1. [5 p] Your brother borrows $1,200 from you. Since hes family, you allow him to pay simple interest at 5%. After 6 years, how much does he owe you?

2. [5 p] Alternatively, you could put your $1,200 in the bank where they pay compound interest. If the bank pays you 5% interest, compounded yearly, how much do you have in your account after 6 years?

3. [5 p] If the bank pays a nominal interest of 5% p.a., what is the maximum EAR you could earn on your money? Under what circumstances would that happen?

4. [15 p] You put $1,000 in the bank at a nominal interest rate of 6% p.a. How much will be in your account after 10 years if the bank:

(a) compounds yearly (b) compounds monthly (c) compounds daily

5. [15 p] In each of the 3 cases in the previous question, calculate the EAR earned over the 10 years.

6. [5 p] You deposit $1,500 in the bank today. After 5 years, you are able to withdraw $2,163.48. Assuming yearly compounding, what interest rate did you earn?

7. [10 p] You deposit $1,500 in the bank today. After 5 years, you are able to withdraw $2,163.48.

(a) What Effective Annual Return (EAR) did you earn?

(b) Assuming continuous compounding, what nominal interest rate did you earn?

8. [5 p] You deposit $1,200 in the bank today. You earn 8% interest, compounded quarterly. How many quarters will it take before your bank account contains at least $3,000?

Simple bond problems: consol bonds

9. [10 p] A $1,000 consol bond has a coupon rate of 8%. It pays annual coupons.

(a) If the current market rate is 6%, how much will this bond sell for?

(b) If it sells for $910, what is the current market interest rate?

Simple bond problems: Zero-Coupon Bonds

10. [5 p] A 3-year zero coupon bond with a face value of $1,000 is offered with a return of 7.5%. What does it sell for?

11. [5 p] A 1-year zero coupon bond with a face value of $1,000 just sold for $888.00. What is the expected rate of return on this bond?

Simple bond problems: coupon bonds

12. [5 p] A $1,000 face value coupon bond has an 8.2% coupon rate. It will pay semi-annual coupons. How much will the bond holder receive with each coupon payment?

Solve the following two problems using both the cash flow functions and the TVM functions, to make sure you understand the differences in the solution methods.

13. [5 p] [Cash flows] A 10-year $1,000 face value coupon bond carries a coupon rate of 7.0%. It pays semi-annual coupons. The current market interest rate is 6%. How much will this bond sell for? (Calculate its FPV.)

14. [5 p] [Cash flows] You purchase a 5-year $1,000 face value coupon bond for $930. The bond carries a 6% coupon rate and it pays semiannual coupons. What is the return (Err, YTM) going to be to holding this bond until maturity? (Calculate its IRR.)

Simple amortization (TVM) problems

Use the N, I, PV, PMT, FV buttons to enter data and solve problems. Set your calculator to 12 payments per year and END mode. Be sure to clear the calculator before you start a new problem!

15. [5 p] You borrow $200,000 at 5.75% over 30 years. What is your monthly payment?

16. [5 p] You borrow $150,000 over 20 years. Your monthly payment is $1377.76. What interest rate are you paying?

17. [5 p] You feel you can afford to pay no more than $2,000 per month on a mortgage. Current market rates are 6.5% p.a. How much can you borrow if you want 20 years to pay off the loan?

18. [5 p] You borrow $300,000 at 7.0% over 30 years. After 10 years of making payments, you sell the home. What is the payoff (remaining balance) on the mortgage?

19. [5 p] You want to borrow $225,000 at 8%. If you make payments of $1,750.00 per month, how many payments do you have to make to pay off the loan? (Round up.)

Simple amortization: annuities due (maybe)

-> For questions 20 21, ask yourself whether we are dealing with a normal annuity or an annuity due, and calculate accordingly.

20. [5p.] You have won $386 million in the Mega lottery, to be paid out in 20 equal yearly installments. You are offered a lump sum payment instead. If your required rate of return is 6.2%, how large does the lump sum have to be for you to take it over the yearly payments?

21. [10 p.] You have decided to upgrade your mode of transportation by investing in a Lamborghini priced at $240,000. You are offered a 6-year car loan at 8%, or a 5-year lease at 7.6%. (a) what would your monthly car payment be for the loan? (b) what would be your monthly lease payment?

For the following problems, set your calculator back to END mode. Set your calculator to the appropriate number of payments per year.

Cash flow problems: single or uneven cash flows Use the CFj button for data entry. Calculate NPV or IRR. For questions 22 - 23, set your calculator to 1 payment/year.

22. [5 p] [Cash flows] You are invited to participate in a building project. You would be required to contribute $5 million up front, and over the next 6 years you would receive these amounts: $750,000, $900,000, $1,100,000, $1,200,000, $700,000, and $500,000. What return (IRR) would you be getting on your money?

23. [5 p] [Cash flows] Using the cash flow data in #22, assume that you require a return of at least 8% on your money. What is the net present value (NPV) of this project using 8% as the discount rate?

Cash flow problems: repeating cash flows

Use the CFj and Nj buttons for data entry. Calculate NPV or IRR. For questions 24 - 25, set your calculator to 1 payment/year.

24. [15 p] You invest $1 million in a business venture. It promises to pay you back $120,000 per year the first 10 years, then $50,000 per year for the next 10 years.

(a) What return (IRR) is the project promising?

(b) If your required rate of return is 6.25%, what is the current value (NPV) of the whole project?

(c) If your required rate of return is 7%, what is the profitability index (PI) for this project?

Cash flow problems: cash flows with holes

Be sure to draw the cash flow diagrams for these problems. You need to enter 0 (zero) for CFj for missing payments.

