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Please provide a summary of the Higgins Chapter 7 Problems Questions No. 1,3,5,7, 9
Question 1 –
1. 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?
Year 0 1 2 3 4 5
28 75 160 280 190
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 answer 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.
Question 3 –
A developer offers lots for sale at $60,000, $10,000 to be paid down and $10,000 to be paid at the end of each of the next five years with “no interest to be charged.” In discussing a possible purchase, you find that you can get the same lot for $48,959 cash. You also find that on a time purchase there will be a service charge of $2,000 at the date of purchase to cover legal and handling expenses and the like. Approximately what rate of interest before income taxes will actually be paid if the lot is purchased on this time payment plan?
Question 5 –
A wealthy graduate of a local university wants to establish a scholarship to cover the full cost of one student each year in perpetuity at her university. To adequately prepare for the administration of the scholarship, the university will begin awarding it starting in three years. The estimated full cost of one student this year is $45,000 and is expected to stay constant in real terms in the future. If the scholarship is invested to earn an annual real return of 5 percent, how much must the donor contribute today to fully fund the scholarship?
There was not enough space to include Question 7 & Question 9 but they are provided on page 290 and 291 for the writer to have a look at. (e – book uploaded for reference)
If the writer has any questions please feel free to reach out to me.