of years increases?

c. What will be the value in seven years of $12,000 invested today?

d. How much would you pay for the right to receive $5,000 at the end of year 1, $4,000 at the end of year 2, and $8,000 at the end of year 10?

e. How long will it take for a $2,000 investment to double in value?

f. What will be the value in 20 years of $500 invested at the end of each year for the next 20 years?

g. A couple wishes to save $250,000 over the next 18 years for their child's college education. What uniform annual amount must they deposit at the end of each year to accomplish their objective?

h. How long must a stream of $600 payments last to justify a purchase price of $7,500.00? Suppose the stream lasted only five years. How large would the salvage value (liquidating payment) need to be to justify the investment of $7,500.00?

Rate of Return Problems

i. An investment of $1,300 today returns $61,000 in 50 years. What is the internal rate of return on this investment?

j. An investment costs $750,000 today and promises a single payment of $11.2 million in 23 years. What is the promised rate of return, IRR, on this investment?

k. What return do you earn if you pay $22,470 for a stream of $5,000 payments lasting ten years? What does it mean if you pay less than
$22,470 for the stream? More than $22,470?

l. An investment promises to double your money in five years. What is the promised IRR on the investment?

m. The projected cash flows for an investment appear below. What is the investment's IRR?

n. In 1987, a Van Gogh painting, Sunflowers (not reputed to be one of his best), sold at auction, net of fees, for $36 million. In 1889, 98 years earlier, the same painting sold for $125. Calculate the rate of return to the seller on this investment. What does this suggest about the merits of fine art as an investment?

Bank Loan, Bond, and Stock Problems

o. How much would you pay for a 10-year bond with a par value of $1,000 and a 7 percent coupon rate? Assume interest is paid annually.

p. How much would you pay for a share of preferred stock paying a $5-per-share annual dividend forever?

q. A company is planning to set aside money to repay $150 million in bonds that will be coming due in eight years. How much money would the company need to set aside at the end of each year for the next eight years to repay the bonds when they come due? How would your an- swer change if the money was deposited at the beginning of each year?

r. An individual wants to borrow $120,000 from a bank and repay it in six equal annual end-of-year payments, including interest. What should the payments be for the bank to earn 8 percent on the loan? Ignore taxes and default risk.