25. [10 p] You are invited by your no-good brother-in-law to participate in a dubious investment scheme. Your participation will cost you $10 million up front. The promised yearly cash flows you will receive (the first one a year from now) are:

3 years of $3 million each 3 years of $2 million each 3 years of $1 million each

(a) [ 5] What is the expected IRR for this project?

(b) [ 5] Due to the risky nature of the venture, your required rate of return is 16%. What is the NPV of the project?

26. [10 p] In the above scheme, actual payback was slightly delayed, due to unforeseen difficulties. The first $2 million payment was received 2 years after the preceding $3 million one, and the first $1 million payment 3 years after the preceding $2 million one.

(a) [ 5] What was the actual IRR?

(b) [ 5] What was the actual NPV (using a 16% required return)?

27. [10 p] If in the above scheme payback was as promised, except the first payment was not received until 4 years after your investment,

(a) [ 5] What was IRR now?

(b) [ 5] And what was NPV in this case, again using a 16% discount rate?

For questions 28 - 29, set your calculator to 12 payments/year.

28. [5 p] You borrow $150,000 over 20 years to buy a house. Your monthly payment is $1,377.76. What yearly interest rate are you paying? (Calculate IRR.)

29. [5 p] You feel you can afford to pay no more than $2,000 per month on a mortgage. Current market rates are 6.5% p.a. How much can you borrow if you want 20 years to pay off the loan? (Calculate FPV.)

Perpetuities

30a. [5 p.] You are offered a consol bond which will pay a yearly coupon payment of $500. If the current market interest rate for long bonds is 7.5%, what is the fair value of this bond?

30b. [5 p.] You are offered a $500 a year consol bond for a price of $8,250.00. What is the market interest rate right now?

31a. [5 p.] ABC company paid a dividend of $2.25 per share last year. The board of ABC has decided that future dividends will be increased by 5% per year. What is the value of a share of ABC stock, if the relevant discount rate is 12%?

31b. [5 p.] What will the price of ABC stock be 5 years from now?

Yields, taxes, inflation

32a. [5 p.] You are offered a 30-year Treasury bond which has 25 years left until it matures. It pays semi-annual coupon payments at a coupon rate of 8%. The current market price for the bond is $817.44. What yield would you earn if you held this bond to maturity?

32b. [5 p.] Your personal tax rate for federal income taxes is 28%, and your state taxes investment income at a flat rate of 7%. What is your net after-tax yield to holding the above bond?

32c. [5 p.] If during the time you own this bond we have an average inflation rate of 7.5% per year, what is your real after-tax return to this investment?

Misc. yields

33. [5 p.] You are offered participation in an investment project that promises to pay a return of 12% per year. Use the Rule of 72 to determine how many years it will take you to quadruple your original investment.

34a. [5 p.] You loan a buddy $1000 and 73 days later he pays you back $1200. What is your holding period return for this loan?

34b. [5 p.] What is the annual APR for this loan?

34c. [5 p.] What is the effective annual return (EAR) for this loan?

35a. [5 p.] You invest $100,000 in a Madoff scheme. Six years later, he returns $300,000 to you. What was your effective annual return (EAR) to this investment?

35b. [5 p.] If you had put your money in the bank instead, and the bank compounds interest on savings on a monthly basis, what APR would you have to earn to get the same EAR (=APY) as in the previous scheme?

36a. [5 p.] You are offered participation in an investment project (A) where you will be required to put up $5 million up front, and the hoped

10

for cash flows returned to you over the first 10 years of the project are: $1 million, $750,000, $750,000, $750,000, $750,000, $750,000, $500,000, $500,000, $500,000, $2 million. Compute the payback period for this project.

36b. [5 p.] The required rate of return for projects like this is about 5% right now. Calculate the discounted payback period (DPB) of the project.

36c. [5 p.] You can put your $5 million into an alternative project (B) instead; this project has projected 8-year cash flows of $3 million, $500,000, $2 million, $500,000, $1 million, $250,000, $250,000, $250,000. At a discount rate of 5%, which of the two projects has the better NPV?

36d. [5 p.] At a discount rate of 12% which project has a higher NPV?

36e. [Bonus: 10 p.] What is the discount rate at which we are indifferent between the two projects? (Finding the answer may be tricky.)

Extra credit work Answer sheet

1. ____1560____________ 8. _____12 Quarters___

2. ____$1608.11________ 9a. ___$1,333.33________

3. ____5.13% Comp Daily_ 9b. ____8.79%_________

4a. _$1,790.15__________ 10. ___$804.96__________

4b. __$1,819.40_________ 11. ___12.61%__________

4c. _$1,822.03___________ 12. __$41.00____________

5a. ____________________ 13. ___$1074.39_________

5b. ____________________ 14. ___7.71%__________

5c. ____________________ 15. ___$1,167.15_________

6. ___7.6%_____________ 16. ___9.29%__________

7a. ___7.6%_____________ 17. ___$369,230.77______

7b. ____________________ 18. __$257,437.15_______

(Page 2)

19. ___293______________ 30a. __________________

20. ___$1,285,516,451____ 30b. ___________________

21a. __$4,207.98_________ 31a. ___________________

21b. __$4,820.52________ 31b. ___________________

22. ____________________ 32a. ___________________

23. ____________________ 32b. ___________________

24a. ____________________ 32c. ___________________

24b. ____________________ 33. ___________________

24c. ____________________ 34a. ___________________

25a. ____________________ 34b. ___________________

25b. ____________________ 34c. ___________________

26a. ____________________ 35a. ___________________

26b. ____________________ 35b. ____________________

27a. ____________________ 36a. ____________________

27b. ____________________ 36b. ___________________

28. ____________________ 36c. ____________________

29. ____________________ 36d. ____________________

36e. ____________________