Module 5(1)

University of Connecticut
Math 3615: Financial Mathematics Problems
Examples – Module 5
1.An investor invests 1,000 in a contract that will generate income payments of 200,
200, 300, and 500, occurring 1, 2, 3, and 5 years (respectively) from the date of the investment. (Note that there is no cash flows at t=4.)
What is this investment’s IRR (expressed as an annual effective rate of return)?
If the investor’s target rate of return is a n 8% annual effective rate, what is the NPV of the investment?
The investor intends to invest the payments received from the investment into a money market account that will generate a 6% annual effective rate of return until the end of the 5th year of the investment.
What is the total return of this combination of investments (the original
investment and the money market account)?
Does this reinvestment strategy increase or decrease the calculated IRR?
Why?
2.You are given the following information about an investment account:
If the dollar-weighted return is equal to 1.4 times the time-weighted return, what is the date (X) of the withdrawal?
(Assume 30-day months and a 360-day year.)
3.You are given the following information about an investment account:
If the time-weighted return for this investment is 5%, what is the dollar-weighted return?
(Assume 30-day months and a 360-day year.)
4.An investor purchases a 10-year bond on its issue date for 10,500. The bond has a
10,000 face amount (and maturity value) and it pays annual coupons at a 9%
(annual) coupon rate.
If the bond is held to maturity (and does not default), what is the investor’s yield (internal rate of return)?
Suppose that the above bond has a 9% coupon rate (as before), but pays semi-annual, instead of annual, coupons. In that case, what is the inv estor’s yield
(internal rate of return), expressed as a nominal rate, convertible semi-annually?
What is this yield expressed as an annual effective rate?
5.Suppose that you are an actuarial intern for an automobile insurance company.
The company calculates its auto insurance premiums assuming that the customer pays the full annual premium at the beginning of the year of coverage. However, it also offers its customers a monthly payment plan. Customers who choose the company’s monthly p ayment make 12 consecutive monthly payments, and each payment is equal to 8.75% of the annual premium. The first monthly payment is due on the date that coverage begins (which is also the date that the annual
premium would be due).
Your supervisor has asked you to determine the interest rate that the company is earning on the money it lends to these monthly payment customers (by allowing them to defer most of the annual premium. You are to ignore the additional
expenses of collecting multiple premiums during the year (as well as any losses the company suffers if a customer does not pay all 12 monthly payments).
What annual effective rate of return is the company earning on the amounts it “lends” to customers when they choose the monthly payment plan?
After you have calculated the rate of return for the company’s current monthly payment plan, your supervisor asks you how the company can increase that rate of return by 100 basis points (i.e., 1 percentage point). You suggest that this can be done by increasing the amount that the customer is required to pay each month.
By how much would the insurance company need to increase the percentage
(currently 8.75%) of the premium that customers pay each month in order to
improve its rate of return by 100 basis points?
Answers
1.(a) 5.740% (b) -$64.91 (c) 5.834% (d) increase, because the reinvestment
rate is greater than the IRR.
2.April 6, 2008
3.18.00%
4.(a) 8.247% (b) 8.256% convertible semiannually; 8.426% effective
5.11.35% New payment = 8.7852%。